engineer problem solving problems

Oct 13, 2019

10 Steps to Problem Solving for Engineers

Updated: Dec 6, 2020

With the official launch of the engineering book 10+1 Steps to Problem Solving: An Engineer's Guide it may be interesting to know that formalization of the concept began in episode 2 of the Engineering IRL Podcast back in July 2018.

As noted in the book remnants of the steps had existed throughout my career and in this episode I actually recorded the episode off the top of my head.

My goal was to help engineers build a practical approach to problem solving.

Have a listen.

Who can advise on the best approach to problem solving other than the professional problem solvers - Yes. I'm talking about being an Engineer.

There are 2 main trains of thought with Engineering work for non-engineers and that's trying to change the world with leading edge tech and innovations, or plain old boring math nerd type things.

Whilst, somewhat the case what this means is most content I read around Tech and Engineering are either super technical and (excruciatingly) detailed. OR really riff raff at the high level reveling at the possibilities of changing the world as we know it. And so what we end up with is a base (engineer only details) and the topping (media innovation coverage) but what about the meat? The contents?

There's a lot of beauty and interesting things there too. And what's the centrepiece? The common ground between all engineers? Problem solving.

The number one thing an Engineer does is problem solving. Now you may say, "hey, that's the same as my profession" - well this would be true for virtually every single profession on earth. This is not saying there isn't problem solving required in other professions. Some problems require very basic problem solving techniques such is used in every day life, but sometimes problems get more complicated, maybe they involve other parties, maybe its a specific quirk of the system in a specific scenario. One thing you learn in engineering is that not all problems are equal. These are

The stages of problem solving like a pro:

Is the problem identified (no, really, are you actually asking the right question?)

Have you applied related troubleshooting step to above problem?

Have you applied basic troubleshooting steps (i.e. check if its plugged in, turned it on and off again, checked your basics)

Tried step 2 again? (Desperation seeps in, but check your bases)

Asked a colleague or someone else that may have dealt with your problem? (50/50 at this point)

Asked DR. Google (This is still ok)

Deployed RTFM protocol (Read the F***ing Manual - Engineers are notorious for not doing this)

Repeated tests, changing slight things, checking relation to time, or number of people, or location or environment (we are getting DEEP now)

Go to the bottom level, in networking this is packet sniffers to inspect packets, in systems this is taking systems apart and testing in isolation, in software this is checking if 1 equals 1, you are trying to prove basic human facts that everyone knows. If 1 is not equal to 1, you're in deep trouble.At this point you are at rebuild from scratch, re install, start again as your answer (extremely expensive, very rare)

And there you have it! Those are your levels of problem solving. As you go through each step, the more expensive the problem is. -- BUT WAIT. I picked something up along the way and this is where I typically thrive. Somewhere between problem solving step 8 and 10.

The secret step

My recommendation at this point is to try tests that are seemingly unrelated to anything to do with the problem at all.Pull a random cable, test with a random system off/on, try it at a specific time of the day, try it specifically after restarting or replugging something in. Now, not completely random but within some sort of scope. These test are the ones that when someone is having a problem when you suggest they say "that shouldn't fix the problem, that shouldn't be related" and they are absolutely correct.But here's the thing -- at this stage they have already tried everything that SHOULD fix the problem. Now it's time for the hail mary's, the long shots, the clutching at straws. This method works wonders for many reasons. 1. You really are trying to try "anything" at this point.

2. Most of the time we may think we have problem solving step number 1 covered, but we really don't.

3. Triggering correlations.

This is important.

Triggering correlations

In a later post I will cover correlation vs causation, but for now understand that sometimes all you want to do is throw in new inputs to the system or problem you are solving in order to get clues or re identify problems or give new ways to approach earlier problem solving steps. There you have it. Problem solve like a ninja. Approach that extremely experienced and smart person what their problem and as they describe all the things they've tried, throw in a random thing they haven't tried. And when they say, well that shouldn't fix it, you ask them, well if you've exhausted everything that should have worked, this is the time to try things that shouldn't. Either they will think of more tests they haven't considered so as to avoid doing your preposterous idea OR they try it and get a new clue to their problem. Heck, at worst they confirm that they do know SOMETHING about the system.

Go out and problem solve ! As always, thanks for reading and good luck with all of your side hustles.

If you prefer to listen to learn we got you covered with the Engineering IRL show!

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Technical Tactics
10+1 Steps to Problem Solving

Engineering Problem Solving ¶

Some problems are so complex that you have to be highly intelligent and well-informed just to be undecided about them. —Laurence J. Peter

Steps in solving ‘real world’ engineering problems ¶

The following are the steps as enumerated in your textbook:

Collaboratively define the problem

List possible solutions

Evaluate and rank the possible solutions

Develop a detailed plan for the most attractive solution(s)

Re-evaluate the plan to check desirability

Implement the plan

Check the results

A critical part of the analysis process is the ‘last’ step: checking and verifying the results.

Depending on the circumstances, errors in an analysis, procedure, or implementation can have significant, adverse consequences (NASA Mars orbiter crash, Bhopal chemical leak tragedy, Hubble telescope vision issue, Y2K fiasco, BP oil rig blowout, …).

In a practical sense, these checks must be part of a comprehensive risk management strategy.

My experience with problem solving in industry was pretty close to this, though encumbered by numerous business practices (e.g., ‘go/no-go’ tollgates, complex approval processes and procedures).

In addition, solving problems in the ‘real world’ requires a multidisciplinary effort, involving people with various expertise: engineering, manufacturing, supply chain, legal, marketing, product service and warranty, …

Exercise: Problem solving

Step 3 above refers to ranking of alternatives.

Think of an existing product of interest.

What do you think was ranked highest when the product was developed?

Consider what would have happened if a different ranking was used. What would have changed about the product?

Brainstorm ideas with the students around you.

Defining problems collaboratively ¶

Especially in light of global engineering , we need to consider different perspectives as we define our problem. Let’s break the procedure down into steps:

Identify each perspective that is involved in the decision you face. Remember that problems often mean different things in different perspectives. Relevant differences might include national expectations, organizational positions, disciplines, career trajectories, etc. Consider using the mnemonic device “Location, Knowledge, and Desire.”

Location : Who is defining the problem? Where are they located or how are they positioned? How do they get in their positions? Do you know anything about the history of their positions, and what led to the particular configuration of positions you have today on the job? Where are the key boundaries among different types of groups, and where are the alliances?

Knowledge : What forms of knowledge do the representatives of each perspective have? How do they understand the problem at hand? What are their assumptions? From what sources did they gain their knowledge? How did their knowledge evolve?

Desire : What do the proponents of each perspective want? What are their objectives? How do these desires develop? Where are they trying to go? Learn what you can about the history of the issue at hand. Who might have gained or lost ground in previous encounters? How does each perspective view itself at present in relation to those it envisions as relevant to its future?

As formal problem definitions emerge, ask “Whose definition is this?” Remember that “defining the problem clearly” may very well assert one perspective at the expense of others. Once we think about problem solving in relation to people, we can begin to see that the very act of drawing a boundary around a problem has non-technical, or political dimensions, depending on who controls the definition, because someone gains a little power and someone loses a little power.

Map what alternative problem definitions mean to different participants. More than likely you will best understand problem definitions that fit your perspective. But ask “Does it fit other perspectives as well?” Look at those who hold Perspective A. Does your definition fit their location, their knowledge, and their desires? Now turn to those who hold Perspective B. Does your definition fit their location, knowledge, and desires? Completing this step is difficult because it requires stepping outside of one’s own perspective and attempting to understand the problem in terms of different perspectives.

To the extent you encounter disagreement or conclude that the achievement of it is insufficient, begin asking yourself the following: How might I adapt my problem definition to take account of other perspectives out there? Is there some way of accommodating myself to other perspectives rather than just demanding that the others simply recognize the inherent value and rationality of mine? Is there room for compromise among contrasting perspectives?

How ‘good’ a solution do you need ¶

There is also an important aspect of real-world problem solving that is rarely articulated and that is the idea that the ‘quality’ of the analysis and the resources expended should be dependent on the context.

This is difficult to assess without some experience in the particular environment.

How ‘Good’ a Solution Do You Need?

Some rough examples:

10 second answer (answering a question at a meeting in front of your manager or vice president)

10 minute answer (answering a quick question from a colleague)

10 hour answer (answering a request from an important customer)

10 day answer (assembling information as part of a trouble-shooting team)

10 month answer (putting together a comprehensive portfolio of information as part of the design for a new $200,000,000 chemical plant)

Steps in solving well-defined engineering process problems, including textbook problems ¶

Essential steps:

Carefully read the problem statement (perhaps repeatedly) until you understand exactly the scenario and what is being asked.

Translate elements of the word problem to symbols. Also, look for key words that may convey additional information, e.g., ‘steady state’, ‘constant density’, ‘isothermal’. Make note of this additional information on your work page.

Draw a diagram. This can generally be a simple block diagram showing all the input, output, and connecting streams.

Write all known quantities (flow rates, densities, etc.) from step 2 in the appropriate locations on, or near, the diagram. If symbols are used to designate known quantities, include those symbols.

Identify and assign symbols to all unknown quantities and write them in the appropriate locations on, or near, the diagram.

Construct the relevant equation(s). These could be material balances, energy balances, rate equations, etc.

Write down all equations in their general forms. Don’t simplify anything yet.

Discard terms that are equal to zero (or are assumed negligible) for your specific problem and write the simplified equations.

Replace remaining terms with more convenient forms (because of the given information or selected symbols).

Construct equations to express other known relationships between variables, e.g., relationships between stoichiometric coefficients, the sum of species mass fractions must be one.

Whenever possible, solve the equations for the unknown(s) algebraically .

Convert the units of your variables as needed to have a consistent set across your equations.

Substitute these values into the equation(s) from step 7 to get numerical results.

Check your answer.

Does it make sense?

Are the units of the answer correct?

Is the answer consistent with other information you have?

Exercise: Checking results

How do you know your answer is right and that your analysis is correct?

This may be relatively easy for a homework problem, but what about your analysis for an ill-defined ‘real-world’ problem?

Job Descriptions

What Are the Best Problem-Solving Techniques for a Construction Engineer?

Last Updated on June 11, 2023 by Admin

As a construction engineer , problem-solving is an essential part of your job. The efficient execution of construction projects depends on how well you can manage unexpected challenges and obstacles that arise along the way. Given the complexity of many construction projects, it is vital to have a good problem-solving toolkit at your disposal. In this article, we explore the key problem-solving techniques that construction engineers can use to navigate the challenges they face.

Table of Contents

Understanding the Role of a Construction Engineer

A construction engineer is a professional who plays a vital role in the construction industry . They are responsible for overseeing the design, planning, and implementation of construction projects. A construction engineer is a highly skilled individual who has a deep understanding of the construction process, including the various materials, techniques, and tools used in the industry.

The role of a construction engineer is critical because they are responsible for ensuring that construction projects are delivered on time, within budget, and to the required quality standards. They work closely with architects, contractors, and suppliers to ensure that projects are completed successfully.

Key Responsibilities of a Construction Engineer

Construction engineers have a wide range of responsibilities that require a combination of technical, managerial, and interpersonal skills. Some of their key responsibilities include:

Developing project plans and timelines: Construction engineers are responsible for creating project plans that outline the scope of the project, the timeline for completion, and the resources required to complete the project. They work closely with architects and contractors to ensure that the project plan is feasible and realistic.
Preparing cost estimates and budgets: Construction engineers are responsible for preparing cost estimates and budgets for construction projects. They consider factors such as labor costs, material costs, and equipment costs when preparing these estimates.
Overseeing the hiring of contractors and suppliers: Construction engineers are responsible for hiring contractors and suppliers to work on construction projects. They evaluate bids and proposals from potential contractors and suppliers to ensure that they are qualified and capable of completing the project.
Monitoring construction progress and ensuring quality standards are met: Construction engineers are responsible for monitoring construction progress and ensuring that quality standards are met. They inspect construction sites regularly to ensure that work is being done according to plan and that safety standards are being followed.
Ensuring compliance with safety regulations and legal requirements: Construction engineers are responsible for ensuring that construction projects comply with safety regulations and legal requirements. They work closely with regulatory bodies to ensure that projects are compliant with local, state, and federal regulations.

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Challenges Faced by Construction Engineers

Despite careful planning and preparation, construction projects face a range of challenges that can derail progress and interrupt timelines. Some of the most common challenges that construction engineers face include:

Unforeseen design changes: Design changes can occur during the construction process, which can impact the timeline and budget for the project. Construction engineers must be able to adapt to these changes and ensure that they are implemented in a timely and efficient manner.
Unavailability of resources and materials: Construction projects require a wide range of resources and materials, and delays in the delivery of these items can impact the timeline for the project. Construction engineers must be able to manage these delays and ensure that the project stays on track.
Weather-related delays and disruptions: Weather-related delays, such as heavy rain or snow, can impact the construction process and delay the timeline for the project. Construction engineers must be able to plan for these delays and adjust the project timeline accordingly.
Budget overruns: Construction projects can be expensive, and it is not uncommon for projects to go over budget. Construction engineers must be able to manage costs and ensure that the project stays within budget.
Safety incidents and accidents: Construction sites can be dangerous places, and safety incidents and accidents can occur. Construction engineers must be able to manage these incidents and ensure that safety standards are being followed to prevent future incidents.

Overall, the role of a construction engineer is critical to the success of construction projects. They are responsible for managing resources, coordinating teams, and ensuring that projects are delivered on time and within budget. Despite the challenges that they face, construction engineers are highly skilled professionals who play an essential role in the construction industry.

Importance of Problem-Solving in Construction Engineering

Construction engineering is a challenging field that requires a unique set of skills. One of the most critical skills that construction engineers must possess is problem-solving. The ability to quickly assess a situation and come up with effective solutions can help keep projects on track and within budget. Here are some of the critical areas where problem-solving skills come in handy for construction engineers:

Navigating Complex Projects

Construction projects are often complex and involve many moving parts. From managing subcontractors to coordinating with architects and engineers, there are many different components to consider. The ability to analyze and understand the different components of a project is essential to delivering it successfully. This requires a problem-solving mindset that can break down complex issues into smaller, manageable tasks.

For example, imagine that you are working on a project that involves building a new hospital. There are many different stakeholders involved, including doctors, nurses, and hospital administrators. Each group has different needs and requirements, and it can be challenging to balance them all. A construction engineer with strong problem-solving skills can assess the situation and come up with a plan that meets everyone’s needs.

Ensuring Safety and Compliance

The construction industry is heavily regulated, with safety standards and legal requirements that must be followed. Construction engineers must stay up to date with these regulations and ensure that their projects comply with them. The ability to identify compliance issues and come up with effective solutions is an essential part of the job.

For example, imagine that you are working on a project that involves building a new high-rise building. There are many safety regulations that must be followed to ensure that the building is safe for occupants. A construction engineer with strong problem-solving skills can identify potential safety hazards and come up with solutions to mitigate them.

Managing Time and Resources

Construction projects operate under tight timelines and budgets. The ability to manage time and resources effectively is essential to delivering projects on time and within budget. Problem-solving skills can help construction engineers identify areas where resources can be optimized to achieve project objectives.

For example, imagine that you are working on a project that involves building a new bridge. The project has a tight deadline, and there are limited resources available. A construction engineer with strong problem-solving skills can identify ways to streamline the construction process and optimize the use of available resources to ensure that the project is completed on time and within budget.

In conclusion, problem-solving skills are essential for construction engineers. They help navigate complex projects, ensure safety and compliance, and manage time and resources effectively. By developing strong problem-solving skills, construction engineers can deliver successful projects that meet the needs of all stakeholders.

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Root Cause Analysis

Root cause analysis is a problem-solving technique that involves identifying the underlying causes of a problem. The technique involves asking a series of “why” questions to get to the root cause of the problem. Once the root cause has been identified, construction engineers can come up with effective solutions to prevent the issue from occurring again.

Brainstorming and Mind Mapping

Brainstorming and mind mapping are creative problem-solving techniques that involve generating ideas and organizing them visually. These techniques are useful for generating ideas and solutions in a collaborative and structured environment.

The 5 Whys Technique

The 5 whys technique is a problem-solving technique that involves asking “why” questions to get to the root cause of a problem. The technique involves asking a series of five “why” questions to identify the underlying cause of the problem. Once the root cause has been identified, construction engineers can come up with effective solutions to prevent the issue from occurring again.

SWOT Analysis

SWOT analysis is a problem-solving technique that involves identifying the strengths, weaknesses, opportunities, and threats of a project. This technique is useful for understanding the internal and external factors that can affect a project’s success. By identifying these factors, construction engineers can come up with effective solutions to mitigate any risks.

Decision Matrix Analysis

Decision matrix analysis is a problem-solving technique that involves weighting and ranking multiple criteria to make a decision. This technique is useful for evaluating different options and choosing the best one based on a set of pre-defined criteria.

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Implementing Technology to Aid Problem-Solving

In addition to problem-solving techniques, construction engineers can also leverage technology to aid in problem-solving. Here are some of the key technologies that can be used:

Building Information Modeling (BIM)

BIM is a digital representation of a building or infrastructure project. The technology allows for collaboration between different stakeholders, which can help identify potential issues and solutions before construction begins. BIM can be used to optimize workflows, reduce errors and waste, and improve project outcomes.

Project Management Software

Project management software is a tool that can help construction engineers manage projects more effectively. The software allows for the creation of project plans, schedules, and budgets. It also provides real-time visibility into project progress and helps teams collaborate more effectively.

Virtual Reality and Augmented Reality

Virtual reality and augmented reality technologies can be used to simulate construction projects in a virtual environment. This technology can help identify potential issues and visualize solutions before construction begins. The use of VR and AR can help reduce errors, improve safety, and optimize workflows.

As a construction engineer, problem-solving skills are essential to delivering successful construction projects. By understanding the different problem-solving techniques and leveraging technology, construction engineers can navigate the challenges they face and ensure that projects are delivered on time and within budget.

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1st Edition

Problem Solving for New Engineers What Every Engineering Manager Wants You to Know

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Description

This book brings a fresh new approach to practical problem solving in engineering, covering the critical concepts and ideas that engineers must understand to solve engineering problems. Problem Solving for New Engineers: What Every Engineering Manager Wants You to Know provides strategy and tools needed for new engineers and scientists to become apprentice experimenters armed only with a problem to solve and knowledge of their subject matter. When engineers graduate, they enter the work force with only one part of what’s needed to effectively solve problems -- Problem solving requires not just subject matter expertise but an additional knowledge of strategy. With the combination of both knowledge of subject matter and knowledge of strategy, engineering problems can be attacked efficiently. This book develops strategy for minimizing, eliminating, and finally controlling unwanted variation such that all intentional variation is truly representative of the variables of interest.

Melisa Buie makes lasers and solves problems. In her role as Director of Operations, she works on both engineering and business problems. She joined Coherent and began lecturing at San Jose State University in 2007. She has also worked as a Research Scientist for Science Applications International Corporation working at the Naval Research Laboratory in Washington, D.C. where she made theoretical lasers. Melisa was a Member of the Technical Staff and Engineering Manager at Applied Materials, Inc. prior to joining Coherent. Melisa’s first book is Problem Solving for New Engineers: What Every Engineering Manager Wants You to Know which will be published in the summer of 2017. Melisa has co-authored of more than 40 publications and holds 6 patents. Melisa’s degrees include a PhD in Nuclear Engineering/Plasma Physics from the University of Michigan and a MS in Physics from Auburn University. She has a Six Sigma Black Belt from the American Society for Quality. She will complete a certification program in innovation leadership at Stanford University Graduate School of Business in 2017. She lives in Palo Alto, CA. .

Critics' Reviews

"Dr. Buie’s Problem Solving for New Engineers presents a terrific introduction into the realistic experimental workspace and data analysis for new engineers and scientists. This well-written one-stop overview of experiment planning, execution and data reduction will be a beneficial stepping off point to anyone entering into the laboratory for the first time, as well as experienced experimenters reviewing what might go (or went!) wrong." -John Paff, Engineering Technology Manager, Spectra-Mat, Inc. "Finally a book that cultivates the rich landscape between human creativity and ingenuity, which motivates the scientist and engineer, and the rigors of applied experimental practice. Looking back over many years of engineering research development and manufacturing activities, I am ever surprised how common problem solving skills and experimental methodologies are infrequently cultivated alongside the prodigious evolution of technical knowledge and our means to generate data and simulate results. A thoughtful and approachable problem solving primer has long been needed for new engineers which combines core experimental principles used in engineering, science and applied statistics. In academic settings, such subjects are still taught as parts of course work across disparate disciplines. But in contemporary industry, their combination becomes a mandatory core skill set and is key to success in the technical quality and communication of any engineer's creative endeavor. In Buie's book we have a contemporary amalgamation of applied experimental principles and methods presented in an approachable and motivating format. Dr. Buie draws from history, case studies, and real examples that breathes life into what might otherwise become a dry subject. Her passion for experimental investigation and its teaching is strongly evident as she traverses a subject matter that might take years of academic and industrial practice for an engineer to integrate and master." -Len Mahoney, Ph.D., Unit Process Engineer, Avago Technologies "Problem Solving for New Engineers offers a way to shape learning gained in school and bridge the gap to becoming a savvy, strategic problem solver, reducing the "groping in the dark" phase of mastering a discipline. This book enables the wisdom of mastery by providing key understandings and methods that are at the heart of an experimental discovery mindset. Approaches to moving fascination and wonder into realized outcomes are based in a context of inquiry, exploration and discovery that refine disciplined problem solving by happily traveling the unknown - one experiment at a time." -Diana Hagerty, Project Manager at General Atomics Aeronautical Systems "Melisa Buie is not only creative in her approach, but utterly aware of the challenges we face as engineers and scientists in practice. As I was going through the pages, I realized that the book mirrors my own experience. I wish something like this has been available when I was starting out." From Saman Choubak, Ph.D., Senior Research and Development Engineer at PepsiCo "Problem Solving for New Engineers, written by Dr. Melisa Buie, serves the fresh new engineers with plenty of methods, required for successful experimentation and process development in modern companies, with focus on, but not limited to nature sciences. The problem I observe so frequently with new engineers coming from the university - How to apply the knowledge about how experiment were performed by others, to efficient setup of our own experiments -is discussed at different levels and guidance is provided for closely every step on the way from collection the requirements to evaluation and qualification of the new process. Personally I most appreciate the balance between overview of methods a deep enough explanation, rather free of equations, which will not let you skip the rest of any chapter and fair comparison of the one-factor-at-a-time experimenting all of us learned at the university and statistical design of experiment. The text invites you to experiment on your own and eradiates the pleasure on investigation and development itself. Author’s knowledge of science history converts the scientific topic to easy to read lecture, you will enjoy also as bedtime story." -Pavel Nesladek, Ph.D., Member of Technical Staff, Advanced Technology Mask Center "I wish I had this book when I was a college student! I might have decided to become and engineer or a scientist. Melisa Buie brings her background in industry and academia together in a balanced and effective way. This is not your usual dry textbook. I laughed out loud in places! It’s a must have "how to" reference book focused on important engineering and scientific concepts, communicating experiments and research effectively and being a successful engineer or scientist in academia or private industry. The material is presented in an exciting, real and sometime humorous way by using stories, sharing life experiences and revisiting discoveries of the great scientists throughout history. As someone who has been responsible for recruiting new engineers fresh out of college, reading this book should be a prerequisite for being hired." -Noël Kreidler, Owner, Kreidler Solutions, providing over 25+ years of experience in Talent Acquisition and Human Resources "In today’s fast paced technology industry, being able to efficiently attack issues and clearly share learning is critical. As Dr Buie points out, many engineers entering the workforce have a strong science background but their real life problem solving skills are not as developed. This book is a wonderful overview of problem solving strategies, experiment design and data analysis needed to succeed in a world driven by constant discovery. I especially appreciate the sections on graphing, as poorly communicated learning within cross functional teams can lead to wasted time and effort down the road. This text should be required reading for all newly hired engineers and a welcome reference for those of us who have worked in this industry for many years." -Jeremiah Pender, Ph.D., Sr. Engineering Development Manager, Applied Materials, Inc. "Buie provides insight into problem solving and experimentation that is far beyond what is found in a typical textbook. This book provides the framework for how statistical tools and experimental strategies learned in the classroom fit into the laboratory and onto the production floor. This is a must read for new engineers who are transitioning from school to the work place. For seasoned problem-solvers this book provides a great refresher and new insight into being better experimenters." -Karen Copeland of Boulder Statistics "An easy to understand and enjoyable to read introduction to the important concepts of variation, measurements, and statistical design of experiments that will give readers creative tools to discover invaluable insights into the solution of complex scientific and engineering problems."　 - From David Trindade, PhD, Fellow and Chief Officer of Best Practices, Bloom Energy

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An Engineer's Guide to Solving Problems Paperback – January 31, 2014

Engineers want to get employed and stay employed..

An Engineer's Guide to Solving Problems targets engineering students and fresh graduates.

The transition from engineering school to real world problem solver can be rough. Suddenly, there is not just one correct response for a problem. There might be an infinite number of correct solutions, where some are simply better than others. Some problems are so layered and twisted that their solutions seem absurdly complex.

Arm yourself for success with the methods in this book:

The Five Questions every problem solver must answer.
The best and worst ways to communicate your ideas.
New ways to see what other observers miss.
Mastering the right tools.
Six warnings to heed when you think you have a solution.
Critical challenge questions you must answer before you declare victory.

Employers and customers cherish engineers who consistently meet their toughest challenges. This book delivers simple methods, practical advice, and entertaining stories to help you sharpen your skills.

This book is intended for mature readers. The author occasionally uses strong language to humorous effect or makes references not intended for children.

The Second Edition includes some updates plus a new cover and shorter title. The first edition was originally published as The Dog Barks When the Phone Rings: An Engineer's Guide to Solving Problems .

Print length 252 pages
Language English
Publication date January 31, 2014
Dimensions 6 x 0.57 x 9 inches
ISBN-10 0988747626
ISBN-13 978-0988747623
See all details

Product details

Publisher ‏ : ‎ Kokomo Press LLC; 2nd ed. edition (January 31, 2014)
Language ‏ : ‎ English
Paperback ‏ : ‎ 252 pages
ISBN-10 ‏ : ‎ 0988747626
ISBN-13 ‏ : ‎ 978-0988747623
Item Weight ‏ : ‎ 12 ounces
Dimensions ‏ : ‎ 6 x 0.57 x 9 inches
#1,945 in Technology (Books)

About the author

Bob schmidt.

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1 Identifying Problems & Customer Needs

1.1 Identifying the Problem

Albert Einstein is famously credited for stating, “If I had an hour to solve a problem, I’d spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.” While there is little evidence that Einstein was responsible for this remark, the substance of the quote has resounded with scientists and engineers. At the root of the statement is one simple ideology – the most critical and challenging part of the problem-solving method is the definition of the problem.

The idea of meticulously defining the problem is often overlooked by new and inexperienced engineers. Without discipline, the thrill of the design process can overshadow the need for a rigid foundation. Engineering students, trained from the beginning to solve problems as efficiently as fast as possible, easily become fixated on one solution early without really knowing what problem it solves. Failing to correctly identify the problem can result in cost, time, and reputation deficits further down the design pipeline.

Why is it Critical to Define the Problem?

Defining the problem is critical to ensure that the customer and the design engineer agree on the needs that must be addressed by a solution. If the customer and the design engineer do not agree on the problem, it is likely, if not certain, that the design engineer will create a solution to a problem that doesn’t satisfy the customer. To ensure conception of a proper solution, the design engineer is responsible for asking the right questions about the problem both of the customer and other end users.

Consider the following hypothetical: you are a mechanical engineer that aims to develop a chair for a larger company’s headquarters located in Platteville, WI. Upon hearing the need for a chair, you set out to design the best, most capable office chair that has ever existed. The office chair is equipped with lumbar support, armrests, wheels, an ejection seat, and all of the other amenities one could ask for. When you go to present it to the customer, they grow concerned that the chair was intended for use in conference rooms. The inclusion of armrests increases the width of the chairs, which decreases the number of chairs that can fit around a table. Newly inspired, you go back to the drawing board and eliminate the armrests. When you present the result to the customer, they are satisfied with everything except for the cost of the unit. Once again, you return to the drawing board, eliminate the wheels and ejection seat while retaining lumbar support, and present the result to the customer once more. The customer then expresses that they are satisfied with the new cost, but they would have preferred the inclusion of wheels instead of the lumbar support. You grab your office chair, load it up in your vehicle, and head back to your shop to design what will hopefully be your last concept.

Now, consider the case where the size, cost, and other necessary features of the chair were discussed prior to the development of the first model. The problem would have been solved with a greatly reduced number of prototypes. This is the motivation behind defining the problem – to ensure that, in the end, the problem is solved as correctly, efficiently, and elegantly as possible.

The Anatomy of an Engineering Problem

In its purest form, an engineering problem consists of a basic need (pains) , a desired outcome (gains) , and the context of the problem . The basic need, or customer pains, is best defined by the problem that a customer hopes to address. The basic need is meant to motivate the further progression of the design process, so it should be written clearly and concisely. In the chair example above, the basic need that requires attention is the lack of seating arrangements in the conference rooms.

The desired outcome, or customer gains, is a set of qualitative criteria that the product must fulfill upon its completion (i.e. the goal of the product). It is not meant to act as an exhaustive list of customer needs (which come later), but rather as a high-level description of the functionality of the product. Determining desired outcomes is a preliminary step to listing the customer needs, which require quantitative descriptions. In the chair example, the seating arrangement must be composed of individual pieces (i.e. no benches). More desired outcomes include the ability to easily move the chairs around, the ability to place the chairs around the table, the focus on comfort, and the need to meet a budget.

The contextualization of a problem is meant to increase the awareness of the design team about the customer’s situation. Contextualization includes asking about the company’s previous attempts to manage or solve the problem, the conditions that the company is working in, the suppliers of the company’s existing hardware (in the event of compatibility issues), and other company-specific information. Contextualization notably does not include attempts outside of the company to solve similar problems – this occurs in the research stage of the design pipeline.

If done properly, this process should give the design engineer a good idea about whether or not their firm has the capacity and knowledge base to tackle the project (although the assessment can change in later stages with the introduction of new information).

Are You Solving the Wrong Problem?

The customer’s problem definition often reveals underlying issues about the customer’s interpretation of the problem. In some cases, the customer may be convinced that they require one prescribed solution to solve their problem. If the design engineer determines that another solution is more suitable for the application, it is good practice to discuss the different approaches to ensure that both parties are on the same page. If the design engineer presents a more elegant and more efficient solution to a problem, it could save the customer both time and money.

Consider a case where the customer has a custom lathe that can only hold round stock up to two inches in diameter. The customer wants a lathe that can hold round stock up to three inches in diameter; so they enlist the help of an engineer to design a new lathe. The customer may not be aware that the existing lathe chuck can be swapped for a new custom chuck to accommodate bigger diameter stock. In this case, a lack of feedback from the design engineer could end up costing the customer (and the design engineer) both time and money. In this hypothetical, it is critical that the engineer communicates the alternative solutions to the customer prior to moving to the next stage of the design process.

1.2 Addressing Customer Needs

Customers aren’t engineers.

Have you ever had a conversation where the person you were talking to used jargon you did not understand? For example, a mechanic trying to explain to a customer how the first cylinder of their engine is running rich due to the fuel injector sensor malfunctioning. Huh? This barrier of communication is something design engineers must overcome. Most customers do not have an engineering degree. Therefore, functions and features they request may be vague or outright impossible. Picture a customer asking for a flying car that runs on renewable energy by next year. It sounds like a great idea to the customer, but the technological limits make it impossible with the current available technology. Thus, the year timeline is improbable.

Engaging with the customers is inevitable to get permission for changes and to present progress on projects. Being able to effectively communicate with the customer is a must. Thus, it is imperative to avoid engineering jargon in these interactions because the customer may not fully comprehend the terminology used to describe the design. Educating them on engineering jargon is a waste of both your time and the customer’s time. Instead, quantify their vague requests by communicating with them in terms they will understand.

1.3 Converting Customer Needs to Quantitative Metrics

After receiving or generating the customer needs statement and verifying that there is not already a viable solution on the market, the customer needs can be mapped to quantitative metrics. Customers tend to use vague, qualitative descriptions to describe their needs. The design engineer must convert the customer needs from qualitative statements of product function into quantitative measures. This step is important because design is driven by customer needs that are often difficult for customers to articulate. For the design to function what the customer envisioned, clearly defined and measurable objectives must be defined early in the design process instead of reliance on common qualitative descriptions such as “I want something that’s easy to use”, “I want something easy to clean”, or “I want something that looks nice”.

The initial design process involves investigating needs from the customer and interacting with the customer to find out what is essential. At the outset, customers might not realize that they want to prioritize something in their design such as weight, size, cost, or functionality. So, it’s important to ask many questions about what they expect from the design. After client/customer interviews, new objectives will likely be added to the customer needs statement, which is a living document that evolves with the design process as all stakeholders learn more about the product or process being created.

In addressing descriptions given by the customer about the product, design engineers must ask questions aimed at finding the how, why, and what of the goal product. The “how” questions address the function of the product, and what process it is aimed to perform. For instance, the engineering design team can ask, “how long will this product be used daily?” The “why” questions must reach an explanation as to the reasoning behind the customer seeking this objective; this may allow the engineers to derive the importance of the customer’s goals. The “what” questions aim to specify features the customer seeks in their goal product. In the conference room chair example given above, one might ask “why is the chair a better alternative over a bench?” The “what” questions can ask, “in what settings will this product be used?” In directing specific questions at the customer, the engineer can begin to categorize the customer’s objectives and define their priority level.

Asking Questions

Conducting an interview with the customer will help them communicate their vision to the design team. In this process, the design engineer(s) must ask the right questions to obtain quantifiable objectives and produce an excellent product for the customer. Customers are not expected to have vast engineering knowledge. Their vision for their desired product normally contains vague descriptions that the engineering team must decipher. For instance, if a customer is interested in realizing a “beautiful” lamp, then the design engineering team must investigate deeper to understand what “beautiful” means for the customer in terms of the product being created. Does it illuminate a certain square footage? Is the light it produces a particular color and brightness? Is the lamp a certain height? Does it accept a specific kind of bulb? All of these “beautiful” lamp elements can be quantified and measured to determine whether customer expectations are met.

1.4 Textbook Problem Analogy to Engineering Design

Engineering coursework involves solving problems after they have already been defined; this situation is almost never the case in real engineering design. The customer and the engineer have different knowledge bases. So, it is important for the design engineer and customer to work synergistically. The consequences of failing to do so parallel the consequences of misinterpreting a textbook problem.

If customer needs are misinterpreted, the wrong product will be designed. This is analogous to misinterpreting a textbook problem statement and solving for the wrong variable.
If the desired outcome are not understood, the product may solve basic needs, but it may introduce other problems or complications for the customer. This is analogous to not stating assumptions while solving a problem, not using enough significant figures, or even overcomplicating the problem due to a misunderstanding.
If the context for the design is not understood, the solution may not work for the particular customer it was designed to please. This is analogous to ignoring the initial values in an initial value problem or the boundary conditions of a differential equation.

1.5 Organizing the Needs via Kano Model Analysis

Role of kano model analysis.

In the world of engineering design, understanding and prioritizing customer needs are essential for creating successful products and services. One valuable tool for analyzing and organizing these needs is the Kano Model, which can help guide design engineers in their client-based projects.

The Kano Model, developed by Professor Noriaki Kano in the 1980s, is a theory of product development and customer satisfaction. It provides a framework for understanding and categorizing customer preferences and needs, helping businesses and engineering teams create better products and services. By understanding and applying the model, teams can better identify their value propositions and Hedgehog Concepts, which will be discussed in detail in Chapter 6. The Kano Model can ultimately help create products that stand out in the competitive market.

When customers provide an extended list of needs to be met by the product or service being developed, good organization becomes crucial for an effective design process. Customers have different conscious and subconscious priorities, and to compete successfully, designers must understand these needs better than customers can articulate them. In the context of a capstone project, the insights gained from the Kano Model Analysis prove particularly valuable when identifying the value proposition (Chapter 6) and conducting down-selection to choose the most suitable design for prototyping (Chapter 8).

Categorizing Customer Needs with the Kano Model

The Kano Model classifies product features into three main categories, each with a different impact on customer satisfaction. The model can also be visually represented as a graph, with the two axes indicating the level of functionality and customer satisfaction.

The horizontal axis (x-axis) represents the level of functionality or the extent to which a product or service feature is implemented. This ranges from “Not Fulfilled” on the left side to “Fully Fulfilled” on the right side.
The vertical axis (y-axis) represents the level of customer satisfaction, ranging from “Dissatisfied” at the bottom to “Satisfied” at the top.

Three lines on the graph represent the relationship between customer satisfaction and the level of functionality for three main category of needs: performance needs, basic needs, and attractive needs. Understanding the relationship between customer satisfaction and functionality for each category of needs allows designers to concentrate their efforts on the most impactful features and improvements.

a. Performance Needs

These needs, also known as one-dimensional needs, directly influence customer satisfaction depending on how well they are executed and how many are executed. Customers usually articulate these needs in the Customer Need Statement and consciously evaluate them when deciding upon product alternatives. Performance needs often follow the “the more the better” requirement, meaning that the level of customer satisfaction linearly increases as the level of need execution increases.

Example 3.1a: 3D Bioprinter Linear Accuracy

You are tasked with designing a 3D bioprinter. Your customer states that the bioprinter must discharge cells with a linear accuracy of less than one cell diameter. This need falls within the performance category of the Kano Model, as it directly influences customer satisfaction based on how well it is executed.

On the Kano Model plot, different levels of accuracy can be represented along the performance line:

If the bioprinter achieves an accuracy of less than 1 cell diameter, it would be placed somewhere in the middle of the performance line. This level of accuracy meets the customer’s need and would result in a moderate level of satisfaction.
If the bioprinter achieves an accuracy of less than 0.1 cell diameter, it would be positioned high up on the performance line. This high level of accuracy exceeds the customer’s requirement and would lead to a higher level of satisfaction.
Conversely, if the bioprinter’s accuracy is less than 10 cell diameters, it would be situated low on the performance line. The printer fails to meet the customer’s need, resulting in a lower level of satisfaction.

b. Basic needs

Basic needs, or must-be needs, are threshold attributes that form the “price” for getting in the door. Customers expect these needs to be met by all products in the category, and they are typically unspoken and not included in the Customer Need Statement unless violated. Even if executed exceptionally well, basic needs do not increase customer satisfaction. However, failing to meet these needs will lead to significant customer dissatisfaction.

Example 3.1b: BSL-1 Cleanroom

In the context of the 3D bioprinter from Example 3.1a, the customer has mentioned that the bioprinter will operate in a cleanroom with a Biosafety Level (BSL) 1. This need falls within the basic category of the Kano Model, as it represents a threshold requirement that customers expect to be met but will not increase satisfaction if exceeded.

If the bioprinter successfully operates in and maintains the BSL-1 cleanroom standards, it would be placed high up on the basic line. This means the basic need has been met, and the customers’ dissatisfaction is minimized. However, meeting this requirement would not significantly increase customer satisfaction, as it is a basic expectation that customers take for granted.
Conversely, if the bioprinter fouls the cleanroom, compromising the BSL-1 standards, it would be positioned low on the basic line. This failure to meet the basic requirement would result in severe customer dissatisfaction.

c. Attractive needs

Attractive needs, or attractive features, are innovations that give products a “wow factor.” They delight customers when delivered but will not dissatisfy customers when missing. Attractive needs are usually unspoken by the customer and absent in the Customer Needs Statement, as customers often don’t know they want them. These needs can anchor a Hedgehog Concept, providing a unique selling point for the product.

Example 3.1c: Number of Cell Types

In the context of a 3D bioprinter, an attractive feature has been identified: the ability to print multiple cell types. By default, the customer expects the bioprinter to be capable of printing only one cell type. Attractive features, as per the Kano Model, have the potential to delight customers when present but do not cause dissatisfaction when absent.

On the Kano Model plot, different levels of cell type printing capabilities can be represented along the attractive line:

If the bioprinter can print only one cell type, it would be positioned low on the attractive line. As the attractive feature is not present, the customer’s expectations remain unaltered, and their satisfaction level stays neutral.
If the bioprinter can print several cell types, it would be situated high on the attractive line. In this scenario, the customer would be impressed by the enhanced capability, leading to a significant increase in satisfaction.

This example illustrates the potential impact of attractive features on customer satisfaction. By incorporating the ability to print multiple cell types, designers can differentiate their bioprinter from competitors, providing a unique selling point and exceeding customer expectations.

Attractive Needs “Migrate” Over Time

Over time, customer expectations evolve, and attractive needs can drift to performance needs and eventually become basic needs. This migration highlights the importance of continuous innovation to maintain a competitive edge in the market. As customers become accustomed to certain features, they begin to expect them as standard, underscoring the need for designers to stay ahead of the curve in anticipating and meeting customer desires.

Example 3.1d: Rearview Camera in Automobiles

When rearview cameras were first introduced in cars, they were considered a luxury feature, typically available in high-end models. Drivers appreciated the added convenience and safety that rearview cameras provided, as they made parking and reversing easier and reduced the risk of accidents. At the time, rearview cameras were not a standard feature in all cars, so having one made a vehicle stand out and offered a “wow factor” for drivers.

Over the years, as the technology became more accessible and affordable, rearview cameras started to be included in a wider range of vehicles. Consumer expectations shifted, and the rearview camera transitioned from an attractive need to a basic need. Today, many countries have even made it mandatory for new vehicles to be equipped with rearview cameras. As a result, customers now expect all new cars to have this feature, and a vehicle without a rearview camera would be seen as lacking an essential safety feature, leading to customer dissatisfaction.

Example 3.1e: Wi-Fi Connectivity

When Wi-Fi technology was first introduced in the early 2000s, laptops with built-in Wi-Fi capabilities were considered innovative and provided a “wow factor.” The ability to connect to the internet wirelessly was a significant improvement over relying on Ethernet cables, offering convenience and portability. At that time, not all laptops came with built-in Wi-Fi, making it an attractive feature that differentiated those that did.

As the technology became more widespread and user expectations evolved, Wi-Fi connectivity in laptops transitioned from an attractive need to a basic need. Today, customers expect all laptops to come with built-in Wi-Fi capabilities. A laptop without Wi-Fi connectivity would be viewed as lacking an essential feature, leading to customer dissatisfaction.

Key Takeaways

An engineering problem consists of a basic need, a desired outcome, and the context of the problem.
Customers use vague, qualitative descriptions to elucidate their needs. Design engineers must work closely with customers, asking the right questions to obtain quantifiable objectives.
Customer needs get converted to quantitative metrics, which are both numerical and measurable.
If the basic need is misinterpreted, the wrong product is produced.
If the desired outcome is not understood, the product may solve basic needs but introduce other problems or complications.
If the context is not understood, the solution may not work for the particular customer.

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How to Solve Any Problem in Engineering in Three Basic Steps

by Dee Reyes
September 10, 2021 September 13, 2021

$engineer problem solving problems$

An engineering student is always bombarded with numerical and worded problems that need step-by-step solutions to arrive to the answers. Solving these problems enable learning of the subject matter at hand with an aim to apply the principles in real life. After all, that’s what engineering is for.

But how does one approach a problem correctly? Just follow these three basic steps:

State the given.

Particularly for worded problems, the first critical step in solving any engineering problem is to gather the given information and known quantities.

There will be cases that your professor will feed you with values you don’t need to confuse or test your ability to separate what is needed in the problem. But sometimes, there are values that are not provided like the value of g or pi which are also essential. It has to be made sure as well that all the values belong to the same system of units, like in measurements feet versus meter, kilogram versus pound, so convert the values right away as necessary to avoid confusion later.

Moreover, do not forget the so-called boundary conditions, or constraints that apply to the problem.

Find the required.

The problem usually states explicitly what it is looking for, so focus on that. It is recommended to assign a symbol for the unknown.

Write it so you would not forget including the unit. It’s just like setting a goal that you need to arrive to.

Show the solution.

It sounds simple, but a solution is more than just a computation – it needs to have first a free body diagram (FBD), or a sketch complete with labels to be able to visualize the variables in aid of interpreting the problem.

Even if it is not needed, as the one who solves the problem it might give you a better understanding of the given values. Name and label the parts of the sketch accordingly.

Based on the FBD, the next questions you need to ask yourself are the following, not necessarily in particular order:

What principles or formulas are to be applied in this problem?
What could be the underlying assumptions or conditions?
Is there only one way to interpret the problem or one way to solve it?
Can the sketch be simplified further?

Once everything has been settled and simplified, do the math algebraically then numerically with the calculator. It pays to be careful to press the right buttons, so at this point there is no reason to make a mistake if you are doing the correct math.

You can perform several computations with your mind having the confidence with your arithmetic, but then this could be prone to human error. Each level of the equation should be written to avoid this and even the most basic 3×3 is to be done in a calculator to make sure it is the correct answer 9.

To complete the solution, box the final answer for it to be identified right away, which should be in line with the “required” item previously defined. In some cases, it might need to be presented in graph or tables.

But before submission, double check each step of the solution. Always.

1 thought on “How to Solve Any Problem in Engineering in Three Basic Steps”

Student Approaches to Engineering Problem-Solving - School of Engineering Education - Purdue University

Student Approaches to Engineering Problem-Solving

Event Date:	March 10, 2011
Speaker:	Elliot P. Douglas
Speaker Affiliation:	Department of Materials Science & Engineering, University of Florida
Time:	3:30 p.m.
Location:	ARMS B071
Contact Name:	Demetra Evangelou
Contact Phone:	494-4158
Contact Email:	[email protected]

Open-ended problem solving is a skill that is central to engineering practice. As a consequence, developing skills in solving such problems is imperative for engineering graduates. Open-ended problems are often ill-defined and can have more than one viable solution, which can create additional challenges for students and teachers. For example, solving open-ended problems can require consideration of a complex array of constraints, and the paths to a solution are many. This presentation presents results from a mixed methods project to understand open-ended problem solving of engineering undergraduate students. The overall goal of this project is to describe and understand the contributions of reflective judgment (i.e., students’ views of knowledge) and their cognitive ability (i.e., working memory capacity), when solving open-ended problems. We are particularly interested in specific problem-solving strategies undergraduate engineering students use when dealing with the ambiguity of open-ended problems.

Data were collected using a multi-stage process. Students were first given a set of quantitative instruments that measured their engineering content knowledge, epistemic views on knowledge, and working memory capacity. In the second stage students were asked to solve four problems that differed in their open-endedness and complexity; students were provided a text to use as a resource while solving the problems. Some of these students solved the problems using a think aloud protocol in which they were videotaped while speaking aloud about the strategies they were using. These students were subsequently interviewed to gain further information on their problem-solving processes. A number of insights regarding problem-solving by students have been obtained. For example, there was a significant negative correlation between time spent on the text and score on the problems. From the qualitative data three primary problem-solving strategies were identified: extreme fixation/distraction; fixated and uncertain; systematic and linear. Overall, the results indicate the importance of educating students in how to solve engineering problems that are complex and open-ended.

Dr. Elliot P. Douglas is Associate Chair, Associate Professor, and Distinguished Teaching Scholar in the Department of Materials Science and Engineering at the University of Florida. His research activities are in the areas of active learning, problem solving, critical thinking, and use of qualitative methodologies in engineering education. Specifically, he has published and presented work on the use of guided inquiry as an active learning technique for engineering; how critical thinking is used in practice by students; and how different epistemological stances are enacted in engineering education research. He has been involved in faculty development activities since 1998, through the ExCEEd Teaching Workshops of the American Society of Civil Engineers, the Essential Teaching Seminars of the American Society of Mechanical Engineers, and the US National Science Foundation-sponsored SUCCEED Coalition. He has received several awards for his work, including the Presidential Early Career Award for Scientists and Engineers, the Ralph Teetor Education Award from the Society of Automotive Engineers, and being named the University of Florida Teacher of the Year for 2003-04. He is a member of the American Society for Engineering Education and the American Educational Research Association and is currently Editor-in-Chief of Polymer Reviews .

DOI: 10.1002/j.2168-9830.2006.tb00885.x
Corpus ID: 109203147

Everyday Problem Solving in Engineering: Lessons for Engineering Educators

D. Jonassen , Johannes Strobel , C. B. Lee
Published 1 April 2006
Engineering, Education
Journal of Engineering Education

790 Citations

Cambridge handbook of engineering education research: engineers as problem solvers, engineering students’ experiences of workplace problem solving, ill-structured problem solving in a workplace simulation environment: challenges of the learning experience and skills developed, delayed guidance: a teaching-learning strategy to develop ill-structured problem solving skills in engineering, perception of complex engineering problem solving among engineerıng educators, first year engineering students problem solving in different scenarios, evaluating the problem-solving skills of graduating chemical engineering students, a systematic approach to implementing complex problem solving in engineering curriculum, comparison of experts and novices in problem-based learning for engineering education, engineering practice: teaching ill-structured problem solving in an internship-like course, 52 references, designing research-based instruction for story problems, instructional design models for well-structured and iii-structured problem-solving learning outcomes, toward a design theory of problem solving, problem based learning in a chemical engineering undergraduate laboratory, problem solving in a natural task as a function of experience, problem-based learning in aerospace engineering education, an assessment strategy to determine learning outcomes in a software engineering problem-based learning course, the effective, efficient professor., problem-based learning in biomedical engineering curricula, moving to problem‐based learning in the nz engineering workplace, related papers.

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Engineering: The nature of problems

Introduction

The optimistic approach to a problem is to view it as a challenge and an opportunity – a chance to make progress. In this course, the nature of problems is explored by looking at the way they are used as a stimulus for finding solutions. It is presumed from the start that you want to be involved in the process of finding solutions and that you are not expecting simply to be given the answers.

One example that is investigated in this course concerns how to devise lighter bicycle frames, and the way to assess the merits of alternative materials from which to make them. There is no single way to move from a problem like this to possible solutions. In fact there are often several ways to set about finding several solutions, but there are a few general factors that are important to the search.

First it is important to appreciate the needs from which a problem arises. For the bicycle frame it's not just a lighter material that is required, but rather it is one that can be deployed to bear specific loads imposed on a fully functional frame.

Next it is valuable to understand the challenge well enough to be able to specify the nature of solutions, perhaps using the formal languages of engineering, mathematics, science and problem solving. For example, it is unwise to take part in a discussion on 'the best materials for bike frames' without a technical appreciation of both the job a frame has to do and the relevant attributes of the candidate materials. Establishing what you don't yet know usually starts by recognising how effectively you can tell someone else where the challenges arise. You must be able to communicate with a wide range of people, sometimes 'calling a spade a spade', and at other times describing precisely what the word 'spade' actually means.

In passing from a problem towards possible solutions it is essential to be able to evaluate and quantify the technical aspects. Another general factor in the search for solutions is the use of algebra and numbers to compare options and to inform choices. Some calculations are simple evaluations that can be done directly with or without an electronic calculator. Others need a line or two of algebraic analysis. Yet others are too tedious or too complicated to tackle without a computer-based approach using spreadsheets or more sophisticated software.

In the end, the best motivation for learning comes from simply requiring the knowledge in order to make progress.

This OpenLearn course provides a sample of level 2 study in Engineering .

Learning outcomes

After studying this course, you should be able to:

view solutions as belonging to particular categories, broadly classified as: innovation by context; innovation by practice; routine

see how external factors affect engineering projects, and appreciate the range of engineering involved in meeting the basic needs of our society

recognise and apply a range of problem-solving techniques from each stage of the engineering design cycle, to include the following: physical modelling; mathematical modelling; iteration; use of reference data; refining an engineering specification

identify when models are likely to be useful and when they are no longer valid

recognise and distinguish between the following technical terms: differential equation; simultaneous equation; boundary condition; constraint; finite element analysis (FEA); mathematical model; physical model; prototype; demonstrator; anthropometric; ergonomic; product specification; functional specification.

1 Problems and innovation

1.1 solving problems.

It could be said that our species is defined by its irresistible urge to solve problems – it's what makes us human. Strange, then, that the word 'problem' has such negative overtones. I think that the root of this paradox is that the word is used both when we identify a need – the first link in the problem-solving chain – and when we undertake the process of meeting that need. It is the identification of the need and the realisation that it is real and must be met that creates the anxiety and the negative feelings ('Houston, we have a problem …'). The process of finding a solution is the exhilarating part that makes us thirst for more.

I think of my love of skiing. Sometimes I get to the top of a mountain and look down at the precipitous slope I must now descend to get back to safety and a good hot meal, and I am gripped by fear, perhaps even to the extent of wondering whether I'll survive this time. What provides the pleasure, apart from the thrill of speed, is using my skill (such as it is) to meet my need to be safe again.

'The Engineer: Skier on the Technological Piste' is perhaps too bizarre a title for a course, so welcome instead to T207_1 The engineer as a problem-solver: the nature of problems .

T207_1 is taken from an Open University course entitled ' The Engineer as Problem Solver '. The fact that we have prepared a course with this title shows that we think there is something useful to say about the process of solving engineering problems. It seems to imply that there is a technique to be learned – a preferred method. To a degree, this is true; experience has taught us that there are certain ways of proceeding which tend to lead to better solutions than others. This course is designed to give you a flovour of the skills and knowledge that will help you to make active and informed decisions when tackling your own engineering problems.

In engineering, solutions to problems come in three categories:

innovation by context;

innovation by development;

This is going to need some explanation, so here goes.

The categories differ from one another in the extent to which the solution is a step into the unknown, and this is why it may be chosen before the solution itself is known.

Table 1 Old context/new context versus old technology/new technology
	Old technology	New technology
New context	innovation	invention
Old context	routine solution	innovation

As you can see, there are four sectors in the table, defined by the technological newness of the solution, and the newness of the context in which it is to be applied.

The 'customer' for the solution will often have a very definite idea of the sector in which they wish the engineer to operate. For example, a new heart pacemaker will be heavily constrained in many respects: only certain materials will have been approved for the casing, as they have to be biocompatible; certain safety features must be included, such as methods of making sure the casing is hermetically sealed, making the device immune to electromagnetic interference, limiting the power and frequency of the heart stimulation; as well as other limits such as on the minimum lifetime of the battery and the need to provide sufficient warning of its decline to allow it to be replaced in time. The list is much longer than this. The effect is to discourage excessive innovation (by which I mean a significant change to the way something is made or the way it works – or a new type of thing entirely) and the chances are that an innovation by development will be the order of the day.

We define innovation by development as changing the bit that doesn't work, or that could work better, to improve the function of the whole product or design for reasons of cost, performance, ease of manufacture or gaining competitive edge.

This tight constraining of innovation does not preclude entirely the invention of a new type of pacemaker, but it is unlikely that a manufacturer will be asking its engineers to throw away the rule book and dream up something new. If an innovative pacemaker is to appear, it will be because someone has had a sudden inspiration, and the idea is so very good and the potential benefits so great that a manufacturer is prepared to take a large risk and go through years of testing to gain safety approval.

It is usually where safety is a critical factor that we find a tendency to reduce the amount of innovation, so it would be equally easy to find an example from the oil industry, or from the aerospace or military fields. Very conservative purchasers are the other main reason for holding back on innovation. Perhaps surprisingly, the industrial process control market is one such area. Engineers responsible for the design and installation of processing plant usually take a lot of persuading that a new type of flowmeter, say, will be better than the one they know and have been using for many years.

At the other extreme, there are just as many examples where innovation is essential to the success of a project. There's even a well-known mail-order catalogue whose very name includes the word. The market for gadgets and gizmos is huge, and rather prone to the vagaries of fashion. These two characteristics make it a powerful driver for innovation. Last year's temperature-indicating tea cosy with built-in radio, flashlight and satellite navigation system may have sold a million, but it's a little passé now ( Figure 1 ).

Another important instance where we know in advance that an innovation is required is where the existing technology is very mature, and has been incrementally developed as far as it is possible to take it, yet we have identified a need to improve the performance of the product still further. In this case, we can clearly see that innovation will be the only way to get there. An example of this is the bubble-jet printer. In the late 1970s and early 1980s, the vast consumer and small-business market for printers could not stand the cost of laser printers, yet was demanding better quality, less noise and higher speed from the alternative, which was the dot-matrix printer. This works by transferring ink from a typewriter ribbon onto the paper, using an array of electromagnetically actuated pins. These had been improved over many years, and were about as good as they could get. They had reached the limits of how fine a pitch they could be arranged on at a reasonable price but, even so, they were still rather slow and noisy.

What was required was an innovation, and this came in the form of the bubble-jet, which was an entirely new technology based on the ability to etch arrays of very fine holes in a polymer substrate using photolithography. The ink is transferred to the paper by creating pressure pulses behind the appropriate hole, using electrical heating. A single drop of ink is then ejected at high speed and strikes the paper. At a stroke, the new technology provided marked improvements on speed, pitch and noise level, and all without increasing the cost of the product.

1.2 Innovation by context

The word 'innovate' simply means 'make new'. We have chosen in this course to narrow the meaning of this term to be more or less synonymous with 'invention'. I would argue that innovation by context is as much a process as a result. By that, I'm using the term to mean something more like 'creativity'; and it's creativity that lies at the heart of all engineering. More than anything else in our professional lives, we engineers are excited by the prospect of being responsible for the creation of something better than we had before. This does not mean that all engineers are inventors in the sense that the word is normally understood (i.e. taking out patents on some new gadget). Innovation by context is the fruit of the creative process going on in the mind of the engineer when solving a problem, and can be anything from a clever change in the design of a computer program that allows it to run faster or use less memory, to something revolutionary like the jet engine.

For an engineer, creativity is a daily activity. Sometimes, the result is a big enough innovation to call an invention, and to patent, but mostly it's just small but necessary steps in reaching the goal. You can be creative even if your solution is of the type we classify as routine, as we'll show later. There are numerous great examples of innovative solutions, some of which are inventions. How about the first aqueduct, canal, drain, concrete, pilotless aircraft, the building of the Eden Project in Cornwall, the new roof over the British Museum, radar (mapping the skies, speed cameras and predicting weather), the first mobile phone, waterproof fabric, the microwave oven, the compact disk, Dyson's bag-less vacuum cleaner? … the list goes on. It's difficult to pick one example for looking at in more depth, but one of the best and most simple examples of innovation by context has been the transformation of radio into a self-sufficient technology, described in Box 1 .

Box 1 Innovation by context – an example

In 1991, inventor Trevor Baylis saw a television programme about AIDS workers in Africa. In poor countries radio broadcasting had always played a part in health education, but in this programme the workers were explaining how batteries were expensive or unavailable and electricity supplies unreliable or simply non-existent. The programme provided Baylis with a problem, and inspired him to find an innovative solution.

Baylis's invention, as you have probably guessed, was the clockwork radio, Figure 2 . He wasn't the first person to use springs to generate electricity, but prior to his design the energy had only ever been produced this way for short bursts at a time – here is the context . The innovation is in applying springs to the provision of low-power electricity for consumer electronics. Baylis invented a mechanism that gave forty minutes of play from just twenty seconds of winding. The winding action coils a spring, attached to a gearbox, which is connected to a dynamo. When the spring is released the gearbox controls the steady discharge of energy to produce electricity, and the radio works. The dynamo provides three volts at between 55 and 60 milliwatts, but the design also incorporates a solar-powered source to extend its performance.

Thus power is generated from human input, backed up by free and widely available solar power. Baylis realised that his new technology had huge potential. However, this was only half the task: he also needed to reduce the amount of power consumed by the radio, and this is where the less glamorous and less visible (but at least as important) part of the innovation was done. A team of electrical engineers worked to make improvements in small increments until the power consumption was pared down enough to allow the radio to work for a reasonable amount of time between rewindings of the spring.

Reaction to the radio was initially somewhat sceptical but eventually, in 1994, a prime-time BBC TV programme ( Tomorrow's World ) agreed to feature the idea. Two entrepreneurs who happened to be watching contacted Baylis immediately, going on to form a company with the intention of putting the clockwork radio into production. 'Freeplay', as they were called, raised a government grant for initial development costs and then found investors, to date selling over three million units. The company has the endorsement of heads of state, international aid organisations, royalty, celebrities, the European Union, the United Nations and more, and has gone on to develop other similar products.

The original problem – that of providing a self-sufficient technology so that radios could be widely available in developing countries – has been solved not only in theory but also in practice, the true test of an innovation.

1.3 Innovation by development

Innovation by development is about changing the bit that doesn't work, or that could work better, to improve the function of the whole for reasons of cost, performance, ease of manufacture or competitive edge. You probably noticed in Box 1 'Innovation by context – an example' that Baylis had to incorporate a number of developmental innovations as well. Improvements in materials or production equipment or techniques can present solutions to manufacturing difficulties, and so development becomes incremental not only in a product, but in a chain of production.

It's where the big money lies for companies wanting to keep one step ahead of their competitors without the (in general) higher risks and longer timescales of innovation – 'our powder washes brighter', 'this battery lasts longer' or 'this car is quieter to drive'.

Most technological items in everyday use have been subject to innovation by development. You can see the results in the motor industry, in aeroplanes, trains, mobile phones, computers, fridges, cookers, plastics, household implements … it's more difficult to think of something that hasn't been subject to innovation by development! Box 2 Innovation by development – an example explores a typical product development.

Box 2 Innovation by development – an example

The Black & Decker Workmate portable workbench ( Figure 3 ) has been the DIY and professional craftsman's best friend for thirty years now. At first sight, it is a product that has not changed much at all in that time; but if you look more closely, you will see that it has undergone a considerable amount of innovation by development. However, this has been done over such a long period of time that you need to put the original next to a new one to spot the differences. We can look at some of these changes and try to guess why they were made.

The original Workmate had a pair of long leadscrews ( Figure 4a ), one on each side, to move the jaws of the vice-cum-work surface. The length of these screws was over 30 cm, and they moved the half of the table furthest from the user relative to the other half, which was static. This enabled the bench to offer one of its best selling points: the ability of the vice to accept a large range of workpieces, including wedge-shaped and very wide ones.

The current design has switched things around, so that it is now the part of the top nearest the user that moves, but the leadscrews are very much shorter and therefore lighter ( Figure 4b ). This would normally restrict the range of widths of workpiece that can be accepted, but this has been restored by making the other part of the top removable. To accept pieces with a width that is outside the range of the leadscrews, this part of the top is simply unlocked from the framework and moved into one of the alternative locations for it, providing a new range of jaw separations that overlap slightly with the previous position.

Make a list of the effects of the change to the design of the Workmate's vice mechanism, noting the beneficial and detrimental effects for each one from the manufacturer's and the user's point of view.

Why do you think this change has been introduced?

Cost saving on leadscrews:

better margin for manufacturer, lower price for user.

Reduction in weight:

reduced distribution cost for manufacturer, easier to carry for user.

Screw does not now pass under the opening of the vice:

no direct effect for manufacturer, reduced likelihood of clogging with sawing debris (and therefore excessive friction) for user.

Extra operation of removing and replacing the moving jaw required for changes in workpiece width that exceed the leadscrew travel:

no direct effect for manufacturer, less convenient for user for small changes in workpiece width that nevertheless require relocation of the moving jaw, though quicker to change jaw separation for large changes in workpiece width.

The effects on both the user and manufacturer of all but the first change are slight. Therefore, the likely reason for the change is the first one – cost saving. This is partly offset by a cost to the manufacturer in making the change – the cost of the design work, changes to drawings, parts lists and order schedules. Note that the cost reduction has a beneficial effect for both the user and the manufacturer.

1.4 Routine solutions

This is the last of our three categories, and possibly the most difficult to define because the approach is not as definite. Routine solutions involve configuration or reconfiguration of existing devices or components, without innovation, because something is broken or needs to be repositioned, or there is simply a better way to do it. If you change the locks in your house or car, you are reconfiguring them; if you tune the car, calibrate the central heating, set the coordinates for your satellite navigation system, change from an overhead lamp to a wall light, or even just change station on your television, you are applying a routine solution to a problem by reconfiguring the bits. As I write, I'm reminded of the ongoing attempt by a group of stalwarts to reconfigure the standard keyboard, originally designed to prevent the letter levers clashing on a manual typewriter, into something more user-friendly for today's computer user.

The biggest examples of challenges requiring routine solutions are, literally, physically big. Things that need configuring are often remote, such as a fibre-optic signal booster in a cable at the bottom of the Atlantic, or, at the other extreme of the planet, a satellite; both of which (as it happens) are critical to intercontinental telecommunication. Box 3 Routine solution – examples looks at some examples.

Box 3 Routine solution – examples

The Hubble space telescope ( Figure 5 ) was conceived in the 1970s. The intention was that it would capture astronomical images, unimpeded by the Earth's atmosphere, and transmit data and images 640 km back to Earth, enabling us to answer some of our most fundamental questions about the universe. It was sent into orbit in April 1990, at a cost of about US$ 2 billion.

However, just weeks into its flight the mission was very nearly lost before it had truly begun, when NASA scientists discovered that the main concave mirror of the telescope had been ground too flat by a depth of 4 micrometres, resulting in images at high magnification that were too fuzzy to be useful.

The operators who control Hubble's flight work in team rotation, driving it 24 hours a day every day of the year, sending an average of over 100 000 instructions a week. The first opportunity to carry out maintenance, install new instruments and correct the error (by giving it 'glasses' in the shape of five pairs of corrective mirrors) came in December 1993, after two years of planning. Engineers operating the telescope trained extensively for the reconfiguration of Hubble. First the telescope had to be set aside from its usual research operations to a 'ready for servicing' condition and capture attitude, then the aperture door was closed and high-gain antennas stowed. Astronauts on board a Space Shuttle made five gruelling space-walks to carry out the installation work. Once this was completed and tested, both Hubble and the Shuttle were configured for battery charging. When charged, everything on the telescope was reactivated and it was released back into orbit. To everyone's very great relief the mission was a success, and Hubble soon began transmitting the great pictures that had been anticipated.

Why do we describe this as 'routine'? Clearly the solution being sought was not expected to be innovative – the commitment to reflective optics was unchangeable. Similarly, the cost of a series of incremental improvements would be prohibitive. What was called for, and what was done, was routine reconfiguration of the bits.

A less glamorous example is found in electronic circuit design. New amplifiers, data acquisition cards and so on are launched every year.

Many are new arrangements of standard components – resistors, capacitors, integrated circuits, etc. The problem solving here has been concerned with choosing component values and characteristics to achieve enhanced performance.

You should, by now, have a better idea of how to classify solutions to problems, challenges and opportunities. The three groups above overlap. It's possible for a solution to be equally valid in more than one group at a time. It's important to consider the context of whatever you're facing – the invention of the mobile phone was an innovation in terms of electronics, subsequent innovation by development has been largely incremental, and during this development there have been considerable routine design changes. If you're deciding where the solution to a problem belongs, try to narrow it down to its basic elements.

Group the following tasks as being problems likely to find solutions that are routine in nature, that involve innovation by development or require innovation by context :

Making a lighter ladder

Specifying components for a home-computing workstation

Defining specifications for building services in a new factory, e.g. ambient temperatures in different rooms/areas, air conditioning, waste air extraction, etc.

Designing a taller crane

Replacing lead-based solders with non-lead alternatives

Bridging a wider gap

Setting network and modem parameters for an office PC system

Designing an ejector seat for a helicopter (ouch!).

Specifying components for a home-computing workstation (selecting from among existing components)

Setting network and modem parameters for an office PC system (selecting from existing options)

Defining specifications for building services in a new factory, e.g. ambient temperatures in different rooms/areas, air conditioning, waste air extraction, etc. (selecting from among existing components)

Innovation by development:

Designing a taller crane (extend a shorter crane)

Making a lighter ladder (refine the design to reduce weight)

Bridging a wider gap (extend an old design)

Replacing lead-based solders (devise new alloys)

Innovation by context:

Designing an ejector seat for a helicopter (ejector seats were conceived for fixed-wing aircraft and can't simply be transferred to the pilot's seat in a helicopter).

2 Where does the need arise?

There is a rather obvious question that has to be raised at some point, so we may as well get it over with now: Why do we present ourselves with all these problems? After all, life would be easier without them and we could all go off and do jobs that don't involve them. Do we really need to know everything about the universe? Or to send people into space, at significant cost and human risk? Do we really need to send sound and pictures through space? Do we really need to communicate with people we've never met? Do we really need to educate people about health?

I hope you have at least agreed with the last one, and you can probably see a connection that runs through the points that were used as evidence in the last section. What it illustrates is an order of priority of human needs, ranging from the immediate and essential, to the remote and desirable, and that engineers are active at every level.

Arrange the following items in order of human physical need, with the most basic requirement at the top:

Communication

Entertainment

This is only my list, and your own personality will probably dictate how you placed the bottom six. The point is that we can survive no more than a few minutes without oxygen, a day or two without water, and a week or two without food. In extreme environments we can't survive without shelter and/or warmth. As for the rest: well, on this particular scale they can be seen as life's luxuries, although in relatively rich societies we are expecting more and more as our right rather than privilege. Engineers are involved in meeting all these needs at every level and at every depth of complexity.

However you organised the above list, you can see that there is a hierarchy of human requirement where the needs become increasingly refined and complex, and that there are problems, challenges and opportunities for the engineer at every level. All the items in the list could be expanded to consider the engineering involved. Box 4 Meeting the liquid challenge looks at how we meet the fundamental need for a supply of clean water.

Box 4 Meeting the liquid challenges

To all practical intents and purposes, water on Earth is part of a closed system – there is no more or less water on the Earth's surface now than when the first humans were alive. It is approximately 1400 million cubic kilometres of the ultimate recyclable resource, and it is random in its availability. We use it to drink, cook, wash and flush sewers, and without it any one of us would die within a week. Apart from the very air we breathe, it has to be our most basic need.

In temperate zones in the northern hemisphere, we are lucky enough to get a reliable amount of rainfall, which we can store in artificial reservoirs. Water has to be collected from lakes and reservoirs, wells, rivers and underground pools, then treated and transported for domestic and commercial use on a mammoth scale (Figure 6).

Think about the engineering involved in designing, building and lining reservoirs; designing and laying pipes of the right material and capacity; controlling water flow through the pipes; filtration and purification; delivery to domestic and business premises; removing, storing and treating sewage; managing the logistics of supply and demand; and the financial and technical administration of the water system. We may have cause to grumble about the occasional shortage in supply during long dry summers, but our system is generally robust. Generations of engineers have been responsible for the development of reliable water provision around the world (though there are still places where the challenges remain). If you have ever visited a country where you had to rely on sterilised or boiled water, you will appreciate it all the more.

In many poor countries the history of problems caused by drought or contaminated water is well documented. It is currently estimated that 2.4 billion people worldwide lack access to basic sanitation, and over a billion are drinking unsafe water. The engineering challenges posed in these countries (mainly in Eastern and Southern Africa, and South Asia) are different from those met in most of Europe as the rainfall is less reliable, work is often funded by overstretched charities and, although a long-term infrastructure is needed, there is also an urgent necessity to provide instant clean water. Engineers are working on a small, local scale, sometimes having to show innovation with the materials and resources available and meet needs by practicality at the expense of efficiency. They might have to find water below ground, or find a means of purifying water from a river. Engineers may also find themselves becoming educators – passing on their skills and advice to local communities who can then carry out work for themselves.

Internationally, as in any industry, there are groups of engineers and scientists committed to research and development at the boundaries of our existing knowledge. The most recent high-profile discoveries in the water industry are to do with the desalination of sea water, a huge and largely untapped aqueous resource.

Many sectors of engineering are involved in meeting such a basic need as the supply of fresh water. The three classifications of solution – innovation by context, innovation by development and routine – are all represented many times over, and there are numerous angles of opportunity and challenge. If you consider a similar breakdown for each of the needs you listed in Exercise 2 , you begin to get some idea of how and where engineering solutions are required. Here's a summary for this case:

designing, building and lining reservoirs;

designing and laying pipes of the right material and capacity;

controlling water flow through the pipes;

filtration and purification;

delivery to domestic and business premises;

removing, storing and treating sewage;

managing the logistics of supply and demand;

the financial and technical administration of the water system.

3 Needs and problems

The last section has established that engineering is about satisfying needs. In fact, with so many needs, it's a wonder that not everyone is an engineer! So, now that we have talked about both needs and problems, the logical progression is to examine the relationship between them.

Take the water example as being a fundamental need. We can state it thus:

This village needs a supply of clean water.

When given that statement, we have a natural tendency immediately to start looking for potential solutions – a trough for rainwater, purification for river water, a pump for underground water and so on. We will start asking questions to get a clearer definition of the need – What's the average rainfall? Is the village near a river? Do we know of any existing supplies? What physical resources are available? How much water is needed daily – is ten litres each enough? What do we mean by 'clean'? etc. Seamlessly, the need becomes a problem that requires a solution. The definition of requirements makes it precise.

The problem becomes how to transfer and purify sufficient water from a source, say a river, half a kilometre away.

With this amount of detail we have a problem definition, and all that's left is to find a solution …

(a) State, in a few words, the need which prompted the development of the Baylis wind-up radio.

(b) Make a list of bullet points that identify the engineering requirements involved in meeting the need for communication, like the list at the end of Box 4 'Meeting the liquid challenge' .

(a) The need for reliable, affordable access to broadcast health information in remote areas.

(b) adequate radio reception equipment

adequate power provision (clockwork and solar)

adequate manufacture and assembly

shipping and distribution

robust business plan.

4 Looking for solutions

4.1 advancing knowledge.

Over the centuries, engineers have faced and solved a huge number of problems of one sort or another. Each time a problem is solved, knowledge is advanced, something usually gets written down, and so today we have a wealth of experience to draw on. Equally, problem-solving techniques have also been developed and evolved through use and refinement, which is rather handy. Not only do we have some idea of existing solutions to similar problems, but we also have an indication of how to go about finding our own solutions.

As we're trying to get a picture of the whole, let's begin by looking at a typical, simple, problem-solution process and then we can break it down into separate elements. Figure 7 is one attempt to map out such a process, from the top down.

I should add, however, that there is no single right way to do this and there are, inevitably, all sorts of diagrams available to illustrate the process of creating solutions to problems. Engineering is a huge field, and procedures are usually shown with a bit more detail than in Figure 7 because they are specific to, say, software design, mechanical, chemical, civil engineering, etc.

4.2 From a need to a problem

So, working from the top down, the process starts with 'need' and 'problem'; see Figure 8 .

Although we usually work by identifying a need that converts to a problem, that requires a solution, don't forget the extra arrow at the side, taking this first part of the process full circle. The questions that draw out the problem may also refine needs, or indeed extract further needs that were not stated, acknowledged or recognised at the very beginning. We've already looked at where these needs come from on a global scale but, unless you are an academic researcher or a totally independent inventor, by the time you reach this stage of design the need is usually coming very directly from a customer. The customer may be your employer, or an external client, who has somehow identified the need to develop a new product or significantly modify, improve or repair an existing one. It's obvious that the better the specification, the less time and money will be wasted in designing or producing a product or solution that doesn't meet the requirement.

There are different types of specification – for example, a 'product' specification and a 'functional' specification. If the supplier has more knowledge about the specific product than the customer then a functional specification is appropriate. However, if the supplier is just making a design to order then a full product description must be agreed. The writing of these formal documents that attempt to ensure that the solution matches the requirements has become something of an art. The specification may become a legal contract that binds the engineer to the task, instead of a practical guide to the route and therefore the solution to a problem. While nobody would argue that you should not have some sort of guarantee that you're going to get what you are paying for, it does seem to be a shame that the more control is exerted in this way, the less room there will be for creativity and hence innovation in devising solutions. Used properly, the specification can be arrived at by an open exchange of views and ideas between the two (or more) parties involved, so that the engineering team goes away to look for solutions with a clear record and understanding of both the need and the problem. An example of the process that leads to a specification can be seen in Box 5 From problem to specification .

Box 5 From problem to specification

Between the 1930s and 1980s, millions of industrial and domestic refrigerators and freezers were produced which used chlorofluorocarbon (CFC) gases as the refrigerant and in insulating materials. CFC gases didn't degrade the fridge, were non-flammable, not poisonous in the event of a leak, and seemed to be an ideal replacement for the original refrigerants such as ammonia that were smelly, corrosive, poisonous and not particularly efficient. However, it transpired that CFC gases are damaging to the environment, depleting the ozone layer that protects us from the harmful ultraviolet components of the sun's rays. A need was thus identified – for fridges and freezers that are environmentally friendly ( Figure 9 ).

It is worth noting that this statement of needs is not at as fundamental a level as the earlier one in the water example. This illustrates the existence of the hierarchy of need. We need the ability to create cooled environments not only for keeping food fresh, but also for countless industrial processes. We are able to state the need in terms of fridges and freezers because there is a long history of market requirement and product development that moves the starting point of our need statement on from 'we need to keep our food fresh', through 'we need to make things cold' to 'we need fridges and freezers'.

There is a general principle here in the formulation of statements of need: the more fundamental the terms in which it is written, the greater the variety of solutions open for consideration, but the greater the possible number of dead ends. There is therefore a balance to be struck between maximising the chances of a really creative solution, and wasting time considering unsuitable ones. So, the statement 'the village needs a supply of clean water' leaves more options open than 'the village needs a water pump and filtration to get clean water from the river'.

To take this statement of the need the next step forward, we have to write a problem specification, which ideally will contain all the information necessary for working out a set of possible solutions.

Our need was stated as 'environmentally friendly fridges and freezers'. We can further refine this to 'we need alternative refrigerant gases to CFCs'. In doing this, we have excluded the possibility of using an alternative technology to the compression/expansion heat pump that is ubiquitous in refrigerators and freezers. There is a very good reason for this: the closed-cycle mechanical heat pump is the most energy-efficient known means of refrigeration, and to go to something that uses more energy could add an unacceptable environmental cost.

We can now state the requirements for the solution: A refrigerant gas with the following properties:

Not an ozone depleter

Compatible with conventional heat-pump technology

Non-corrosive

Non-hazardous (i.e. non-toxic, non-flammable)

Not an unacceptable source of some other pollution

Able to be manufactured in comparable volumes and costs to CFCs.

This is a technical specification. Clearly, it is at what could be called the top level; there are no numbers against any of these requirements. Once these have been added, though, we will have the beginnings of a formal document to bind the engineer to the task. The specification may even specifically exclude certain types of solution (as with the Hubble telescope repair).

There is a need to reduce the amount of pollution from airborne particulates in cities all over the world. A major factor is exhaust emissions from diesel engines. The search is on for an alternative fuel that doesn't produce the pollution locally.

Write a specification (as a list of bullet points) for an alternative automotive fuel that sets out the problem and is clear about the requirements that must be met in the solution.

The problem is to find or manufacture an alternative fuel for vehicles, because the existing fuels cause too much pollution in the towns and cities where they are used most intensively. The characteristics of the new fuel should include the following:

a significantly lower producer of particulate emissions

not a significantly worse producer of any other pollutants (including CO 2 , which would result if it is less energy efficient to produce and use)

no more toxic in unburnt form than existing fuels

no more hazardous than diesel

approximately the same cost to produce and use as existing fuels and possible to produce in similar volume (in terms not of litres, but of vehicle kilometres) to existing fuels

preferably compatible with existing internal combustion engines, i.e. no solutions that are 'innovation in context' (though not necessarily if a longer-term solution is wanted – vehicle lifetimes are relatively short, so a new technology could be brought in).

4.3 Possible solutions

According to Figure 7 , our map of the problem-solving process, once we've defined the problem according to the need the next step is the creative bit – to look for 'possible solutions', Figure 10 .

Depending on the need, this may require innovation by context, innovation by development or a routine solution. Contrary to what you might expect, innovation is not the only interesting or challenging option – there may be any number of potential solutions using standard parts, but only one really elegant combination. As good engineers, in an ideal context (remember this point), we are not just looking for a solution; we are looking for the best solution. However, although practising engineers will be looking for the best solution, they do not always have the time or resources actually to reach it. Even if they did have as many resources as they wished, it might still not be possible to know what the best solution is, or whether it has been reached. So if the engineer cannot know when 'best' has been reached, we see that compromise is an abiding characteristic of solving engineering problems.

Creative thought has to come without inhibition, influence or bias, and if you consider how difficult that is in the light of the problem in SAQ 3, then it makes sense that we shouldn't just expect it to happen. We can exercise our brain in much the same way as we exercise our bodies, and we can sharpen particular abilities by repeated action of the same or similar process. There are whole courses available in finding creative solutions, working up from simple questions to complex theoretical posers. The more you practise 'thinking outside the box', the better you will become. Foster, in a book called How to Get Ideas , has a good summary:

Think laterally. Think visually. Play “What if?” Look for analogues. Look for things to combine. Ask yourself what assumptions you're making, what rules you're following. Screw up your courage and attack. Foster (1996) p. 159

This is fine for working alone and stimulating your own creativity with no one around to question your ideas. In most commercial or industrial situations, however, you are more likely to be working as part of a group or team. Here, the so-called brainstorming approach is popular. There need not be a hierarchy within a brainstorming group – you mix contemporaries from different disciplines or representatives of other departments, with the assurance that each member is accorded respect and allowed to express suggestions 'without prejudice'. In a group situation everyone should feel totally at ease, free to put forward any idea that occurs, however lateral, apparently silly or unlikely. Next, the group is at liberty to ask questions and put the idea up for enquiry, but reasons to discard any idea must be rational and valid. Thus the atmosphere, relaxed and receptive, is open to completely new and innovative solutions.

Not all engineering is about innovation. Techniques such as brainstorming, used as above, and creating Spider diagrams of ideas, are a way of bringing ideas together, but not all the ideas will be original.

Box 6 Spider diagrams

A technique widely used for stimulating free thought is the spider diagram (sometimes known as a spray diagram). It works on the principle of removing the hierarchy of importance, implied when items are written in list form. Instead, the title of the problem or need is put at the centre, and as items are thought of, they are placed in more or less random positions on the paper. The connections between related items are then represented by lines, to produce a multi-limbed structure that gives the diagram its name. Usually, the process of drawing the relationships between items stimulates the addition of further items. Once the relationships have been made, it is possible to group several items together in themes, and a tree-like structure emerges. The diagram is now useful as a map of the whole topic, its critical issues, and the relationships between them. Figure 11 is an example.

In all but the most 'blue sky' organisations, constraints are present in terms of cost, time, capacity, environment, manufacturing capability – you think of it, it's a constraint. Add to this the limits imposed by our knowledge of the physical world – things like data storage capacities, material, fluid or gas properties, Anthropometrics and ergonomics and so on – and the problem up for attention has either shrunk significantly or has become more complex.

Box 7 Anthropometrics and ergonomics

An engineer uses anthropometric data when designing something that will be operated or used by a person, or rather more specifically, by any unknown person. It represents the weight and measurements of the average man, woman and child, usually presented in centiles (the 50th centile being the median average), and covers everything from basic height to the length of a little finger.

What the average person can do , on the other hand, is presented as ergonomic data. This is about how hard we can push, what pressure we can exert on a foot pedal, the most comfortable reach, etc. In the same way that we use tables of data for solid, gas or fluid properties in the specification of materials, we use anthropometrics and ergonomics to design for people.

Tables 2 and Tables 3 show the kind of information that is typically gathered and used.

Table 2 Anthropometric data f or adult British population (age 19–65 years)
	Male		Female
Body dimension	Mean/mm	SD*/mm	Mean/mm	SD*/mm
Stature	1740	70	1610	62
Eye height	1630	69	1505	61
Shoulder height	1425	66	1310	58
Elbow height	1090	52	1005	46
Sitting height	910	36	850	35
Sitting eye height	790	35	740	33
Sitting shoulder height	595	32	555	31
Sitting elbow height	245	31	235	29
Thigh thickness	160	15	155	17
Buttock-to-knee length	595	31	570	30
Buttock-to-popliteal length	495	32	480	30
Knee height	545	32	500	27
Popliteal height	440	29	400	27
Shoulder breadth (bi-deltoid)	465	28	395	24
Hip breadth	360	29	370	38
Chest (bust) depth	250	22	250	27
Shoulder-to-elbow length	365	20	330	70
Elbow-to-fingertip length	475	21	430	19
Forward grip reach (from the back of the shoulder blade)	780	34	705	31
Upper limb length	780	36	705	32

*SD=standard deviation, representinga statistical departure from themean value.

Table 3 Ergonomic data: maximum finger pushing force in newtons
	Thumb	Index finger	Middle finger	Ring finger	Little finger
Mean force/N	17	11	10	8	5
Range/N	14–20	8–14	8–12	5–10	3–9

The back of a particular airline seat is 100 mm thick. Explain why it would be unreasonable to install 12 rows of seats in a cabin with a floor length of 7 m. Suggest, with a brief justification, a more reasonable number of rows.

The space available per seat with 12 rows in 7 m would be

Of this, 100 mm must be allowed for the seat back, leaving just 483 mm for passengers' legs. According to Table 2 , the mean buttock-to-knee length of an adult male is 595 mm and that of women is 570 mm. Thus, there is insufficient space for an average man or an average woman.

A more reasonable capacity might be based on the mean, male, buttock-to-knee length (595 mm) plus one standard deviation (31 mm), plus the depth of the seat back (100 mm) for each seat. That amounts to 726 mm per seat. The number of rows would then be 7000/726 = 9.6; in practice this would need to be rounded down to 9 rows with 777 mm per seat.

For comparison, typical economy-class seat spacings are 710 to 860 mm, and the UK Civil Aviation Authority's current minimum (under review) is 660 mm.

The search for solutions must involve a thorough appreciation of the problem. It may involve detailed analysis and calculations based on scientific and engineering principles and using technical data. This is mathematical modelling, and it is useful at many stages in the process of identifying solutions; it is specifically addressed later in Section 4.5.

In practice then, finding a solution is usually a delicate balance between finding 'the best design' and getting something into the market-place 'by yesterday'. Earlier on I asked you to remember a point:

As good engineers, in an ideal context, we are not just looking for a solution; we are looking for the best solution.

Now you see why I added the condition about context. I think that any course that hopes to contribute to the formation of professional engineers has a responsibility to make this clear. Over the duration of an engineering qualification, you will learn a little about many of the tools you need to solve problems. You are likely to specialise, and learn more about, say, mechanical, civil or electrical engineering, building services, software, chemical processes, nuclear power and so on. It would be impractical to expect you to study every problem-solving technique tailored to every conceivable context. However, a good course of study will make sure that you are aware of the constraints that we have discussed above, and that you have some practice in bringing together maths, science or technology in ways that create practical, physical solutions. That way, when you call on your skills 'for real', you won't be surprised when your 'best' solution is ditched in favour of the one that has a quarter of the durability but costs half the money and can be made within the organisation. Instead of being depressed about this, understand and use those constraints to shape your next design; if you know that such limits will be imposed, make them your goals and work to achieve them.

Getting back to our problem-solving diagram, you may have noticed that Figure 10 shows another circuit – a loop from possible solutions, to evaluating solutions, and back to the problem. You may also remember that the problem is linked back to a need ( Figure 8 ), and so at this stage any suggestion may take you right back to the start, asking new questions about the need and refining or redefining the problem, quite possibly by going back to the customer. The trick here is not to redefine the problem in order to suit your solution, but to be sure that your solution is meeting the need .

4.4 Evaluate solutions

If the obvious solution has been identified and everyone is in agreement, then a formal evaluation of solutions is unnecessary, and we would move on to modelling the design. However, if there is dissent then some stricter method of elimination is required, and this is usually achieved through a process of rank-ordering. There is little to be lost and potentially much to be gained by returning to the customer at this point for opinion, clarification or guidance.

4.4.1 Selecting the best candidate

Assuming there is more than one likely looking candidate solution, we need to make a selection now so that we don't waste time taking all the candidates through the next steps, which become progressively more expensive and time-consuming. The rigour and formality of this step is very variable, but in general all schemes boil down to the same process you might use to choose some consumer item, such as a TV set. You would have a list of criteria that are important to you, and you would evaluate each candidate against those criteria. In many cases the list is short enough, or a single criterion of such importance relative to the others, for it to be possible to have it in your head. Usually it is worth writing down that list (which should look like the specification), and assigning a weighting to each criterion according to its relative importance. You then give each candidate solution a score against each criterion. When multiplied by their respective weightings, these scores add up to a figure of merit for each solution. The one with the largest number wins.

A benefit of using a system such as this is that it tells you quantitatively what kind of a 'squad' of substitute solutions you have to draw from (to use a sporting analogy). This is important because it tells you whether or not you really ought to take more than one on to the next step and beyond, until there is a clearer preference. It also tells you whether or not you have only one possible solution that's going to be worth considering. If this is the case, it may be good news if you are confident it will work, or it may prompt you to go back now and try to generate some more ideas.

Let us try this approach with the example of choosing a TV set. First, we ask what are our criteria, and what relative importance do we attach to each of them? This can be set out in a table:

Criterion		Relative importance (weighting 0–10)
1	Large screen	8
2	Good picture quality	10
3	Good sound quality	8
4	Compatible with other audio/video systems	10
5	Attractive cabinet	5
6	Cost	10

Next, we need to score each of our candidate models of TV set against each of the criteria, then multiply the scores by the appropriate 'importance' weighting.

	Model 1		Model 2		Model 3
Criterion	score (0–10)	× weight	score (0–10)	× weight	score (0–10)	× weight
1	10	× 8	6	× 8	6	× 8
2	6	× 10	5	× 10	10	× 10
3	5	× 8	4	× 8	6	× 8
4	10	× 10	0	× 10	5	× 10
5	3	× 5	10	× 5	8	× 5
6	8	× 10	7	× 10	10	× 10
Sum of weighted scores	375		250		386

For each model we arrive at the sum of the weighted scores.

On the basis of this, we might eliminate Model 2, but we might need to consider some additional criteria to choose between Model 1 and Model 3.

4.5 Model the best solution

In moving from the 'possible solutions' to the 'best solution' box, Figure 12 , we have to assume that a certain amount of evaluation has been done in the previous loop. The solution is still on paper, and probably not much more than a sketch, but something is badly wrong if the best solution to come forward has not been recognised to be at least feasible in the most basic terms of function, cost and implementation. The next step is to model the solution to estimate how well it will perform. Depending on the subject of the problem, this could take many forms.

The model itself doesn't have to be physical and sometimes a mathematical model can be used. A pretty thorough knowledge of relevant physical properties of real systems, materials and structures is required if a model is to be of any practical use.

4.5.1 Mathematical models

Computers in the last few decades have, in many cases, made mathematical modelling a lot easier. Models that used to require hours of manual cranking through long equations can now be created on a screen using specialist software. Processes can be recreated – modelled – in the time it takes to press a few buttons.

For example, when designing a pipe network to carry a gas or fluid, such as in the village water supply problem, you might wish to know how the flow would be distributed within the network, i.e. at what rate the fluid would exit from each distribution point. In order to calculate this, you would need figures for: fluid density; the number of pipes in the system; the length and diameter of pipes joining each connector; the friction factor for each pipe (a constant determined by the roughness of the pipe wall); pressure losses at the pipe fittings; volumetric inflow at each connector; and so on. Imagine the calculations necessary to cover all of these, in what is actually a relatively uncomplicated arrangement of pipes.

Engineering has a whole host of branches, covering a huge variety of physical quantities. The following are examples of where computer-based techniques are used.

Thermal and stress analyses model the distribution of quantities like temperature and stress across a shape or an area, and are useful for spotting potential weak points in a design.

Computational fluid dynamic studies analyse turbulent flow in gases and liquids, such as in the simulation of weather.

Universal Modelling Language simulates computer software.

Circuit simulators model the performance of electronic circuits.

Of course, not all modelling is done on computers. Creating a mathematical model of something can be as simple as drawing a picture, putting in the mandatory dimensions and using the diagram or some simple calculations using algebra to determine the remaining quantities. For instance, look at the Box 8 Mathematical modelling example .

Box 8 Mathematical modelling example

In another aspect of the village water supply problem outlined earlier, part of the design of the network may include some sort of storage tank. Let's assume that the tank is cylindrical and that it has been specified to be capable of holding 1500 litres (1.5 m 3 ). In order to keep costs down, we want to use the minimum amount of material in constructing the tank and must therefore use mathematics to model the problem, finding the minimum surface area capable of holding the required volume.

The first step is to write down algebraic expressions for the key factors – volume and surface area in terms of the unknown quantities (radius r and length l of the cylinder) that are to be determined.

Surface area (two ends plus the side):

Next, combine these expressions by using information from one equation to simplify the other.

Rearranging the equation for volume to express it in terms of length:

We can substitute this expression for l into that for the surface area, bringing the problem down to one unknown, r , as the volume V is specified:

Multiplying out and tidying up:

There are two ways to find the minimum area for the required volume. The first is trial and error, for which a calculator or computer spreadsheet is invaluable. Try, for instance, a radius of 1 m and one of 2 m – which gives the smaller area? What value would you choose next? Try it. Often plotting a graph of the results helps you see where to direct your attention.

The second method is based on calculus, an analytical technique that should be familiar to you from your study of courses in mathematics. If it is not, you will have to stick to trial and error. For those who can follow it, the calculus approach is given below; otherwise move on to the text following Figure 13 .

Differentiate the expression for the surface area with respect to r :

For maxima and minima, d s /d r = 0 (remember that d s /d r is the gradient of the curve of s against r ), so:

Substituting the value V = 1.5 m 3 :

We can use the earlier expression for the volume to find l :

Mathematical modelling tells us that the tank must be 1.24 m high with a radius of 0.62 m – that is, the length l is equal to the diameter (2 r ). Figure 13 shows how the shape of a cylinder looks as the ratio of r and l varies. It is obvious from our everyday experience that the cylinder which will hold the most water is the one that is neither extremely thin nor extremely short. Our numbers from the calculation look reasonable in this respect; if you looked at the cylinder side-on, it would look square.

In the mathematical modelling example we arrived at an 'optimum' cylinder which had a square cross-section (diameter equal to its length). But let's challenge this result by asking if any assumptions have led us away from the best solution.

A major assumption was made in setting up the problem, just before the mathematical modelling was presented. What was it? Do you think it was a reasonable one?

Can you think of reasons why the cylindrical shape may not be the best solution to this very specific problem?

Hint : think about the context and how this imposes constraints of its own.

The assumption was made that a cylindrical shape is going to be the best, and all we need to decide is the ratio of length (or height) to diameter. In fact, the shape that encloses the largest volume with the smallest surface is a sphere.

It seems reasonable to assume that, in this context, a spherical shape should not be used, as the problems of forming and joining or welding the sheet are considerable, and the necessary equipment is not likely to be available.

Here is my list of reasons why the cylinder may not be preferred – you may have thought of others:

the shape of available sheet material

the ability to cut circles and form the sheet into curves

the space it has to fit in

cultural preference for or aversion to a particular shape.

Making the cylindrical tank from a rectangular sheet of metal will create offcuts of material where the top and bottom circles have been cut out of the sheet. Show that if the most efficient cuboidal shape had been used instead (i.e. a cube), it would use less sheet material than the cylindrical shape. Assume that the width of the sheet material for each case is ideal.

The total area of the sheet is therefore 7.866 m 2 .

To make the tank cylindrical, we need the dimensions previously calculated, i.e. a diameter of 1.24 m and a height also of 1.24 m.

If our sheet of metal was 1.24 m wide, we could make the two ends and the sides of the cylinder from a piece that was (2 × 1.24) + (π × 1.24) = 6.376 m long – sketch it if you need to.

This has an area of 1.24 × 6.376 = 7.906 m 2

The cylindrical tank uses 7.906 − 7.866 = 0.040 m 2 more sheet material (but this difference is only about 0.5%).

4.5.2 Physical models

A physical model of an artefact or component is often built on a reduced scale, in size and/or by using materials that are cheaper and easier to manipulate than those intended for production. At this stage, we are not necessarily producing what you might think of as a prototype, but investigating particular aspects of the design. For instance, maybe we would produce a racing-bike frame to a new design but in a cheap material such as balsawood, in order to assess the air flow around it in a wind tunnel.

A good example of this is the way modelling was used in solving the problem of the steering for the Thrust SSC supersonic car ( Figure 14 ), the first land vehicle to travel faster than the speed of sound (Mach 1), covering a kilometre in an amazing 2.9 seconds.

One of the first questions that needed to be asked, even before aerodynamic issues were considered, was 'can a rear steering mechanism work at speed?'.

Ron Ayers, the engineer in charge of aerodynamics on the car, explains:

[So] we had to steer with the rear wheels. As soon as we suggested that, all the experts on car dynamics waved their arms in the air and said it was unstable, it could never work, think of forklift trucks and shopping trolleys and other irrelevant comparisons. However, Professor Crolla at Leeds University did a theoretical study for us and said yes, it could work under certain circumstances and gave us those circumstances. There were, however, still plenty of critics who said it wouldn't work. The rear-wheel steering Mini was built to demonstrate that you can steer a vehicle from the back [ Figure 15 ]. Although it's a lot smaller than Thrust SSC, the wheel configuration and track, etc., is in fact a scaled-down version of the full-sized car. We drove that ancient Mini with this kind of extension out the back at 90 mph up and down the test track at MIRA and proved that it was very controllable – that we really could, with finger-tip control, keep it on the line. Glynne [Bowsher, the mechanical and structural designer] designed it and built it with his brother-in-law. It's his brother-in-law's Mini, actually. I think they spent £300 and it cost three weeks and two near-divorces.

Figure 15 shows that the model looks nothing like the car that in 1997 made engineering history by smashing the barrier of sound! The Thrust team used mathematical and physical modelling intensively throughout the development of the car. Given the costs involved in trialling the final product, they needed to be as sure as possible that it was going to work. A model is built to prove it will work and to collect data or to test some aspect of design.

Identify which aspect of the Thrust SSC was not being addressed by the physical model using the adapted 'Mini'.

The most important aspect of the Thrust SSC not addressed by the physical model is the aerodynamics and how this affects the steering at full speed.

We will return to modelling at the end of this free course on the problem-solving process. When we look at it again, we will present two contrasting cases. The first is a familiar product, namely the bicycle, and will show the merits of careful 'hand calculations'. The second, probably less familiar, is an acceleration sensor for triggering vehicle airbag systems. It will illustrate the use of a more complicated, computer-based model.

4.6 Assess and review

Following our problem-solving map, we have reached the stage of 'assess and review solution', Figure 16 .

If we've got everything right first time in the preceding stages, then the solution successfully meets the need, with no obvious nasty side effects, and we can pass directly to 'build prototype/demonstrator', pausing briefly for cheers and back-patting all round. On the other hand … this may be the time to recognise that the 'best solution' hasn't worked. This isn't necessarily as disastrous as it sounds; unless the solution was particularly simple, there are likely to be elements that have been found to be successful where others have not. This usually means that you are not entirely back to the drawing board, but will have to revise the bits that haven't worked and replace them with other suggestions that have been on ice from the 'possible designs' stage. If we were prolific with ideas then there may be an orderly queue of replacement solutions, such as alternative materials, configurations of components, substitute objects (in software design) or whatever. However, if there is no obvious alternative then we may end up having to reconsider the original need ( Figure 17 ).

There's no shame in going back to the customer at this point and asking for clarification. It may even be that your solution worked according to the need they expressed, but some incidental aspect has proved unworkable and so the problem needs restating. Returning to the water problem and the need to transport water from the river – perhaps you have discovered that the flow of the river isn't enough to meet the needs of the village. In this case, there is no need to abandon the solution entirely, as it will still be possible to supply water from the river, but a supplementary water source must be identified and harnessed, and this will be the new problem. You put forward possible solutions … and so the cycle begins again.

4.7 Build prototype/demonstrator

The physical models we talked about earlier are prototypes or demonstrators of a sort. However, for the purposes of making a clear distinction in the process, I'm referring here to prototypes or demonstrators as functioning preliminary models of the essential finished product or construction or service, bringing together all the elements of the design that may or may not have been previously physically tested ( Figure 18 ). This is still a model – if appropriate, it may be a full-sized, full-colour replica – but it may also be a scaled-down version where only the vital working parts are fully functioning.

In the village water supply problem, you may produce a model version of the layout of pipes to ensure that they will conform to the landscape, or you may not need to produce a demonstrator at all. The point is, where necessary, to make sure that all the essentials will come together and operate as anticipated.

In software design, for example, the prototype may be a program that combines all the essential elements of code, written by various teams and controlling various parts, but with a dummy user interface. The vital commands will be in place, but asides such as 'glossy' add-ons (for example the electronic games on a mobile phone) are not necessary to the success of the solution, and may be designed separately and added to the overall design at a later stage. Note that to do this, you have to be very sure that these extras will not affect any important aspect of the rest of the product. In a well-run project, you will have to prove to the rest of the team or the project leader that this is a valid assumption before being allowed to leave it off the demonstrator.

Put simply, with good planning and thorough preparation and groundwork the demonstrator should work when tested in the conditions in which it will be expected to perform.

4.8 Assess and review again

If you've been following the stages of our problem-solving map, then the chances are you're ahead of me here ( Figure 19 ). Yes, if it works, hurrah; if it doesn't then off we go again, all the way back to 'possible solutions' and selecting the best of the rest. Or maybe even going back to the beginning. No one will be amused by a failure at this stage, when considerable investment in time and money has already been made. We should be looking at fine-tuning only, collecting data to give the marketing people, and finalising decisions about fabrication, manufacture, production quantities (if relevant) and processes. In mathematics, this process of refining a solution to get ever closer to a final value is called iteration.

4.9 Final implementation

The line you take here obviously depends on the problem you set out to solve. If you were creating a new product for retail or industry, then the final step of the process would be to put that product into manufacture and watch it go off into the world to begin its life cycle ( Figure 20 ). If the solution were a one-off, such as the village water supply problem we considered at the start, then it would be built and installed.

Not all engineering problems will fall neatly into this pattern, inserting need at the top and extracting a solution at the bottom. Furthermore, not all problems and challenges are to do with designing something from scratch – many real challenges are concerned with a more restrictive need to improve or repair an existing system. Engineers work in different ways, under a variety of conditions and often without the luxury of the time, resources or finance it would take to follow the above process to the letter for every need that was presented. The process will vary according to the nature of the problem, and the experience and understanding of the team engaged to find the solution.

Explain why the list of criteria used in selecting the best candidate solution will look like the specification. State the reason for assigning weightings to each criterion.

The specification should be the document that defines everything that is wanted from the solution. Therefore this is the most natural basis from which to generate the list of selection criteria. A full specification will contain a large number of items, including some which are preferences rather than absolute, hard-and-fast necessities. If no weighting is applied, then the ranking of the candidate solutions could be incorrect in relation to the real need, simply because the best solution has a lower score on several relatively unimportant criteria.

In the next two sections I want to show some aspects of the problem-solving process at work.

5 A problem in bicycle design

5.1 the development of the bicycle.

Section 4 has looked at how we can follow a logical route or map, from the expression of a need, to arrive at possible solutions to a problem. In Sections 5 and 6 we look in more detail at two quite different examples of engineering problems. Our first example is the historical development of the bicycle frame; the second concerns a vital component of a car's airbag system.

The weight of a bicycle frame is a major burden that the cyclist has to bear. There have certainly been times when I felt I needed a lighter bike, usually when going up hills. So, I want us to begin 'identifying and evaluating solutions' for the problem of how to make a bicycle frame lighter, while retaining its performance. A little historical background is important as we are not the first to address this problem.

The modern bicycle frame is central to a huge international business, dominated by American and Chinese markets. In the USA, current estimates put the market at about 15 million bicycles per annum and, in an increasingly environmentally conscious society, the future looks pretty much guaranteed. In this context, the bike is a mature product in an established market, but at some point in history there were no bicycles and the first design must have been produced in order to meet a need. We can guess that this need was for a mode of transport that was quicker than walking and that didn't need feeding.

In fact, the first vehicle that worked with two wheels in a line (the very basic characteristic that came to define a bicycle) was introduced in France in 1791 with a non-steering front wheel, no pedals and a wooden horse's head! For its time, this 'bicycle' was an innovation, and unbelievably it didn't change much for the next twenty years or so. In 1817 a steerable front wheel was introduced (in Germany) and pedals made their first appearance in 1839 (in Scotland). The chain, the sprocket-driven rear wheel and equal-sized front and back wheels were added in England in the early 1880s and were followed by pneumatic tyres, two- and three-speed hub gears and then derailleur gears before the turn of the century.

Each of these major changes came about through engineers finding solutions through innovation by context, but along the way there were literally hundreds of small innovations by development and numerous routine design improvements. For example, in 1879 Charles E. Pratt wrote in his handbook The American Bicycler :

From 1868 until the present time the patented improvements have been numerous, and the mechanical details of construction have been thoroughly worked out, until the machine has become a marvel of ingenuity and of workmanship; and the modern bicycle has been developed to its present state of perfection in strength, lightness, ease of propulsion, certainty of control, and gracefulness of design and operation.

This is an accolade that would swell any engineer's head, but it implies that any advances since 1879 have been extraneous!

The pneumatic tyre was a novel use of a sealed tube of pressurised air to provide the running surface of a bicycle wheel. Say whether you view its introduction as an innovation or a routine improvement.

The pneumatic tyre was an innovation by context. Tyres had not been made in this way before, though the idea of sealing pressurised air into a container was not new (e.g. balloons, footballs, etc.).

An interesting aside to the technological advancement of the bike is in respect of the effect that engineering has on society. The bicycle is generally attributed as being pivotal in the liberation of women in the USA and Europe. Women in England were able to travel independently and in relative safety for the first time, particularly after Queen Victoria made it a socially acceptable practice by riding her tricycle alone in public. A postmistress in the USA, Amelia Bloomer, designed the first trousers for women – bloomers – specifically for riding bikes. The same Amelia Bloomer went on to spearhead the Suffragette fight for women's right to vote in the USA.

Bringing the bike up to date, the maturity of the contemporary model can be seen by comparing Sir Edward Elgar's Sunbeam of 1903 ( Figure 21 ), a relatively sophisticated design in the history of the bike, with a modern all-terrain bicycle ( Figure 22 ). The ancillary equipment has changed but the functional form of the frame structure is still based on a triangulated tubular diamond shape.

Today's market for bicycles is highly competitive, and manufacturers strive to appear better by being different. The 'engineering problem' that I identified at the start was to do with making a lighter frame. It is important therefore to separate real structural and performance improvements to the frame from fashionable gimmicks that might even add weight. To facilitate such comparisons it is necessary to understand the fundamentals of the product, and that calls for a bit of modelling.

So, back to basics: what is a bicycle frame?

Write a brief specification (five or six lines) for a bicycle frame, considering its physical form and what it must be physically capable of achieving.

In engineering terms the need is for a space frame that enables two wheels to be held in place and supports the forces developed by the rider's mass and his or her efforts. The frame should be rigid enough to keep the rear wheel in line with the chain wheel, which is attached to the pedals. In addition the front forks must also rotate to allow the front wheel to steer at low speeds.

The bicycle can be seen as a variation on a seven-membered truss ( Figure 23 ), a frame structure that is a common element in structural and mechanical engineering.

If the axles of the wheels replace the side supports, the bike begins to reveal itself, as shown in Figure 24 .

This structure is capable of supporting a central load as shown and will clearly subject the truss-based space frame to the same in-plane forces – compression in the struts and tension in the tie-wires. There are only a few simple adjustments left to turn the basic structure of Figure 24 into a 'functional' bicycle frame configuration, Figure 25 .

One of the tie-wires has been removed in order to allow the front wheel to rotate, and the strut attached to the front wheel has to be free to rotate at the pin joint. Add a saddle, chain, pedals and handlebars and away you go.

By making a comparison with a simple structure that can be fully analysed, we have been able to confirm the fundamental elements of the bicycle structure, the bit that carries the major forces. However, there is a difficulty. As we shall see in the next block, Figure 24 represents what is called a statically determinate structure. Removing one component risks turning it into a mechanism: that is, it may change shape in response to forces. Removing the bottom-left tie in the truss of Figure 24 would cause it to collapse unless something were done to rectify or compensate for its absence. If part of the top-left pin joint is fixed and does not allow the attached side-strut to swivel about the joint axis, the strut is turned into a cantilever, which restores stability to the structure but at a price. The original strut, now acting as a cantilever, is no longer subject to just axial compression, but has additional forces that lead to bending about the frame region called the headstock. Such a configuration creates high stresses in the material, in this case reaching a maximum at the top of the cantilever fork close to the headstock. The relatively simple problem of allowing this cantilever to rotate is soon solved by the use of bearings that can support forces whilst rotating. Hence, the 'bicycle' shown schematically in Figure 25 could function, if manufactured from adequate materials for the struts, ties and cantilever.

The next thing to do is to see how we can, in general, evaluate solutions based on different materials. Then we'll reintroduce the specific needs of a bicycle frame.

5.2 Material comparisons

I want to depart from the specific example of the bicycle to make some more general points.

In most simple structural analysis the self-weight of the structure is ignored, as it is considered to be small in comparison with the loads carried. However, as an illustration of engineering practice in the search for efficient structures to employ in product design, it is worth examining how the strength and weight of particular materials compare.

These comparisons are illustrated through the use of modelling. As an example, let's estimate the maximum length of a hanging tie-rod and the maximum height of a column. See Box 9 Long ties and high columns .

Box 9 Long ties and high columns

Figure 26 shows a parallel-sided rod of material of density ρ and yield stress σ y hanging from a support.

The stress in the cross-sectional area A increases on each horizontal plane as you go up the rod. It will fail by yielding in the uppermost section when the stress there reaches the yield stress, which is a characteristic of the material. If this occurs when the rod is h metres long, we can say that:

Force on the failure plane

If the material yields then the force on the plane at failure =

Hence, equating these values gives:

Notice that the cross-section term A cancels out from the equations.

A mild steel has a density of 7800 kg m −3 and yield stress 300 MN m −2 What is the maximum length of rod that could be dangled from a high building without yielding under its own weight? Take g = 9.8 m s −2 .

Using the equation σ y = ρ gh , and rearranging:

Hence the rod could be almost 4 km long before it would break under its own weight.

But could we build the tower from which to hang this extremely long rod?

Consider building a brick tower from which we could suspend a rod for testing. Brick has a crushing strength σ c of 70 MN m −2 and a density of 2000 kg m −3 . What is the maximum height of a parallel-sided tower that can be built without crushing the bottom course of bricks? Assume the mortar thickness to be negligible and of higher strength.

The relevant equation comes from relating the weight of bricks above the bottom layer to the force required to crush it. The result is:

The crushing strength and density of the brick are inserted into the formula to give:

That's right, over 3.5 km (2 miles) high!

Hence the crushing strength of brick would limit the construction of a tower to test the steel rod. You would have to taper it to be narrower at the top.The limiting equation for both long ties and struts is:

Rearranging this gives a general expression for maximum length in terms of the maximum self-supporting height:

Now (1/ g ) is a constant, and if g stays constant h is proportional to (σ/ρ). This quantity is a measure of a material's ability to support itself in tension or compression (depending on which value is used for the strength). It is called a 'merit index for self-supporting strength. This means long self-supporting ties and long self-supporting struts are more feasible if the merit index (σ/ρ) is big. Not surprisingly, this occurs with high-strength, low-density materials.

5.3 Back to the bicycle

Let's assume that our bicycle frame could still be constructed from ties and struts. If we want to select the material to minimise the weight of a frame for a particular frame strength, we need to devise a merit index as follows.

The mass of the tie-rods and struts needed for the frame is given by:

where h is the length of a component and A is its cross-sectional area. The failure force for tensile yielding, F , is given by:

in which σ y is a property of any chosen material. Eliminating A from Equations (1.1) and (1.2) gives:

Usually we want a materials-based index that gets bigger the better the material. Hence it is better to express our index in terms of (1/ m ), which gets bigger the lighter the frame.

Hence, rearranging Equation (1.3) gives:

Now for a tie-rod of particular length h , able to resist a particular force F , the bigger the value of the material merit index (σ y /ρ) the lighter the frame could be for the same performance.

From identical considerations, the bigger the value of (σ c /ρ) the lighter a frame could be made for a specified performance.

Using a comparable approach you can also select a merit index to find light struts and ties that limit elastic strain, giving a particular deflection under a given load.

In these circumstances selecting the material with the highest value of ( E / r ), where E is the Young's modulus, has the potential to give the lightest frame components that deflect by a particular amount under load.

Table 4 shows absolute values and some merit indices for a range of recently used frame materials.

Table 4 Absolute values and merit indices for frame materials
Characteristic:	σ	σ		ρ
Units:	MN m	MN m	GN m	kg m	kN m kg	kN m kg	MN m kg
Material:
Alloy Cr—Mo steel	700	700	210	7870	88	88	26
Aluminium alloy	350	350	70	2800	125	125	25
Titanium alloy	650	650	105	4500	144	144	23
Carbon-fibre composite	500	200	60	1100
Magnesium-based alloy	300	300	45	1780	176	176	25

You can see the great potential for carbon-fibre composites and the strong competition between the other frame materials, particularly for the deflection-based index E/ ρ. However, there are three major limitations that need consideration before we all go out and start manufacturing carbon-fibre bike frames for a living:

Firstly, because the frame is subjected to much more complex load patterns than axial tension and compression within ties and struts, it turns out that additional merit indices are required.

Secondly, the figures for carbon-fibre composite are based on idealised production conditions where the optimum amount of carbon fibres can be reliably incorporated into the appropriate matrix, whereas the figures for the metallic alloys are those that can be expected regardless of manufacturing conditions.

Finally, the techniques needed to manufacture advanced composites in complex three-dimensional shapes with good surface finish are extremely expensive, so the external factor of cost limits the potential market to the successes and failures covered in Box 10 Carbon-fibre composites to win at all costs .

Box 10 Carbon-fibre composites to win at all costs

The development of commercially viable carbon fibres for engineering purposes was only made possible because large quantities, supplied to the sports goods industry, sustained early progress and allowed prices to fall to acceptable levels. The fishing rod and golf club shaft industries have to be thanked for supporting the manufacture of very expensive early production quantities. The high ratios of tensile strength to weight allowed golf club shafts to deflect to higher values without snapping. For some players this increased the distance of their tee shots. The same properties were also very attractive for whippy fishing rods that had higher strengths than equivalent bamboo and glass-fibre predecessors, Figure 27 .

Identify the types of need for which carbon-fibre tubes are attractive solutions.

The need is for lighter tubular structures that have the same, or better, strength and stiffness characteristics as compared with conventional materials.

More recently, carbon-fibre composites have been used to make other simple structures that benefit from the high E/ ρ ratio for the material. Lightweight products that give minimal deflections include wing sections for aerospace vehicles and racing cars ( Figure 28 ), and 'roach poles' for fishing, which make it possible to use a particular technique to reach further across wide stretches of water than was previously manageable.

Very recently there have been some great successes and failures associated with complex three-dimensional carbon-fibre composite products. In cycling, a carbon-fibre composite frame which is very light and very stiff has been found not to be indestructible – at least one has failed in an accident under conditions that a metal frame might have survived.

Many short stubby struts, or 'chocks', used for supporting dry-docked ships, stored goods, vehicles and the like, need to be made as cheaply as possible. Figure 29 shows an example of a cardboard pallet. Table 5 gives values of crushing strength ρ c and cost C in euros per cubic metre for some materials.

(a) Derive a merit index that increases as the total cost K of supporting compressive load L with a strut of height h decreases. Hint : You will need to introduce the cross-section area A into the total cost and the maximum load – you can then eliminate it from a combination of the two expressions.

(b) Calculate the index for the candidate materials in Table 5 , and select the cheapest option.

Table 5 Characteristics of some candidate materials
Material	Crushing strength σ /MN m	Cost /€ m
Softwood	7	40
Hardwood	15	20
Mild steel	300	1500
Recycled thermoplastic	18	560
Cellular cardboard	0.7	15

The cross-section A needed is given by:

The total cost K is given by:

The number 1/ K will increase as the cost K goes down.

Rearranging the equation and substituting for A gives:

Hence for a fixed load L and strut height h the required merit index is σc/C . Hence, not surprisingly, materials with a high crushing strength to low cost per unit volume are preferred. You should note that this analysis does not place a limit upon the space required by the cross-section of the strut A , which can get large for low-density materials. I have calculated the merit index for each of the materials, Table 8 .

Table 8 Merit index σc/ for the candidate materials
Material	σ / / MN m
Softwood	0.17
Hardwood	0.75
Mild steel	0.20
Recycled thermoplastic	0.03
Cellular cardboard	0.05

So at these prices the preferred chocks are hardwood, followed by mild steel, hence their prevalence in commerce for such tasks. Note that, although the crushing strengths are unlikely to change, the relative prices can change in response to local availability, which can influence the merit index.

Returning to the analysis of the bicycle frame, although the frame shown in Figure 25 could function, its performance would be limited to resisting forces in the vertical plane of the frame. Unfortunately, it is essential that frames resist the out-of-plane forces that are generated when a cyclist leans the bike over for hill climbing, sprints and cornering as shown in Figure 30 .

This is when the maximum stresses are generated, as other forces add to the rider's own body weight. Flexible tie-wires and even thin rods have no resistance to such bending forces and so must be replaced by solid cantilever devices that have bending and torsional resistance, to limit the deflection shown in Figure 31 . The pin joints are also eliminated to add to this bending resistance.

Finally, as can be seen in Figure 31 , the rear triangle is divided to allow the rear wheel to be centrally located, and the front forks are usually divided in a similar way to produce the familiar bicycle-frame configuration. Such deflections are an indication of the overall frame stiffness.

In this section, although we have revealed the potential for using different materials, we have not found a 'best solution' for a lighter frame. In fact, we have done what often happens in the search for solutions. We have refined the problem and demonstrated our need to know more technical background, especially on the behaviour of loaded structures.

6 A problem with sensors

The problem we will look at in this section concerns the analysis of the design of a component used in cars that are fitted with airbags. The airbag has to be inflated rapidly when an electronic circuit in the system decides that a serious collision is taking place. The crucial component in the electronics is the accelerometer, which therefore has to be extremely reliable. Motor manufacturers have turned to a technology called MEMS (micro-electromechanical systems) for these accelerometers, because it enables large numbers of devices to be made at low cost, but with fantastically high reliability. The sensors are made on silicon chips, using the same manufacturing methods and equipment as electronic chips, the difference being that the results are mechanical structures rather than transistor circuits. Figure 32 shows an example of such a sensor. Notice the scale of the device.

Most airbag accelerometers are of the type shown in Figure 32 . They consist of a silicon chip, into which the sensor and the sensing structure are fashioned. It is made entirely of silicon and is in two parts: the first is a lump (often called the proof mass or seismic mass) suspended by means of a spring formed at each end; and the second is a pair of fixed sensing electrodes that enable the electronics to detect the movement of the lump relative to the surrounding platform of silicon.

The way it works is like this: when the chip is subjected to an acceleration, the lump moves a little relative to the chip and the fixed structures on it, in the same way as your shopping might fall off the back seat of the car if you brake hard. The amount of movement depends on the size of the acceleration, the stiffness of the springs, and the mass of the lump. When the lump is deflected, the electrical capacitance between it and the sensing structures on the chip changes, and this change is detected by the electronics, which converts it to a value for acceleration.

From the point of view of building prototypes and mock-up devices to test and refine the design, the trouble with MEMS is that the things you make are very small – too small to poke with a finger to see how they're working, and too small to measure directly how much they move when the acceleration is applied. You can't even build a scale model and make the measurements on that instead, because the material properties don't all scale up in the same way. Crucially for the accelerometer, the mass is proportional to the length-scale cubed (because mass is directly related to volume, not length), but the stiffness of the support springs would scale only in proportion to their length. Therefore, you would have to build your scale model out of a different material from the silicon of the real device if you wanted to mimic its behaviour on a magnified scale whilst maintaining the same ratio of mass to stiffness. A material with the right combination of properties probably doesn't exist.

You can go some of the way towards being sure that your design will work just by doing hand calculations. For instance, you would be able to calculate the stiffness of the springy support structure by using the appropriate formula for a beam of that type. This would enable you to estimate how far the mass would move under a given acceleration. Things get much more difficult if you want to predict how much it will bend if subjected to a sideways acceleration, because the manufacturing process demands that it has lots of holes in it. This makes the structure very complicated, and the standard equations for stiffness of uniform beams don't apply.

So, to test different designs of accelerometer, it looks as though you may have no choice but to make some for real. Unfortunately, the set-up costs for small runs of MEMS devices is very high (electronic chips are cheap only because millions of them are made at the same time).

The way out of this is to use finite element analysis (FEA) to check as many aspects of the device's behaviour as possible before spending money on building any.

FEA is most commonly used to find out what happens to a structure when a mechanical load is applied to it, but it has many more applications. It can be used to predict the temperature distribution in a central heating boiler, the blood flow patterns around an artificial heart valve, the acoustics of a loudspeaker, or the magnetic fields in an electric motor. In short, anything where there is an interaction between a field (e.g. temperature, magnetic, electrostatic, acoustic, flow, force) and an object.

FEA solves the difficult differential equations that are involved by breaking the problem up into many smaller, but related problems. A computer is used to solve a huge number of Box 11 Simultaneous equations , and the solution to the whole problem is presented as a visual display in two or three dimensions. Figure 33 shows a computer model of the accelerometer, ready for analysis by the FEA program.

Box 11 Simultaneous equations

I'm going to present a simple example of simultaneous equations, to illustrate why they crop up in FEA, and why we need computers to solve them even though the equations themselves may be quite straightforward. First, to remind you about simultaneous equations: they occur whenever you want to find the answer to a question where more than one condition has to be satisfied at the same time.

Cutting a piece of wood

A trivial example will get us started. Suppose you have a piece of wood 2.4 m long that you want to cut into two, with one piece four times the length of the other. This problem is so simple that you would do it in your head without realising that you had been solving simultaneous equations, but bear with me as I go in slow motion through the process, as it illustrates the general principle.

The two conditions that must be satisfied give rise to the two simultaneous equations that describe this problem. In ordinary language they are:

'The length of both pieces added together equals 2.4 m.' 'The length of one piece equals four times the length of the other piece.'

If you call the length of one piece x , and that of the other y , then:

By substituting the second equation for x into the first, we can rewrite the first equation like this:

and we quickly find that

Now that we know y , we can use either of our original equations to find that

Our results for x and y are in metres, of course.

A system of springs

We need to take this example a step further to give an insight into why we get simultaneous equations in FEA. If you reformulated the woodcutting problem in terms of springs and forces, you could say: 'I have two springs, but one is four times as stiff as the other. They are linked end to end, and the pair is anchored at one end ( Figure 34 ). I move the free end by a distance of 2.4 mm; how far has the point where the two springs are linked moved?

The force that has been applied to move the free end of the pair of springs is transmitted throughout the spring system, so we know that the force acting on each spring is the same. In a spring, the amount it extends and the force pulling it are related by the stiffness, through the expression F = kx , where F is the applied force, k is the stiffness, and x the extension.

We have said that the stiffness k 2 of one spring is four times that of the other, k 1 . We can write this as:

We have just said that the force experienced by each spring is the same, so we can also say that

where x is the extension of one spring, and y that of the other. We can get rid of the k terms by saying

This is the first of our simultaneous equations, and it says 'the amount the first spring stretches is four times as much as the second spring'.

The other equation states that the extension of both springs added together is 2.4 mm.

We needn't go through the maths because it is exactly the same as the wood-cutting example (except that our results will be in millimetres).

The point between the two springs and the end where the force is applied are effectively nodes in a simple finite element mesh. The springs are just representations of the stiffness of the material. What we have just solved is a small finite element problem. In a real problem, the numbers of calculations that need to be made are much bigger, and we may have 10 000 nodes and 30 000 simultaneous equations, which is why we use a computer. The calculations are generally rather more complex than in the spring example, because usually we are dealing with continuous materials, not 'lumps' like the springs, and there may also be non-linear behaviour.

If instead of two springs we had ten, each with a different stiffness, we could fairly comfortably still solve this by hand, to get the new positions of each node. But what if the springs extended in two or three dimensions, as in Figure 35 ?

The array of springs now resembles a mattress ( Figure 36 ). Imagine a weight were placed on it. You can see how this would now be very awkward to calculate, because the depression of the mattress would cause some of the springs representing the upper and lower fabric skins to change the direction in which they pull, according to how close they are to the weight. The awkwardness comes in the large number of interdependent calculations (simultaneous equations) and that is where a formal approach and the power of a computer are able to come to the rescue.

Returning to finite element analysis, the structure (in the case of the accelerometer, the mass and springs) is first divided up into a large number of small blocks, or elements . The size and shape of these elements can vary. They are made to be much smaller than any features of the structure near them. Usually, their form is tetrahedral or hexahedral (i.e. with four or six faces), but the essential properties they have are that they completely fill the volume of the structure, and that they are connected to their neighbours at their vertices. These elements are usually not regular shapes – they have to be distorted to fit the geometry of the structure being analysed, which could have any shape. Within reason, this distortion does not matter, provided that the elements are properly connected to their neighbours.

If enough elements are used, the continuously varying quantity that is to be determined (in our case the displacement) can be approximated into simpler variations within each element (for example, a linearly varying displacement across the element). According to their position in the structure, each element is assigned material properties. These properties are used to solve, for each element, what is happening within it. Because each node of each element is shared with neighbouring elements, the whole assembly of elements is linked, and the solution arrived at for each element is consistent with those arrived at for all its neighbouring elements.

The process of dividing the structure into these discrete elements is called meshing . The size of the elements in a mesh needs to be considered carefully: if the elements are too large relative to the structure, the result of the analysis will be inaccurate; if they are too small, the analysis may take far too long for the computer to execute. In modern FEA software packages, much of the routine and arduous work of meshing has been taken away, so that the meshes are generated automatically by the software, once the user has answered some questions such as what type of element they want to use.

But all we have done so far is divide the structure into elements and told the computer what they are made of. The program needs to be set going somehow, and this stage is known to FEA practitioners as 'setting the boundary conditions' . The computer needs to be told what other things are known about the problem. This is in a quite literal sense setting out what is happening at the boundaries or edges of the structure. In the case of the accelerometer, you would apply a direction and magnitude for an acceleration. Another boundary condition would be where the mass is attached to the silicon chip, and what sort of attachment this is. Is it fixed in position but free to rotate about one or more axes, or can it slide in one direction?

The deflection of a material, and the stress generated due to an applied load, are simply related to one another by the stiffness of the material. Therefore, solving the problem for deflection also provides the solution for stress. Figure 37 shows the results of running a finite element analysis of a MEMS accelerometer seismic mass subjected to a sideways acceleration. The colour shading shows where the stresses are concentrated.

One important thing to understand about FEA is that there are many opportunities to create a result that looks convincing, but is completely incorrect. Meshing is one such opportunity – usually where the mesh is too coarse to allow accurate calculation. This is most likely to happen near features in the structure, such as holes and corners, as in Figure 38 . This is why in a properly meshed structure the element size is smaller around such features than elsewhere.

It is good practice when doing FEA to run what is called a meshing analysis. This is where the same structure and boundary conditions are run with three or four different levels of mesh refinement, and the results are compared with one another. You can have reasonable faith in the quality of a mesh when the answers are very similar for two different levels of refinement of the mesh. But it is possible to go too far: if the elements get so small as to approach the size of the microstructure of the material (e.g. grains in a metal), then the implicit assumption in FE modelling – that the material is continuous – breaks down.

Another common source of error is incorrectly specified boundary conditions; for example, the wrong type of constraint at anchor points. In the accelerometer, the anchor points are where the springs are attached to the substrate. These should be defined as constraining motion in all three translations and all three rotations.

All this points to a need for independent verification of the results, and this often involves doing real tests on real structures. Ordinary hand calculation is useful too, because even if it doesn't give you accurate data, it is normally possible to get an estimate within a factor of two or three of the right answer, and this allows you to spot really gross errors in the FEA results. The FEA software companies also provide large numbers of worked examples of standard problems to allow you to check that your model behaves correctly.

To sum up these thoughts on the shortcomings of FE analysis, we can say that what we are working with is only a model, and models by their nature are never exactly like the real thing. The skill of the engineer lies in knowing how far the model can be stretched and how deeply probed, and yet still yield information about the real world.

Where does FEA fit into the problem-solving map in Figure 7 ?

FEA is a sort of mathematical model. It is important in the evaluation of possible solutions. It can also be used to test a demonstrator before building it.

7 Responsible engineering

7.1 the engineer and society.

Section 2 outlined some of the needs for engineering. Society relies on engineers to create solutions to the problems involved in meeting those needs.

This is a good time to pause and point out that inevitably, in return for all this fun and power, engineers have a responsibility to society. The people who employ our services, directly or indirectly, have to have an assurance that we are working within certain social, safety and ethical boundaries. Particularly given the increasing trend in the Western world towards litigation, it is in our own best interest to uphold this responsibility.

In considering the responsibilities of engineers, this section also provides an opportunity for putting the whole course in context.

7.2 The professional engineer

It has been suggested that there are four main criteria that identify a profession:

Custody of a clearly definable and valuable body of knowledge and understanding associated with a long period of training. A strong unitary organization which ensures that the profession generally speaks with 'one voice'. Clearly defined and rigorous entry standards, backed up by a requirement to register with the professional association. An overriding responsibility to maintain the standards of the profession for the public's benefit. Collins, Ghey and Mills (1989)

It is the role of the professional engineering bodies (Institutes, Institutions and Societies) to ensure that there is a focal point, and to coordinate the profession. A key issue within this role for a professional body is the support of the continuing professional development (CPD) of its members. This is vital for keeping pace and ensuring safety in a world where new technologies are developing daily. As a contribution to that process this course is aimed at extending your knowledge and awareness over a broad range of engineering activities.

7.3 Ethics and safety

A practising engineer makes ethical decisions, with moral and physical implications of varying magnitudes, on a daily basis. Examples of ethical dilemmas are limitless, ranging from the engineer who takes home the odd pen, file or discarded paper 'for the children', to the engineer who signs off a project without checking the details and identifying a simple arithmetic error of magnitude. The implications of either may be negligible – such as where the cost is more than compensated in unpaid overtime, the error merely accidentally increases the factor of safety – or catastrophic, such as when a discarded piece of paper has sensitive industrial information that ends up with a major competitor, or an arithmetic error decreases the factor of safety and a component fails in use at the cost of human life. For the occasions when the ramifications of our decisions are not apparent to anyone else, then ethics are a matter of personal conscience. However, when the ripples of our actions spread out and cause damage or injury then we are legally responsible for the result. Very often, the difference between the two is a matter of luck.

The very nature of engineering implies that safety must be a primary issue. Even the most remote of robots will have some human interface somewhere along the line, and most engineering design, whether industrial or domestic, requires direct contact at one or more levels. Ethics and safety are often closely interwoven – our responsibility for safety in design is as much moral as it is professional – and there are safety practices to be observed at every stage of the design process.

Much of what we know now has been learned from bitter experience but, amazingly, evidence suggests that we are still inclined to become complacent over long periods of technological triumph, leading us to more narrow margins of safety and, ultimately, repeated disaster. Consider what you know of the most publicised engineering disasters over the last century, and how safety was compromised in each case. Often, these great catastrophes are the result of some very minor error, and not the technological billion-to-one misfortune we might hope to believe – see Table 6 .

Table 6 Causes of some notable engineering disasters
Date	Disaster	Fundamental cause
2000	Concorde: fire and crash, shortly after take-off (113 dead)	Debris on runway and fuel tank susceptible to damage from same
1986	Chernobyl: meltdown of nuclear reactor core, and large-scale radioactive contamination	Safety procedures ignored, and design flaws
1986	Challenger Space Shuttle: exploded 73 seconds into flight (7 dead)	Design flaw in O-ring seals on the booster engines
1981	Hyatt Regency Hotel: suspended catwalk collapsed over a dance floor (114 dead)	Design change and failure to anticipate overload
1979	Three Mile Island: 51 per cent meltdown of nuclear reactor core	Incorrect procedures
1940	Tacoma Narrows Bridge: bridge collapsed	Unexpected wind-induced vibrations

The study summarised in Table 7 investigated 800 cases (and millions of pounds worth) of structural failure, in which 504 people died and 592 were injured. When engineers were to blame, the study categorised the causes of failure (and hence breaches in safety).

Table 7 Causes of failure, where engineers were to blame*
Insufficient knowledge	68%
Underestimation of influence	16%
Ignorance, carelessness or negligence	14%
Forgetfulness, error	13%
Relying on others without sufficient control	9%
Objectively unknown situation	7%
Imprecise definition of responsibilities	1%
Choice of bad quality	1%
Other	3%

*Note that the percentages add up to more than 100 – some failures were attributed to more than one cause.

You can see that in a whopping 68 per cent of cases, 'insufficient knowledge' on the part of the engineers was a contributing factor. Again, this has to be an ethics issue – can we really accept that all these engineers were so lacking in self-awareness that they truly believed in their own abilities, or were some of them just not brave enough to admit they were out of their depth at the time? The lesson is clear. You don't need to store everything you study in a photographic memory compartment, but it is essential to remember that, as a professional engineer, you are accountable for your actions; and this includes recognising when you need to bring in expertise from a colleague or external sources.

7.4 The impact of technology on society

Engineering is apparently driven by the needs of society. The technology that results, in turn, drives other changes in our everyday lives. One of the basic needs identified in Section 2 was for shelter. There are many fine examples of long-surviving structures such as pyramids, aqueducts, bridges, walls, functional buildings, and so on. Remarkably these constructions were completed without the depth of analysis and understanding that is available today (though we don't necessarily know much of the failures). The challenge to be more efficient in terms of space, materials, cost of ownership, etc. gets harder every year. Understanding the properties of static structures is important in creating tomorrow's solutions.

We have seen how a solution falls into one of three categories (innovation by context, innovation by development, and routine solution) according to the need that drives it. Furthermore, the need is shown to be the point of reference that should be kept in sight throughout the process of finding solutions. Unless the need is accurately stated, the ideal solution cannot be obtained – a case of 'garbage in, garbage out'.

We have examined the process of finding a solution step by step, using examples to help us see where and why particular approaches are most appropriate at various stages, such as for instance the best kind of modelling to use. Sometimes it is enough to make some rough calculations by hand in a few minutes, but at other times this is not sufficiently accurate. So at the other extreme, a physical mock-up or computer-aided modelling technique such as finite element analysis may be needed to provide the necessary data.

The bicycle design example enabled us to explore the idea that a solution is always a compromise, but that the best compromise can be found by the use of quantitative tools such as merit indices.

We saw that the solution-finding process generally contains loops, where certain steps are repeated until an acceptable result is obtained. The important point to note about this is that a trip round one of these loops (so long as it's not the loop that leads back from the very end of the process to the very beginning!) is not a failure, but a means of refining the solution.

Finally, we looked at the engineer in the context of wider society and saw that engineering has been central in providing the high quality of life enjoyed by many. The other side of this picture is that a significant proportion of the spectacular disasters we have witnessed involving failure of components have been attributable to poor work on the part of engineers. This lays a heavy responsibility on our shoulders to make sure we know what we're doing.

Acknowledgements

This free course is adapted from a former Open University course called 'Engineering: mechanics, materials, design (T207).'

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Grateful acknowledgement is made to the following sources for permission to reproduce material within this course.

Figure 3 Courtesy of Black & Decker; Figure 5: © NASA; Figure 9: © Ecoscene/Ray Roberts; Figures 14 and 15: Courtesy of Glynne T. Bowsher; Figure 21: Courtesy of the The Elgar Birthplace Trust; Figure 22: Courtesy of Falcon Cycles Ltd; Figure 27: Courtesy of Carbotec UK; Figure 28: Courtesy of McLaren; Figure 38: Courtesy of Ray Matela, Open University.

Table 2: Pheasant, S. (1986) Bodyspace: Anthropometry, ergonomics and the design of work , Taylor and Francis.

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Engineering Problem Solving | Design Process, Steps & Examples

Claudett Minott has been a teacher for over 30 years. She started teaching after receiving a Bachelor's degree in Education. She has worked with remedial students in Science and Math. She has expertise in lesson planning and curriculum writing.

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

What are some examples of engineering problems?

Some examples of engineering problems are the climate crisis and making water clean. These problems can negatively impact humans and if not properly managed and can lead to death.

How can engineers improve their problem-solving skills?

Engineers improve their problem-solving skills by asking questions, imagining solutions, and planning designs. They can also make improvements to their designs after testing them.

What are the steps in engineering problem-solving?

The design process includes defining the problem, researching and brainstorming, finding possible solutions, building a prototype, testing and evaluating, and improving and redesigning. Steps are not always followed in the same order.

Engineering design process, how do engineers solve problems, example of engineering problem solving approach, lesson summary.

An engineer is an individual who designs, builds, analyzes, and maintains machines, structures, equipment, and other complex systems. The engineering design process is a system followed by engineers to identify problems and develop or enhance solutions. There is a standard set of steps that are generally followed in the engineering design process but there may be adjustments made based on the type of project, resources, and other factors. For example, some steps in the process may need to be repeated before moving on to other steps and some engineers do not follow steps in order. They may make changes to a design and do additional brainstorming based on testing data. The engineering design process typically involves:

Defining the problem: this step involves identifying the problem, who it affects, and defining the impact that solving the problem may have. This step involves critical thinking.
Researching and brainstorming: this step involves conducting background research on the problem, and existing solutions, and devising new strategies that may solve the problem.
Finding possible solutions: this step involves choosing the best solution to the problem and rejecting ideas that do not meet the design requirements.
Building a prototype: a prototype is a preliminary or original model of a design from which others are developed or that is used to test a concept. Building a prototype allows the assessment of the idea.
Testing and evaluating: involves assessing the prototype for accuracy and whether there need to be adjustments.
Improving and redesigning: flaws in the design are addressed during this step and changes are made for improvement.

A simplified version of the design engineering process is:

Ask- ask questions
Imagine- imagine solutions
Plan- plan designs
Create- create and test models
Improve-make improvements

What Is an Engineering Problem?

An engineering problem is one that may be analyzed and solved using engineering sciences and methods. One of the biggest engineering problems in the world today is finding ways to improve energy efficiency and reduce the consumption of fossil fuels. There are many ideas that are constantly being tested. Some solutions that have come from the design engineering process are light-emitting diode (LED) and solar lighting as well as automated lighting systems. These solutions reduce energy consumption and collectively impact the consumption of fossil fuels.

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0:04 The Engineering Design Process
1:02 Defining a Problem
2:13 Writing a Problem Statement
3:18 Lesson Summary

How do engineers solve problems? A problem statement is a description of the problem. Engineers typically write a problem statement that explains the problem, provides evidence, and proposes a solution with associated advantages or impacts. A problem statement addresses the who, what, and why questions and may be a part of engineering contracts. Having a written document that outlines the problem and planned steps is an important initiating phase of engineering design and product development.

Defining a Problem in Engineering

Defining a problem in engineering design is important because one cannot know what the best solution may be if they do not fully understand the problem in detail. It requires in-depth knowledge and history of the system, other attempted or successful solutions, and how far-reaching a solution to the problem may be. It is always important to define the problem so that there is no ambiguity when designing solutions, especially when working on a team or when a contract is in place. It is also important that the needs of stakeholders and other involved parties are considered when writing a problem statement. For example, an engineering design may solve a problem, but is not commercially robust, a quality that most investors tend to be most interested in.

Writing the Problem Statement

There are three important factors to consider when writing the problem statement:

Who has the problem?
What is the problem?
Why is it important or worthwhile to solve the problem?

Tips on how to properly write a problem statement:

Explain the problem as clearly as possible, describing its importance and advantages to a solution
Discuss the beneficiaries of the solution
Provide evidence and background information to support the claim
Discuss financial costs and why the solution is worth the cost

The process of finding a solution typically comes after the problem statement is written.

The engineering problem-solving approach in the aforementioned example of using LED lights to improve energy efficiency, began by identifying that it is critical that the consumption of fossil fuels be reduced. The consumption of fossil fuels releases greenhouse gases into the atmosphere, contributing to global warming and the negative effects of climate change. The idea of LED light and other possible solutions were brainstormed after thorough background research was conducted. A prototype was then built, tested, and improved. The product is now commercially available and helps in reducing fossil fuel consumption. The problem statement for this technology answers the three critical questions of engineering problem-solving.

What- global warming

Who- humans and other animals are negatively impacted by global warming

Why- it is important that strategies are put in place to help mitigate the effects of climate change and such as species extinction, wildfires, extreme weather, rising sea levels, devastating diseases, and loss of habitat.

An engineer is an individual who designs, builds, analyzes, and maintains machines, structures, equipment, and other complex systems. The engineering design process is the process engineers follow in order to solve problems. The design process includes defining the problem, researching and brainstorming, finding possible solutions, building a prototype, testing and evaluating, and improving and redesigning. A simplified version of the design engineering process is: asking, imagining, planning, creating, and improving. These steps are not always followed in order, and steps may be repeated.

Defining a problem is important in engineering design because one cannot know what the best solution may be if they do not fully understand the problem in detail. The engineering problem statement explains what the problem is, who has the problem or need, and why it is important to solve the problem. Finding a solution does not come into play until later in the design process. In fact, choosing the best solution is a later stage in the design process that involves coming up with multiple possible options from which to choose the best solution.

Video Transcript

The engineering design process.

Engineering is all about solving problems using math, science, and technical knowledge. Engineers have solved a lot of problems in the world by designing and building various technologies. We have everything from machines that can breathe for you in hospitals to suspension bridges to cross rivers to computers we use every day. All of these things were once designed by engineers using the engineering design process.

The engineering design process describes the steps that an engineer takes to solve a problem. Although some engineers may use different approaches to design, the engineering design process generally involves the same basic steps: define the problem, research and brainstorm, find possible solutions, build a prototype, test and evaluate, and improve and redesign.

Now, let's discuss how engineers go about defining a problem in order to develop a new technological tool, structure, or object.

Defining a Problem

It's impossible to solve the problem if you don't fully understand what the problem even is. So, it makes sense that defining the problem would be the first step in the engineering design process. But understanding the problem isn't as simple as you might think. In the real world, it can involve not only hundreds of people, initial research and investigation, and complex systems, but also unexpected circumstances as well as issues of cost, time, and resources.

The first step in defining a problem is to identify the needs of the people involved. For example, let's say that large wooden crates need to be moved across a factory floor. The problem is that the factory building is split up into rooms with heavy doors that need to be held open to move the crates. Those doors can't be removed completely.

To really understand this problem, you need to identify the needs of the people involved. And to do this, you must answer some important questions. For example, how often do people have to move the crates? How heavy are the crates? Do they vary in size and shape? Is it always the same person moving them? How badly does management want to resolve the problem?

Writing a Problem Statement

Once you've discussed the problem in depth with all relevant parties and used your investigation to figure out what the need is, it's time to write a problem statement , which is a paragraph or larger document that addresses three main questions:

To really understand the nature of the problem, you may need to involve numbers in the mix. For example, you could ask: how much time does it take to move the crates and, considering the cost of time, how much does the process cost? Also, how much would the management be willing to pay to prevent the problem?

The solution depends on how important the problem or crucial the need is and how much people want to solve it. The best solution could be as simple as a door stopper or as complicated as motion-sensitive automatic doors, or it could even involve developing robots to carry the crates so humans don't have to. It's impossible to know which of these solutions is in the right ballpark unless you've truly defined the problem.

The engineering design process is the series of steps engineers take when using math, science, and technical knowledge to solve a problem or address a need. The first step in the engineering design process is to define the problem. This involves first identifying the needs of the people affected by the problem, which may include everything from manual workers to management.

Once you understand everybody's needs in detail and the ins and outs of the situation, you can write a problem statement . This explains the problem, who is involved, and why it's important to solve. Defining the problem will help you figure out what kind of solution is best, whether it's simple or highly complex.

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What is the 3-body problem, and is it really unsolvable?

The three-body problem is a physics conundrum that has boggled scientists since Isaac Newton's day. But what is it, why is it so hard to solve and is the sci-fi series of the same name really possible?

An artist's rendering of Kepler 16-b and its two suns

A rocket launch. Our nearest stellar neighbor. A Netflix show. All of these things have something in common: They must contend with the "three-body problem." But exactly what is this thorny physics conundrum?

The three-body problem describes a system containing three bodies that exert gravitational forces on one another. While it may sound simple, it's a notoriously tricky problem and "the first real worry of Newton," Billy Quarles , a planetary dynamicist at Valdosta State University in Georgia, told Live Science.

In a system of only two bodies, like a planet and a star, calculating how they'll move around each other is fairly straightforward: Most of the time, those two objects will orbit roughly in a circle around their center of mass, and they'll come back to where they started each time. But add a third body, like another star, and things get a lot more complicated. The third body attracts the two orbiting each other, pulling them out of their predictable paths .

The motion of the three bodies depends on their starting state — their positions, velocities and masses. If even one of those variables changes, the resulting motion could be completely different.

"I think of it as if you're walking on a mountain ridge," Shane Ross , an applied mathematician at Virginia Tech, told Live Science. "With one small change, you could either fall to the right or you could fall to the left. Those are two very close initial positions, and they could lead to very different states."

There aren't enough constraints on the motions of the bodies to solve the three-body problem with equations, Ross said.

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But some solutions to the three-body problem have been found. For example, if the starting conditions are just right, three bodies of equal mass could chase one another in a figure-eight pattern. Such tidy solutions are the exception, however, when it comes to real systems in space.

Certain conditions can make the three-body problem easier to parse. Consider Tatooine , Luke Skywalker's fictional home world from "Star Wars" — a single planet orbiting two suns. Those two stars and the planet make up a three-body system. But if the planet is far enough away and orbiting both stars together, it's possible to simplify the problem.

"When it's the Tatooine case, as long as you're far enough away from the central binary, then you think of this object as just being a really fat star," Quarles said. The planet doesn't exert much force on the stars because it's so much less massive, so the system becomes similar to the more easily solvable two-body problem. So far, scientists have found more than a dozen Tatooine-like exoplanets , Quarles told Live Science.

But often, the orbits of the three bodies never truly stabilize, and the three-body problem gets "solved" with a bang. The gravitational forces could cause two of the three bodies to collide, or they could fling one of the bodies out of the system forever — a possible source of "rogue planets" that don't orbit any star , Quarles said. In fact, three-body chaos may be so common in space that scientists estimate there may be 20 times as many rogue planets as there are stars in our galaxy.

When all else fails, scientists can use computers to approximate the motions of bodies in an individual three-body system. That makes it possible to predict the motion of a rocket launched into orbit around Earth, or to predict the fate of a planet in a system with multiple stars.

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— Mathematicians find 12,000 new solutions to 'unsolvable' 3-body problem

With all this tumult, you might wonder if anything could survive on a planet like the one featured in Netflix's "3 Body Problem," which — spoiler alert — is trapped in a chaotic orbit around three stars in the Alpha Centauri system , our solar system 's nearest neighbor.

"I don't think in that type of situation, that's a stable environment for life to evolve," Ross said. That's one aspect of the show that remains firmly in the realm of science fiction.

Skyler Ware is a freelance science journalist covering chemistry, biology, paleontology and Earth science. She was a 2023 AAAS Mass Media Science and Engineering Fellow at Science News. Her work has also appeared in Science News Explores, ZME Science and Chembites, among others. Skyler has a Ph.D. in chemistry from Caltech.

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I Teach Leaders to Solve Problems. Here's My 6-Step Framework

If you want to get good at growth, get good at fixing problems. here's how to do it predictably and repeatedly..

As a strategic coach, I work with high-performance leadership teams to build growth roadmaps. Oftentimes, the companies double in just six to 12 months. These growth rates expose issues and cracks in the business that must be addressed quickly. Identifying these issues quickly and systematically solving them is key to successful and sustained growth. Having both a framework and experience using it will improve any business's prospects.

Here's mine:

1. Review and reflect

I start by carefully reviewing what happened. Collect as much data as possible on what led up to the situation and how things played out. It's key here to get perspectives and opinions from as many sources as possible. I like organizing things in timelines and swimlanes for different people, teams, and departments. Here, we stick to the facts and try to weed out inferences and assumptions.

2. Find critical issues

Once the situation is mapped out, we look for where issues occur. These could be errors, delays, rework, wasted resources, or unnecessary operational complexity. I have the team dig into these and find the most important issues. I like having them plot what they find using a matrix of likelihood and impact so we can focus on a few issues that are causing the most problems.

3. Define the problem

Once we have a handful of things to investigate, I have the team clearly define the problem, why it exists, and how it's causing it. Once everyone is clear and in agreement on this, I have them articulate three to five success criteria that, once met, would mean that we've solved the problem or improved the situation significantly and sufficiently.

4. Look for systemic causes

Once the problem is defined, we can start looking for underlying causes. I like using a fishbone or tree diagram to visually map these out. Each cause needs to be independent and clearly contribute to the problems. Avoid generalizations and edge cases. For example, don't just say increased shipping costs. Say 22 percent of shipments go out as partial orders, which has increased average costs by $1.24 per order.

5. Pull multiple threads

Once we have several options, we can start finding causes of those causes using the same logic. I call this iterative triangulation as we start broad and narrow down the factors as we go. Sometimes we might hit a dead end, and we need to crawl back up the process to investigate another path. Eventually, we'll find a few core issues that are really driving the problem.

6. Listen to your gut

Sometimes this can be a difficult process, and you'll find several factors. First, I suggest focusing on the factors you can actually do something about. Second, focus on those that can be addressed with clear changes to business systems and processes. Finally, I have people check in with their guts; when they get that sinking feeling when they hit an issue, it probably means it's the one to focus on.

Root cause analysis can be more of an art than a science at times, but being systematic and developing a repeatable process will help it not feel like witchcraft. Teams that do this again and again and get good at it can dramatically improve their learning cycle time and can out-deliver and innovate against competitors.

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Problem Solving

Lesson Problem Solving

Grade Level: 8 (6-8)

(two 40-minute class periods)

Lesson Dependency: The Energy Problem

Subject Areas: Physical Science, Science and Technology

Print lesson and its associated curriculum

Curriculum in this Unit Units serve as guides to a particular content or subject area. Nested under units are lessons (in purple) and hands-on activities (in blue). Note that not all lessons and activities will exist under a unit, and instead may exist as "standalone" curriculum.

Energy Forms and States Demonstrations
Energy Conversions
Watt Meters to Measure Energy Consumption
Household Energy Audit
Light vs. Heat Bulbs
Efficiency of an Electromechanical System
Efficiency of a Water Heating System
Solving Energy Problems
Energy Projects

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Lesson

Activity

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Engineering connection, learning objectives, worksheets and attachments, more curriculum like this, introduction/motivation, associated activities, user comments & tips.

Engineering… Turning your ideas into reality

Scientists, engineers and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

Students demonstrate an understanding of the Technological Method of Problem Solving.
Students are able to apply the Technological Method of Problem Solving to a real-life problem.

Educational Standards Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards. All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN) , a project of D2L (www.achievementstandards.org). In the ASN, standards are hierarchically structured: first by source; e.g. , by state; within source by type; e.g. , science or mathematics; within type by subtype, then by grade, etc .

Ngss: next generation science standards - science.

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State standards, national science education standards - science.

Scientists, engineers, and ordinary people use problem solving each day to work out solutions to various problems. Using a systematic and iterative procedure to solve a problem is efficient and provides a logical flow of knowledge and progress.

In this unit, we use what is called "The Technological Method of Problem Solving." This is a seven-step procedure that is highly iterative—you may go back and forth among the listed steps, and may not always follow them in order. Remember that in most engineering projects, more than one good answer exists. The goal is to get to the best solution for a given problem. Following the lesson conduct the associated activities Egg Drop and Solving Energy Problems for students to employ problem solving methods and techniques.

Lesson Background and Concepts for Teachers

The overall concept that is important in this lesson is: Using a standard method or procedure to solve problems makes the process easier and more effective.

1) Describe the problem, 2) describe the results you want, 3) gather information, 4) think of solutions, 5) choose the best solution, 6) implement the solution, 7) evaluate results and make necessary changes. Reenter the design spiral at any step to revise as necessary.

The specific process of problem solving used in this unit was adapted from an eighth-grade technology textbook written for New York State standard technology curriculum. The process is shown in Figure 1, with details included below. The spiral shape shows that this is an iterative, not linear, process. The process can skip ahead (for example, build a model early in the process to test a proof of concept) and go backwards (learn more about the problem or potential solutions if early ideas do not work well).

This process provides a reference that can be reiterated throughout the unit as students learn new material or ideas that are relevant to the completion of their unit projects.

Brainstorming about what we know about a problem or project and what we need to find out to move forward in a project is often a good starting point when faced with a new problem. This type of questioning provides a basis and relevance that is useful in other energy science and technology units. In this unit, the general problem that is addressed is the fact that Americans use a lot of energy, with the consequences that we have a dwindling supply of fossil fuels, and we are emitting a lot of carbon dioxide and other air pollutants. The specific project that students are assigned to address is an aspect of this problem that requires them to identify an action they can take in their own live to reduce their overall energy (or fossil fuel) consumption.

The Seven Steps of Problem Solving

1. Identify the problem

Clearly state the problem. (Short, sweet and to the point. This is the "big picture" problem, not the specific project you have been assigned.)

2. Establish what you want to achieve

Completion of a specific project that will help to solve the overall problem.
In one sentence answer the following question: How will I know I've completed this project?
List criteria and constraints: Criteria are things you want the solution to have. Constraints are limitations, sometimes called specifications, or restrictions that should be part of the solution. They could be the type of materials, the size or weight the solution must meet, the specific tools or machines you have available, time you have to complete the task and cost of construction or materials.

3. Gather information and research

Research is sometimes needed both to better understand the problem itself as well as possible solutions.
Don't reinvent the wheel – looking at other solutions can lead to better solutions.
Use past experiences.

4. Brainstorm possible solutions

List and/or sketch (as appropriate) as many solutions as you can think of.

5. Choose the best solution

Evaluate solution by: 1) Comparing possible solution against constraints and criteria 2) Making trade-offs to identify "best."

6. Implement the solution

Develop plans that include (as required): drawings with measurements, details of construction, construction procedure.
Define tasks and resources necessary for implementation.
Implement actual plan as appropriate for your particular project.

7. Test and evaluate the solution

Compare the solution against the criteria and constraints.
Define how you might modify the solution for different or better results.
Egg Drop - Use this demonstration or activity to introduce and use the problem solving method. Encourages creative design.
Solving Energy Problems - Unit project is assigned and students begin with problem solving techniques to begin to address project. Mostly they learn that they do not know enough yet to solve the problem.
Energy Projects - Students use what they learned about energy systems to create a project related to identifying and carrying out a personal change to reduce energy consumption.

The results of the problem solving activity provide a basis for the entire semester project. Collect and review the worksheets to make sure that students are started on the right track.

Learn the basics of the analysis of forces engineers perform at the truss joints to calculate the strength of a truss bridge known as the “method of joints.” Find the tensions and compressions to solve systems of linear equations where the size depends on the number of elements and nodes in the trus...

preview of 'Doing the Math: Analysis of Forces in a Truss Bridge' Lesson

Through role playing and problem solving, this lesson sets the stage for a friendly competition between groups to design and build a shielding device to protect humans traveling in space. The instructor asks students—how might we design radiation shielding for space travel?

preview of 'Shielding from Cosmic Radiation: Space Agency Scenario' Lesson

A process for technical problem solving is introduced and applied to a fun demonstration. Given the success with the demo, the iterative nature of the process can be illustrated.

The culminating energy project is introduced and the technical problem solving process is applied to get students started on the project. By the end of the class, students should have a good perspective on what they have already learned and what they still need to learn to complete the project.

preview of 'Solving Energy Problems' Activity

Hacker, M, Barden B., Living with Technology , 2nd edition. Albany NY: Delmar Publishers, 1993.

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This lesson was originally published by the Clarkson University K-12 Project Based Learning Partnership Program and may be accessed at http://internal.clarkson.edu/highschool/k12/project/energysystems.html.

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Supporting program, acknowledgements.

This lesson was developed under National Science Foundation grants no. DUE 0428127 and DGE 0338216. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.

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Published: 11 June 2024

Learning cooking algorithm for solving global optimization problems

S. Gopi 1 &
Prabhujit Mohapatra 1

Scientific Reports volume 14 , Article number: 13359 ( 2024 ) Cite this article

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Applied mathematics
Computational science

In recent years, many researchers have made a continuous effort to develop new and efficient meta-heuristic algorithms to address complex problems. Hence, in this study, a novel human-based meta-heuristic algorithm, namely, the learning cooking algorithm (LCA), is proposed that mimics the cooking learning activity of humans in order to solve challenging problems. The LCA strategy is primarily motivated by observing how mothers and children prepare food. The fundamental idea of the LCA strategy is mathematically designed in two phases: (i) children learn from their mothers and (ii) children and mothers learn from a chef. The performance of the proposed LCA algorithm is evaluated on 51 different benchmark functions (which includes the first 23 functions of the CEC 2005 benchmark functions) and the CEC 2019 benchmark functions compared with state-of-the-art meta-heuristic algorithms. The simulation results and statistical analysis such as the t -test, Wilcoxon rank-sum test, and Friedman test reveal that LCA may effectively address optimization problems by maintaining a proper balance between exploitation and exploration. Furthermore, the LCA algorithm has been employed to solve seven real-world engineering problems, such as the tension/compression spring design, pressure vessel design problem, welded beam design problem, speed reducer design problem, gear train design problem, three-bar truss design, and cantilever beam problem. The results demonstrate the LCA’s superiority and capability over other algorithms in solving complex optimization problems.

Introduction

The modelling of biological sciences and genetics and the use of evolutionary operators like natural selection are the basis of evolutionary-based optimization algorithms 7 . One of the first evolutionary-based optimization algorithm, the genetic algorithm (GA) 8 , has been developed using selection, crossover, and mutation sequence operators and a model of the reproductive process. Another popular evolutionary-based optimization algorithm called differential evolution (DE) 9 has been developed as a powerful and quick method to solve problems in continuous spaces and has a strong capacity to optimize non-differentiable nonlinear functions. Some other algorithms in this group, such as cultural algorithms (CAs) 10 , Biogeography-Based Optimizer (BBO) 11 , invasive tumor growth (ITGO) 12 , and learner performance behaviour (LPB) 13 . The development of swarm-based optimization algorithms is focused on simulating the natural behaviours of creatures such as animals, insects, ocean animals, plants, and other living things. One of the most commonly used swarm-based algorithms is Particle Swarm Optimization (PSO) 14 , which takes its inspiration from the reasonable behaviour of fish and birds. The Grey Wolf optimization (GWO) 15 , 16 , 17 has been created using hierarchical leadership behaviour modelling as well as grey wolf hunting tactics. Ant colony optimization (ACO) 18 was created by modelling the behaviour of ant swarms in order to determine the shortest route between a food source and a nest. The humpback whales use of bubble nets for hunting served as inspiration for the Whale optimization algorithm (WOA) 19 . Tunicate Swarm algorithm (TSA) 20 , Crow Search Algorithm (CSA) 21 , Raccoon optimization algorithm (ROA) 22 , Tree seed algorithm (TSA) 23 , Marine predators algorithm (MPA) 24 , Capuchin search algorithm (CapSA) 25 , Chameleon Swarm algorithm (CSA) 26 , and Aquila optimizer (AO) 27 are other swarm-based algorithms 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 .

Based on the modelling of several physics phenomena and laws, optimization algorithms with such a physics-based algorithm have been developed. The Simulated Annealing (SA) 36 , one of the first algorithms in this category, was inspired by the modelling of the annealing process in metallurgical cooling and melting processes. The water cycle algorithm (WCA) 37 simulates the evaporation of water from the ocean, cloud formation, rainfall, river creation, and overflow of water from pits, all of which are inspired by the natural water cycle. A gravitational search algorithm (GSA) 38 has been developed as a result of simulations of the gravitational force that objects exert on one another at various distances. Other physics-based algorithms are atom search optimization (ASO) 39 , multi-verse optimizer (MVO) 40 , Electromagnetic field optimization (EFO) 41 , nuclear reaction optimization (NRO) 42 , optics inspired optimization (OIO) 43 , Equilibrium optimizer (EO) 44 , Archimedes Optimization Algorithm (AOA) 45 , and Lichtenberg Algorithm (LA) 46 . Chemistry-based algorithms have been developed with chemical reactions as inspiration. One of the most famous chemistry-based algorithms is chemical-reaction-inspired meta-heuristic for optimization 47 . Chemical reaction optimization (CRO) 48 is a recently developed meta-heuristic for optimization that takes inspiration from the nature of chemical reactions. A natural process of changing unstable molecules into stable molecules is called a chemical reaction. Another chemistry-based algorithm is artificial chemical reaction optimization algorithm (ACROA) 49 .

Game-based algorithms have been created using simulations of the rules governing various sports and the actions of players, trainers, and other participants. The Volleyball premier league (VPL) 50 algorithm’s major concept has been to create modelling contests for the volleyball league, while the football game-based optimization (FGBO) 51 algorithm’s main idea was to create modelling competitions for the football league. The Puzzle Optimization Algorithm (POA) 52 was developed mostly as a result of the players’ strategy and talent in creating puzzle components. The primary inspiration for the Tug-of-War Optimization (TWO) 53 technique was the players’ collective effort throughout the game. The introduction of human-based algorithms is based on the mathematical simulation of various human activities that follow an evolutionary process. The most well-known human-based algorithm is called teaching-learning-based optimization (TLBO) 54 , and it has been created by simulating the conversation and interactions between a teacher and students in a classroom. Doctor and patient optimization (DPO) 55 algorithm has been made with interactions between doctors and patients, such as preventing illness, getting check-ups, and getting treatment, in mind. Creating Poor and rich optimization (PRO) 56 has been primarily motivated by the economic activities of the rich and poor in society. In order to be successful, human mental search (HMS) 57 has been created by simulating human behaviour on online auction marketplaces. Other human-based algorithms are Tabu Search (TS) 58 , 59 , Imperialist Competitive Algorithm (ICA) 60 , colliding bodies optimization (CBO) 61 , Mine Blast Algorithm (MBA) 62 , seeker optimization algorithm (SOA) 63 , group counseling optimization (GCO) 64 , 65 algorithm, harmony search (HS) 66 , League Championship Algorithm (LCA) 67 , Coronavirus herd immunity optimizer (CHIO) 68 , and Ali Baba and the Forty Thieves (AFT) 69 .

In recent years, meta-heuristic algorithms are applied for solving complex problems in different applications such as optimization of weight and cost of cantilever retaining wall 70 , multi-response machining processes 71 , symbiosis organisms search for global optimization and image segmentation 72 , human social learning intelligence 73 , nanotubular halloysites in weathered pegmatites 74 , numerical optimization and real-world applications 75 , convergence analysis 76 , higher Dimensional Optimization Problems 77 , non-dominated sorting advanced 78 , Lagrange Interpolation 79 . LCA is quite different from the existing meta-heuristic algorithms although it belongs to the category of human-based meta-heuristics. The major difference between LCA and them is its particular human-based background. LCA is inspired by observing how mothers and children prepare food. Another important difference is exploration and exploitation. The proposed LCA algorithm works in two phases such as (i) children learn from their mothers and (ii) children and mothers learn from a chef. The exploration is established through Phase 1 of the algorithm when the children learn from their mothers. In the same way, the exploitation is established through Phase 2 of the algorithm, when the children and mother learn from the chef. Therefore, considering these mentioned factors, there are significant differences between LCA and the existing meta-heuristic algorithms. Table 1 shows the comparative assessment between the proposed LCA algorithm and other meta-heuristic algorithms that have been analyzed in terms of algorithm search mechanisms.

The existing meta-heuristic algorithms have some flaws, concerns, and issues. For example, the Harris Hawk Optimization (HHO) algorithm 83 performs well at solving standard benchmark problems while failing miserably at complex problems such as CEC 2017 and real-world problems. As a result, in order to solve complex problems and functions, the performance of this algorithm needs to be improved. The poor and rich algorithm (PRO) 56 was recently developed and configured to perform well on a few simple and old test functions while failing to solve new and complex test functions such as CEC 2017. As a result, in order to solve complex problems and functions, the algorithm has to be improved. The mechanism of well-known algorithms such as the grey wolf optimizer (GWO) 15 and the whale optimization algorithm (WOA) 19 is very similar, with the main difference being the search range. Here, a critical question arises: What is required to offer and develop new algorithms in the presence of well-known algorithms like those stated above? According to the No Free Lunch (NFL) 87 theorem, no optimization algorithm can solve all optimization problems. According to the NFL, an algorithm’s ability to successfully address one or more optimization problems does not guarantee that it will do so with others, and it may even fail. As a result, it is impossible to say that a particular optimization algorithm is the best approach for all problems. New algorithms can always be developed that are more effective than current algorithms at solving difficult optimization problems. The NFL invites researchers to be inspired to create new optimization algorithms that are better able to address difficult optimization problems. The ideas described in the NFL theorem inspired the authors of this paper to propose a new optimization algorithm namely the Learning Cooking Algorithm (LCA).

In every optimization algorithm, exploration and exploitation play the most important role. So, keeping this in mind, this paper proposes a new human-based algorithm namely the LCA algorithm to maintain a proper balance between exploration and exploitation among optimization algorithms. The LCA algorithm mimics two phases: (i) children learn from their mothers and (ii) children and mothers learn from a chef. The exploration is established through Phase 1 of the algorithm when the children learn from their mothers. For each child, the corresponding mother is chosen by the greedy selection mechanism. This phase helps the algorithm explore the large search space. In the same way, the exploitation is established through Phase 2 of the algorithm, when the children and mother learn from the chef. The chef acts as the global best solution and directs the other swarm particles i.e. the children and mothers to move towards it. The 51 different benchmark functions (which include the first 23 functions of the CEC 2005 benchmark functions) and the CEC 2019 benchmark functions are employed to evaluate the LCA’s capability. Seven well-known algorithms, two top-performing algorithms, and eight recently developed algorithms for solving optimization problems are compared to the performance of the proposed LCA algorithm. This algorithm has also been used to solve seven optimal design problems in order to evaluate the LCA for solving real-life engineering problems. The structure of the paper is designed as follows: “ Learning cooking algorithm ” describes the inspiration for the Learning Cooking Algorithm (LCA) and the mathematical model for the LCA. In “ Simulation studies and results ”, simulation studies, results, and discussion are presented. The performance of LCA in solving engineering design problems is evaluated in “ LCA for engineering optimization problems ”. Conclusions and suggestions for further study of this paper are provided in “ Conclusion ”.

Learning cooking algorithm

In this section, the learning cooking algorithm (LCA) is proposed, followed by a discussion of its mathematical modelling.

Inspiration

Cooking is the process of exposing food to heat. All of the methods constitute cooking, regardless of whether the food is baked, fried, sauteed, boiled, or grilled. According to the evidence, our ancestors began cooking over an open fire some 2 million years ago. Although devices like microwaves, toasters, and stovetops are extensively utilized, some foods are still cooked over an open flame. There are numerous ways to cook, but the majority of them have their origins in the past. These include boiling, steaming, braising, grilling, barbecuing, roasting, and smoking. Steaming is a more recent innovation. Different cooking techniques require varying levels of heat, moisture, and time. First of all, without being cooked, certain foods are not safe to eat. Cooking not only heats food but also has the potential to eliminate dangerous microorganisms. Because they are more likely to carry bacteria while they are raw, meats must be cooked to a specific temperature before eating. Cooking is a learning process in which a beginner (a child) learns to cook from the mother, and then children and mothers learn to cook from the cooking expert by watching television, YouTube, and other social media platforms. This study “Learning Cooking Algorithm,” is divided into two phases: (i) children learn from their mothers and (ii) children and mothers learn from a chef. This idea is similar to meta-heuristic algorithms, in which the problem’s best candidate solution is selected as the algorithm’s final output after multiple initial candidate solutions are improved through an iterative process.

Mathematical model of LCA

LCA is a population-based optimization algorithm that includes cooking learners (children), mothers, and chefs. LCA members are candidate solutions to the problem, as it is modelled by a population matrix in Eq. ( 1 ). Equation ( 2 ) is used to randomly initialize these members’ positions at the beginning of implementation.

where C is the LCA population, $C_i$ is the $i{th}$ candidate solution, $c_{i,j}$ is the value of the $j^{th}$ variable determined by the $i{th}$ candidate solution, the value N represents the size of the LCA population, m is the number of problem variables, the value of rand is chosen at random from the range $\left[ 0,1\right] $ , the upper and lower limits of the $j{th}$ problem variable are denoted as ${UB}_j$ and ${LB}_j$ , respectively. Here, in the LCA algorithm the food items represent the problem variables. The children and mothers try to learn different types of cuisines such as Mexican, Italian, Indian, American cuisines from the chefs around the world.

The objective function values are represented by the vector in Eq. ( 3 ).

where the objective functions are represented by the vector F and $F_i$ represented the of objective function delivered by the $i{th}$ candidate solution.

The values for the objective function are the most important things used to judge the quality of candidate solutions. On the basis of comparisons of the values of the objective function, the member of the population with the best value is referred to as the “best member of the population (Cbest).” Each iteration improves and updates the candidate solutions, so the best member must also be updated. The methodology used to update candidate solutions is the main difference between meta-heuristic optimization algorithms. In LCA, candidate solutions are updated in two main phases: (i) children learn from their mothers and (ii) children and mothers learn from a chef.

Phase 1: children learn from their mothers (exploration)

The first stage of the LCA update is based on the choice of the mother by the children and then the teaching of cooking by the selected mother to the children (Fig. 1 ). The selection of mothers is done by choosing a number of the best members from the whole population. The number of mothers is denoted by $N_{MO}$ which is decided using the formula $N_{MO} =\lfloor 0.1\cdot N\cdot (1-\frac{t}{T} )\rfloor $ . After choosing the mother and trying to learn how to cook, children in the population will move to different places in the search space. This will improve the LCA’s exploration capabilities in the global search for it and the identification of the optimal location. The exploratory capability of this algorithm is therefore demonstrated by this stage of the LCA. Equation ( 4 ) says that the $N_{MO}$ members of the LCA population are chosen as mothers by comparing the values of the objective function at each iteration.

where MO is the matrix of mothers, ${MO}_{i}$ is the $i{th}$ mothers, ${MO}_{i,j}$ is the $j{th}$ dimension, and $N_{MO}$ is the number of mothers, t represents the current iteration and the maximum number of iterations is T .

Children learn from their mothers.

The new location for each member is first determined by using Eq. ( 5 ) in accordance with the mathematical modelling of this LCA phase. Equation ( 6 ) shows that the new location takes the place of the old one if the value of the objective function increases.

where $C_{i}^{P1}$ is the new calculated status for the $i{th}$ candidate solution based on the first phase of LCA, $c_{i,j}^{P1}$ is its $j{th}$ dimension, $F_{i}^{P1}$ is its objective function value, $I_{1}$ is a number chosen at random from the range of $\{1,2\}$ , and the value of $rand_{1}$ is a random number between [0, 1], $MO_{{k_i}}$ , where $k_i$ is chosen at random from the set $\{1,2,\cdots ,N_{MO} \}$ , represents a randomly selected mother to learn the $i{th}$ member, $MO_{{k_i},{j}}$ is its $j^{th}$ dimension, and $F_{MO_{k_i}}$ is its objective function value.

Phase 2: children and mother learn from chef (exploitation)

The second stage of the LCA update is based on the children and their mother selecting the chef, followed by watching a YouTube video to learn the chef’s style of cooking (Fig. 2 ). The selection of chefs is done by choosing a number of the best members from the mother population. The number of chefs is denoted by $N_{Cf}$ which is decided using the formula $N_{Cf} =\lfloor 0.1\cdot N_{MO}\cdot (1-\frac{t}{T})\rfloor $ . The population members will move to the local search after selecting the chef and learning about their various cooking techniques. The $N_{Cf}$ members of the LCA population are chosen as chefs in each iteration based on a comparison of the values of the objective function, as given in Eq. ( 7 ). This phase demonstrates the power of LCA to exploit global search.

where Cf is the matrix of chefs, ${Cf}_{i}$ is the $i{th}$ chefs, ${Cf}_{i,j}$ is the $j{th}$ dimension, t represents the current iteration and the maximum number of iterations is T .

Children and mothers learn from chefs via social media.

In order to represent this concept mathematically, the new location for each member is determined using Eq. ( 8 ). By Eq. ( 9 ), this new position replaces the previous one if it enhances the objective function’s value.

where $C_{i}^{P2}$ is the new calculated status for the $i^{th}$ candidate solution based on the second phase of LCA, $c_{i,j}^{P2}$ is its $j^{th}$ dimension, $F_{i}^{P2}$ is its objective function value, $I_{2}$ , $I_{3}$ , are a numbers randomly chosen from the set $\{1,2\}$ , the values of $rand_{2}$ , $rand_{3}$ are a random numbers between [0, 1], $Cf_{k_i}$ , where $k_i$ is chosen at random from the set $\{1,2,\cdots ,N_{Cf} \}$ , represents a randomly selected chef to learn the $i^{th}$ member and mother, ${Cf_{{k_i},{j}}}$ is its $j^{th}$ dimension, and $F_{Cf_{k_i}}$ is its objective function value.

Repetition procedure, pseudo-Code of LCA and LCA flow chart:

An LCA iteration is completed after the population members have been updated in accordance with the first and second stages. The algorithm entered the following LCA iteration with the updated population. To complete the maximum number of repetitions, the updation procedure is performed in accordance with the first and second phase stages and in accordance with Eqs. ( 4 ) to ( 9 ). The best candidate solution that has been recorded during the execution of LCA on the given problem is presented as the solution when LCA has been fully implemented. The proposed LCA algorithm pseudocode is shown in Algorithm 1, and Fig. 3 shows its flowchart.

Pseudo-code of the proposed learning cooking algorithm.

The computational complexity of LCA

The computational complexity of LCA is discussed in this subsection. The computational complexity of the preparation and initialization of LCA for the problem with the number of members equal to N and the problem with the number of decision variables equal to m is equal to $O(N \times m)$ . The LCA members are updated in two stages during each iteration. As a result, the computational complexity of the LCA update processes is $O(2N\times m\times T)$ , where T is the maximum number of algorithm iterations. As a consequence, the total computational complexity of LCA is $O(N\times m\times (1+2T))$ .

Flowchart of the learning cooking algorithm.

Simulation studies and results

This section looks at how well the LCA performs in applications involving optimization and how it provides the most effective solutions to these types of problems. In LCA, fifty-one different Benchmark functions (which includes the first 23 functions of the CEC 2005 benchmark functions) 88 and ten CEC 2019 benchmark functions 89 are used. The performance of the LCA algorithm is compared with well-known algorithms, top-performance algorithms, modified algorithms, and newly developed algorithms, such as PSO 14 , TSA 20 , SSA 80 , MVO 40 , GWO 15 , WOA 19 , GJO 81 , 90 , LSHADE 91 , CMAES 92 , IGWO 93 , MWOA 94 , TLBO 54 , MTBO 86 , BWO 82 , HHO 83 , MGO 84 , and SCSO 85 in order to evaluate the efficiency of the LCA results. For each of the optimization algorithms under evaluation, the size of the population, maximum iterations, and the number of function evaluations (NFEs) are set at 30, 1000, and 30,000, respectively, with 20 independent runs for each function. Table 2 lists the parameter values for each algorithm. The details of the 51 test functions and CEC 2019 test functions are described in Tables 3 and 4 . For validation, a parametric and non-parametric statistical analysis such as the mean value of the fitness function (average), standard deviation (std), best, worst, median, Wilcoxon rank-sum test, t-test, rank, Friedman test, and convergence curve of algorithms are used. Optimization algorithms base their performance ranking criteria on the t-test value. The NA denotes “Not Applicable” which means that the equivalent algorithm result cannot be compared with other algorithm results. The experiments are performed on Windows 10, Intel Core i3, 2.10GHz, 8.00 GB RAM, and MATLAB R2020b.

Measurements of performance

The average value represents the mean of the best results obtained by an algorithm over various runs, and it can be determined as follows:

where $A_{i}$ denotes the best-obtained solution from $i^{th}$ run and N represents 20 independent runs.

Standard deviation (Std)

The standard deviation is determined to examine whether an algorithm can generate the same best value in multiple runs and to examine the repeatability of an algorithm’s outcomes, which can be calculated as follows:

The lowest of the results received from different runs:

The highest of the results received from different runs:

The ordered data’s middle value.

Wilcoxon rank-sum test

The Wilcoxon rank-sum test is used to determine whether two samples come from the same population.

Optimization algorithms base their performance ranking criteria on the t-test value.

A statistical test like a t-test is employed to estimate the significant differences between the proposed method with respect to other meta-heuristics. These are calculated as follows;

where $Mean_{1}$ , $Mean_{2}$ , $Std_{1}$ , and $Std_{2}$ be the mean and standard deviation for the two algorithms, respectively.

Comparison results of LCA with well-known & top-performing algorithms for 51 benchmark functions

The comparison results of 51 functions are shown in Tables 5 , 6 and 7 , where LCA delivers the global optimal results of all the algorithms on 38 functions and is competitive on the other functions. In LCA, 44 out of 51 benchmark function’s average results are the best. In PSO, 17 out of 51 benchmark functions provide the best average results. Moreover, LCA and PSO provide the same best average results on some functions such as F 16, F 18, F 27, F 35, F 36, $F40-F46$ , and F 50. In TSA, 6 out of 51 benchmark function’s average results are the best. Furthermore, LCA and TSA provide the same best average results on some functions such as F 16, F 18, F 35, F 40, F 41, and F 44. In SSA, 6 out of 51 benchmark function’s average results are the best. Furthermore, LCA and SSA provide the same best average results on some functions such as F 16, F 18, F 27, F 43, and F 46. In MVO, 10 out of 51 benchmark functions provide the best average results. Moreover, LCA and MVO provide the same best average results on some functions such as F 16, F 18, F 24, F 30, F 37, F 43, F 44, and F 46. In GWO, 12 out of 51 benchmark function’s average results are the best. Moreover, LCA and GWO provide the same best average results on some functions such as F 16, F 18, F 24, F 27, F 35, F 37, $F40-F42$ , F 44, and F 46. In WOA, 14 out of 51 benchmark function’s average results are the best. Furthermore, LCA and WOA provide the same best average results on some functions such as F 9, F 11, F 16, F 18, F 24, F 27, F 28, F 35, F 37, F 40, F 41, F 43, F 44, and F 46. In GJO, 13 out of 51 benchmark functions provide the best average results. Moreover, LCA and GJO provide the same best average results on some functions such as F 9, F 11, F 16, F 18, F 24, F 27, F 28, F 35, F 37, $F40-F42$ , and F 44. In LSHADE, 27 out of 51 benchmark function’s average results are the best. Furthermore, LCA and LSHADE provide the same best average results on some functions F 16, F 18, $F22-F24$ , F 27, F 29, F 30, $F34-F37$ , $F40-F42$ , $F44-F46$ , and $F49-F51$ . In CMAES, 11 out of 51 benchmark functions provide the best average results. Furthermore, LCA and CMAES provide the same best average results on some functions F 11, F 16, $F21-F24$ , F 27, F 35, F 36, and F 46. The results of the implementation of LCA and nine competitor algorithms on the functions F 1 to F 15 are reported in Table 5 . The simulation results show that LCA has been able to achieve global optimality in optimizing benchmark functions such as F 1, F 2, F 3, F 4, F 5, F 6, F 8, F 9, F 11, F 14, and F 15. Furthermore, LCA performed better in optimizing benchmark functions F 7, F 10, F 12, and F 13. The optimization results show that LCA is the best of all the optimizers when compared to handling the functions from F 1 to F 15. The optimization results of the LCA, and nine competitor algorithms on the functions from F 16 to F 30 are presented in Table 6 . The simulation results show that LCA has been able to achieve global optimality in optimizing the benchmark functions $F16-F18$ , $F21-F25$ , and $F27-F30$ . Furthermore, LCA performed worst in optimizing the benchmark functions F 19, F 20, and F 26. According to the simulation results, PSO has been able to provide the global optimal in optimizing the benchmark functions F 19, and F 26. The global optimal in the function F 19 is provided by SSA. And then MVO algorithm provides the global optimal in the functions F 19, and F 20. The optimization results of the LCA algorithm and nine competitor algorithms on the functions from F 31 to F 51 are presented in Table 7 . The simulation results show that LCA has been able to provide the global optimal in optimizing the benchmark functions $F31-F37$ , $F40-F46$ , and $F49-F51$ . Furthermore, LCA performed worst in optimizing the benchmark functions F 38, F 39, F 47, and F 48. According to the simulation results, PSO has been able to provide the global optimal in optimizing benchmark functions F 34, F 36, F 47, and F 48. Analysis of the simulation results shows that the LCA algorithm has superior and much more competitive performance than the other nine compared algorithms.

Comparison results of LCA with recent algorithms for 51 benchmark functions

The comparison results of 51 functions are shown in Tables 8 , 9 and 10 , where LCA delivers the global optimal results of all the algorithms on 38 functions and is competitive on the other functions. In LCA, 44 out of 51 benchmark function’s average results are the best. In IGWO, 22 out of 51 benchmark functions provide the best average results. Moreover, LCA and IGWO provide the same best average results on some functions such as F 16, F 18, F 23, F 24, F 27, F 31, $F35-F37$ , $F40-F42$ , $F44-F46$ , and $F49-F51$ . In MWOA, 7 out of 51 benchmark function’s average results are the best. Furthermore, LCA and MWOA provide the same best average results on some functions such as F 9, F 24, F 28, F 35, F 40, F 41, and F 44. In TLBO, 20 out of 51 benchmark function’s average results are the best. Furthermore, LCA and TLBO provide the same best average results on some functions such as F 10, F 11, F 16, F 18, F 24, F 26, F 27, F 31, $F35-F37$ , $F40-F42$ , $F44-F46$ , and $F49-F51$ . In MTBO, 17 out of 51 benchmark functions provide the best average results. Moreover, LCA and MTBO provide the same best average results on some functions such as F 16, F 18, F 24, F 26, F 27, $F35-F37$ , $F40-F42$ , $F44-F46$ , and $F49-F51$ . In BWO, 18 out of 51 benchmark function’s average results are the best. Moreover, LCA and BWO provide the same best average results on some functions such as F 1, F 3, $F8-F11$ , F 16, F 18, F 24, F 25, F 28, F 32, F 33, F 35, F 37, $F40-F42$ , and F 44. In HHO, 15 out of 51 benchmark functions provide the best average results. Furthermore, LCA and HHO provide the same best average results on some functions such as $F8-F11$ , F 24, F 35, $F40-F42$ , $F44-F46$ , and $F49-F51$ . In MGO, 27 out of 51 benchmark functions provide the best average results. Moreover, LCA and MGO provide the same best average results on some functions such as $F8-F11$ , F 16, F 18, F 23, F 24, F 27, F 28, F 30, F 31, $F34-F37$ , $F40-F47$ , and $F49-F51$ . In SCSO, 11 out of 51 benchmark functions provide the best average results. Furthermore, LCA and SCSO provide the same best average results on some functions $F9-F11$ , F 24, F 28, F 31, F 35, $F40-F42$ , and F 44. The results of the implementation of LCA and eight competitor algorithms on the functions F 1 to F 15 are reported in Table 8 . The simulation results show that LCA has been able to achieve global optimality in optimizing benchmark functions such as $F1-F6$ , F 8, F 9, F 11, F 14, and F 15. Furthermore, LCA performed better in optimizing benchmark functions F 7, F 10, F 12, and F 13. The optimization results show that LCA is the best of all the optimizers when compared to handling the functions from F 1 to F 15. The optimization results of the LCA, and eight competitor algorithms on the functions from F 16 to F 30 are presented in Table 9 . The simulation results show that LCA has been able to achieve global optimality in optimizing the benchmark functions $F16-F18$ , $F21-F25$ , and $F27-F30$ . Furthermore, LCA performed worst in optimizing the benchmark functions F 19, F 20, and F 26. According to the simulation results, the TLBO has been able to provide the global optimal in optimizing the benchmark function F 19 and F 26. The MTBO has been able to provide the global optimal in optimizing the benchmark function F 26. Then the SCSO has been able to provide the global optimal in optimizing the benchmark function F 19. The optimization results of the LCA algorithm and eight competitor algorithms on the functions from F 31 to F 51 are presented in Table 10 . The simulation results show that LCA has been able to provide the global optimal in optimizing the benchmark functions $F31-F37$ , $F40-F46$ , and $F49-F51$ . Furthermore, LCA performed worst in optimizing the benchmark functions F 38, F 39, F 47, and F 48. According to the simulation results, IGWO has been able to provide the global optimal in optimizing the benchmark functions F 38, F 39, F 47, and F 48. Analysis of the simulation results shows that the LCA algorithm has superior and much more competitive performance than the other eight compared algorithms.

Convergence analysis for 51 benchmark functions

The convergence curve represents a relation between the fitness function value and the number of iterations. The search agent explores the search area and deviates rapidly in the beginning stage of the optimization process. The main objective behind the convergence analysis is to understand the behaviour and graphical representation of the proposed method. Figure 4 shows the convergence curves of LCA with well-known algorithms for different test functions. From Fig. 4 it is observed that the proposed method LCA converges faster among the benchmark functions except for F 14, F 17, F 18, F 26, and F 36. Moreover, the LCA technique has a larger effect on the convergence of the other algorithms, especially compared with the PSO, TSA, SSA, MVO, GWO, WOA, and GJO. Figure 5 shows the convergence curves of LCA with recent algorithms for different test functions. From Fig. 5 it is observed that the proposed method LCA converges faster among the benchmark functions except for F 14, $F17-F20$ , F 27, F 30, F 31, F 37, F 43, and F 46. Moreover, the LCA technique has a larger effect on the convergence of the other algorithms, especially compared with the IGWO, MWOA, TLBO, MTBO, BWO, HHO, MGO, and SCSO. Thus, it is proven with the improvements that the proposed LCA can achieve a higher search accuracy and faster convergence.

Convergence graph of LCA with well-known algorithms on the different benchmark functions.

Convergence graph of LCA with recent algorithms on the different benchmark functions.

Comparison results of LCA with well-known & top-performing algorithms for CEC 2019 test functions

In this subsection, we discuss the efficiency of the proposed LCA and compare it with well-known algorithms and top-performing algorithms. Table 11 demonstrates the evaluation results of competitive algorithms. In comparison to PSO, LCA produces better results in 2 functions, such as CEC19-1, and CEC19-2 . In comparison to TSA, LCA produces better results in 5 functions, such as CEC19-1, CEC19-2, CEC19-3, CEC19-6, and CEC19-8. In comparison to SSA, LCA produces better results in 2 functions, such as CEC19-1 and CEC19-3. In comparison to MVO, LCA produces better results in 2 functions, such as CEC19-1 and CEC19-2. In comparison to GWO, LCA produces better results in 2 functions, such as CEC19-1 and CEC19-6. In comparison to WOA, LCA produces better results in 2 functions, such as CEC19-1 and CEC19-7. In comparison to GJO, LCA produces better results in 3 functions, such as CEC19-1, CEC19-3, and CEC19-6. In comparison to LSHADE, LCA produces better results in 2 functions, such as CEC19-1 and CEC19-3. In comparison to CMAES, LCA produces better results in 4 functions, such as CEC19-1, CEC19-2, CEC19-3, and CEC19-6. Hence, the proposed LCA algorithm has a good exploitation ability and a good spatial exploration ability, which makes it possible for it to handle optimization problems successfully.

Comparison results of LCA with recent algorithms for CEC 2019 test functions

In this subsection, we discuss the efficiency of the proposed LCA and compare it with recent algorithms. Table 12 demonstrates the evaluation results of competitive algorithms. In comparison to IGWO, LCA produces better results in 3 functions, such as CEC19-1, CEC19-3, and CEC19-6 . In comparison to MGWO, LCA produces better results in 2 functions, such as CEC19-1 and CEC19-3. In comparison to TLBO, LCA produces better results in 3 functions, such as CEC19-1, CEC19-3, and CEC19-6. In comparison to MTBO, LCA produces better results in 3 functions, such as CEC19-1, CEC19-3, and CEC19-6. In comparison to BWO, LCA produces better results in 5 functions, such as CEC19-2, CEC19-3, CEC19-6, CEC19-7, and CEC19-8. In comparison to HHO, LCA produces better results in 1 function, such as CEC19-3. In comparison to MGO, LCA produces better results in 1 function, such as CEC19-3. In comparison to SCSO, LCA produces better results in 1 function, such as CEC19-3. Hence, the proposed LCA algorithm has a good exploitation ability and a good spatial exploration ability, which makes it possible for it to handle optimization problems successfully.

Convergence analysis for CEC 2019 benchmark functions

The main objective behind the convergence analysis is to understand the behaviour and graphical representation of the proposed method. Figure 6 shows the convergence curves of LCA with well-known algorithms for CEC 2019 benchmark functions. From the Fig. 6 , it is observed that the proposed method LCA converges faster among CEC 2019 benchmark functions except for $CEC19-2$ , $CEC19-3$ , $CEC19-4$ , $CEC19-5$ , $CEC19-5$ , $CEC19-5$ , $CEC19-6$ , $CEC19-7$ , $CEC19-8$ , $CEC19-9$ , and $CEC19-19$ . Moreover, the LCA technique has a larger effect on the convergence of the other algorithms, especially compared with the PSO, TSA, SSA, MVO, GWO, WOA, and GJO. Figure 7 shows the convergence curves of LCA with recent algorithms for CEC 2019 benchmark functions. From the Fig. 7 it is observed that the proposed method LCA converges faster among CEC 2019 benchmark functions except for $CEC19-2$ , $CEC19-3$ , $CEC19-4$ , $CEC19-5$ , $CEC19-5$ , $CEC19-5$ , $CEC19-6$ , $CEC19-7$ , $CEC19-8$ , $CEC19-9$ , and $CEC19-19$ . Moreover, the LCA technique has a larger effect on the convergence of the other algorithms, especially compared with the IGWO, MWOA, TLBO, MTBO, BWO, HHO, MGO, and SCSO.

Convergence graph of LCA with well-known algorithms on the CEC 2019 benchmark functions.

Convergence graph of LCA with recent algorithms on the CEC 2019 benchmark functions.

Statistical analysis

The Wilcoxon rank-sum test 95 is used to provide statistical analysis of LCA performance in comparison to competing algorithms. Based on a statistic known as the p value, The Wilcoxon rank-sum test evaluates if the superiority of one approach over another is statistically significant. The results of performing the Wilcoxon rank-sum test to LCA are compared to each of the competing algorithms. The results show that LCA is statistically better than a similar competitor algorithm in any case where the p value is estimated to be less than 0.05. The symbol P denotes the hypothesis. Two-tailed t -tests have been used to compare different statistical results at a significance level of 0.05. The t values are provided with the help of mean values and standard deviations. A negative t value indicates that the statistical outcomes of the LCA optimization errors are significantly less, and vice versa. The corresponding t value is highlighted if the difference is a statistically significant error. The symbols w / t / l denote that LCA wins in w functions, ties in t functions, and loses in l functions. Table 13 shows the Wilcoxon rank-sum test and t-test results for LCA versus well-known and top-performing algorithms for 51 benchmark functions. Table 14 shows the Wilcoxon rank-sum test and t-test results for LCA versus recent algorithms for 51 benchmark functions. Table 15 shows the Wilcoxon rank-sum test and t-test results for LCA versus well-known and top-performing algorithms for CEC 2019 benchmark functions. Table 16 shows the Wilcoxon rank-sum test and t-test results for LCA versus recent algorithms for CEC 2019 benchmark functions. Table 17 shows the average run time of algorithms for the 23 benchmark functions. Table 18 shows the Wilcoxon rank-sum test and t-test validation for LCA versus well-known and top-performing algorithms for 51 benchmark functions. Table 19 shows the Wilcoxon rank-sum test and t -test validation for LCA versus recent algorithms for 51 benchmark functions. Table 20 shows the Wilcoxon rank-sum test and t -test validation for LCA versus well-known and top-performing algorithms for CEC 2019 benchmark functions. Table 21 shows the Wilcoxon rank-sum test and t -test validation for LCA versus recent algorithms for CEC 2019 benchmark functions. The statistical results of the optimization errors demonstrate that LCA has a much superior overall performance when compared with the other algorithms.

In this experiment, the Friedman test 96 , 97 is used to rank the performance of the algorithms under evaluation. This test ranks the value of each algorithm from lowest to greatest and evaluates if there is a significant difference between LCA and the comparative optimization algorithms. Table 22 shows the over-rank report of LCA with well-known and top-performing algorithms for 51 benchmark functions. Table 23 shows the over-rank report of LCA with recent algorithms for 51 benchmark functions. Table 24 shows the over-rank report of LCA with well-known and top-performing algorithms for CEC 2019 benchmark functions. Table 25 shows the over-rank report of LCA with recent algorithms for CEC 2019 benchmark functions. According to Table 22 , LCA has the greatest overall capacity to solve these challenging problems, with a mean rank of 2.1372. According to Table 23 , LCA has the greatest overall capacity to solve these challenging problems, with a mean rank of 1.9019. The results of the Friedman test again prove the superiority of LCA over the other considered optimizers.

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LCA for engineering optimization problems

The capability of LCA to provide the best solution for real optimization applications is discussed in this section. For this purpose, LCA and competing algorithms have been employed in seven real-life problems, such as tension/compression spring design, pressure vessel design problem, welded beam design problem, speed reducer design problem, gear train design problem, three-bar truss design, and cantilever beam problem. The performance of the LCA algorithm is compared with well-known and most recent algorithms such as PSO 14 , TSA 20 , SSA 80 , MVO 40 , GWO 15 , WOA 19 , GJO 81 , IGWO 93 , MWOA 94 , TLBO 6 , MTBO 86 , BWO 82 , HHO 83 , MGO 84 , and SCSO 85 in order to evaluate the efficiency of the LCA results.

Tension/compression spring design problem

The tension/compression spring design problem is explained in 98 , and the goal is to reduce the weight of a tension/compression spring. This problem is constrained by minimum deflection, shear stress, surge frequency, outer diameter limits, and design factors. The design factors are the mean coil diameter D , the wire diameter d , and the number of active coils N . Figure 8 illustrates the spring and its properties. The mathematical formulation of this design problem is as follows,

Tension/compression spring design problem.

Table 26 show the comparison results of the tension/compression spring design problem. Table 27 shows the statistical results of optimization algorithms for the tension/compression spring design problem compared with different algorithms in terms of the mean, standard deviation, minimum, maximum, and median. The results shows that LCA has provided the solution to this problem with optimal values for variables of (5.566E-02, 4.591E-01, 7.194E+00) and an optimal solution of 1.250E-02. The simulation results show that the LCA is superior when compared with other competitor algorithms by providing a better solution and better statistical indicators.

Pressure vessel design problem

The idea is to produce a pressure vessel design with the least cost. Figure 9 illustrates the pressure vessel and the design parameters. This problem has four variables: shell thickness ( $T_s$ ), head thickness ( $T_h$ ), inner radius ( R ), and length of the cylindrical section excluding the head ( L ). This design problem is mathematically deposited as follows:

Pressure vessel design problem.

Table 28 show comparison results of the pressure vessel problem. Table 29 shows the statistical results of optimization algorithms for the pressure vessel problem compared with different algorithms in terms of the mean, standard deviation, minimum, maximum, and median. The results show that LCA has provided the solution to this problem with optimal values for variables of (1.406E+00, 2.712E+00, 6.178E+0, and 2.609E+01) and an optimal solution of 5.886E+03. The simulation results show that the LCA is superior when compared with other competitor algorithms by providing a better solution and better statistical indicators.

Welded beam design problem

A popular welded beam design 99 is given in Fig. 10 to examine the demonstration of LCA in the engineering area. The goal is to discover the optimal design factors for reducing the total manufacturing cost of a welded beam exposed to bending stress ( $\sigma $ ), shear stress ( $\tau $ ), beam end deflection ( $\delta $ ), the bar’s buckling load ( $P_c$ ) and other constraints. This problem has four variables: weld thickness ( h ), bar length ( l ), height ( t ), and thickness ( b ). This design problem is mathematically deposited as follows:

Table 30 show the comparison results of the pressure vessel problem. Table 31 shows the statistical results of optimization algorithms for the pressure vessel problem compared with different algorithms in terms of the mean, standard deviation, minimum, maximum, and median. The results show that LCA has provided the solution to this problem with optimal values for variables of (1.922E-01, 6.087E+00, 9.008E+00, and 2.087E-01) and an optimal solution of 1.715E+00. The simulation results show that the LCA is superior when compared with other competitor algorithms by providing a better solution and better statistical indicators.

Welded beam design problem.

Speed reducer design problem

The speed reducer 100 , is a crucial component of the gearbox in mechanical systems and has a wide range of uses. In this optimisation problem, the weight of the speed reducer has to be lowered with 11 constraints (Fig. 11 ). Seven variables make up this problem, such as b , m , x , $l_1$ , $l_2$ , $d_1$ , and $d_2$ . This design problem is mathematically deposited as follows:

Table 32 show the comparison results of the speed reducer design problem. Table 33 shows the statistical results of optimization algorithms for the speed reducer design problem compared with different algorithms in terms of the mean, standard deviation, minimum, maximum, and median. The results show that LCA has provided the solution to this problem with optimal values for variables of (3.502E+00, 7.000E-01, 2.517E+01, 8.230E+00, 8.300E+00, 3.811E+00, and 5.457E+00) and an optimal solution of 2.990E+03. The simulation results show that the LCA is superior when compared with other competitor algorithms by providing a better solution and better statistical indicators.

Speed reducer design problem.

Gear train design problem

Sandgren proposed the gear train design issue as an unconstrained discrete design problem in mechanical engineering 101 . The purpose of this benchmark task is to reduce the gear ratio, which is defined as the ratio of the output shaft’s angular velocity to the input shaft’s angular velocity. The design variables are the number of teeth of the gears $\eta _{A} (z_{1})$ , $\eta _{B} (z_{2})$ , $\eta _{C} (z_{3})$ ,and $\eta _{D} (z_{4})$ , and Fig. 12 illustrates the 3D model of this problem. The mathematical formulation of the gear train design problem is as follows,

Gear train design problem.

The optimization technique involves finding a scenario that minimises or maximises an objective function while fulfilling a predetermined set of constraints. This case is known as the optimal solution, and it is often explored through an exponential collection of candidate solutions requiring highly expensive execution time. Meta–heuristic approximation techniques have been developed to help with this practical challenge. Even though these problem–solving methods cannot guarantee that the solution is optimal, they are quite capable of providing solutions that are close to optimal 1 , 2 , 3 , 4 , 5 , 6 . Meta–heuristic algorithms use exploitation and exploration, which represent intensity and diversity, as their two methods for determining the optimal solution. The growth of meta–heuristic algorithms has been influenced by a variety of natural phenomena, including animals, insects, wildlife, birds, living things, plants, biomedical laws, chemical reactions, physics laws, human activities, game mechanics, and other natural biological processes. In general, meta–heuristic algorithms may be divided into five categories: evolutionary–based optimization algorithms, swarm–based optimization algorithms, chemistry and physics–based optimization algorithms, game–based optimization algorithms, and human–based optimization algorithmTable 34 show the comparison results of the gear train design problem. Table 35 shows the statistical results of optimization algorithms for the gear train design problem compared with different algorithms in terms of the mean, standard deviation, minimum, maximum, and median. The results show that LCA has provided the solution to this problem with optimal values for variables (5.593E+01, 1.435E+01, 3.146E+01, and 5.593E+01) and an optimal solution of 0.000E+00. The simulation results show that the LCA is superior when compared with other competitor algorithms by providing a better solution and better statistical indicators.

Three-bar truss design problem

Figure 13 illustrates a three-bar planar truss construction in this scenario. The volume of a statically loaded 3-bar truss must be reduced while stress ( $\sigma $ ) constraints on each truss member are maintained. The aim is to find the best cross-sectional areas, $A_{1} (z_{1})$ and $A_{2} (z_{2})$ . The mathematical formulation of this design problem is as follows,

Three bar truss design.

Table 36 show the three-bar truss design problem comparison results. Table 37 shows the statistical results of optimization algorithms for the three-bar truss design problem compared with different algorithms in terms of the mean, standard deviation, minimum, maximum, and median. The results show that LCA has provided the solution to this problem with optimal values for variables of (0.792680179 and 0.397975679) and an optimal solution of 263.86. The simulation results show that the LCA is superior when compared with other competitor algorithms by providing a better solution and better statistical indicators.

Cantilever beam design problem

This problem belongs to the category of concrete engineering problems 102 . By maximizing the hollow square cross-section specifications, the overall weight of a cantilever beam is minimized. Figure 14 illustrates how the cantilever’s free node is subjected to a vertical force while the beam is tightly supported at one end. Five hollow square blocks of constant thickness make up the beam; their heights (or widths) are the decision variables, while the thickness remains constant (in this case, 2/3). The mathematical formulation of this design problem is as follows:

Cantilever beam design problem.

Table 38 show the cantilever beam problem comparison results. Table 39 shows the statistical results of optimization algorithms for the cantilever beam problem compared with different algorithms in terms of the mean, standard deviation, minimum, maximum, and median. The results show that LCA has provided the solution to this problem with optimal values for variables of (5.627E+00, 5.392E+00, 4.439E+00, 3.433E+00, and 3.204E+00) and an optimal solution of 1.3289. The simulation results show that the LCA is superior when compared with other competitor algorithms by providing a better solution and better statistical indicators.

This study has introduced a novel human-based meta-heuristic algorithm, namely the Learning Cooking Algorithm, to mimic the food preparation style in our daily lives. The strategies of LCA were mathematically designed in two phases: (i) children learn from their mothers, and (ii) children and mothers learn from a chef. These phases act like the exploration and exploitation mechanisms, which are vital for any meta-heuristic algorithm. The efficiency of the proposed LCA has been tested on 51 benchmark functions and CEC 2019 benchmark functions, and the results have been compared with eminent and top-performing algorithms. The experimental results demonstrate that the proposed algorithm LCA provides a better outcome to an optimization problem by preserving the proper balance between exploration and exploitation. The execution of the LCA algorithm to address seven real-world engineering problems reveals the superior performance of the proposed algorithm. Although LCA has delivered satisfactory results in solving the problems addressed in this paper, there are certain limitations to this approach in solving some multi-modal separable and multi-modal non-separable functions from the 51 benchmark functions and some functions from the CEC 2019 benchmark functions. In future work, this paper suggests several modifications, such as the inclusion of adaptive inertia factors and levy flight distribution, to improve the performance of the proposed LCA algorithm. It also recommends future research on developing a binary and multi-objective version of the LCA algorithm.

Data availability

Data and MATLAB code used during the study are available from the corresponding author by request.

Yang, X.-S. Nature-inspired Metaheuristic Algorithms (Luniver press, 2010).

Google Scholar

Abbasian, R., Mouhoub, M. & Jula, A. Solving graph coloring problems using cultural algorithms. In FLAIRS Conference (2011).

Shil, S. K., Mouhoub, M. & Sadaoui, S. An approach to solve winner determination in combinatorial reverse auctions using genetic algorithms. In Proc. of the 15th annual conference companion on Genetic and evolutionary computation , 75–76, https://doi.org/10.1145/2464576.2464611 (2013).

Mohapatra, P., Das, K. N. & Roy, S. An improvised competitive swarm optimizer for large-scale optimization. Soft Comput. Probl. Solv. SocProS 2017 (2), 591–601. https://doi.org/10.1007/978-981-13-1595-4_47 (2018).

Article Google Scholar

Mohapatra, P., Das, K. N., Roy, S., Kumar, R. & Dey, N. A novel multi-objective competitive swarm optimization algorithm. Int. J. Appl. Metaheur. Comput. (IJAMC) 11 , 114–129. https://doi.org/10.4018/IJAMC.2020100106 (2020).

Gopi, S. & Mohapatra, P. Fast random opposition-based learning aquila optimization algorithm. Heliyon https://doi.org/10.1016/j.heliyon.2024.e26187 (2024).

Article PubMed PubMed Central Google Scholar

Mohapatra, P., Roy, S., Das, K. N., Dutta, S. & Raju, M. S. S. A review of evolutionary algorithms in solving large scale benchmark optimisation problems. Int. J. Math. Oper. Res. 21 , 104–126. https://doi.org/10.1504/IJMOR.2022.120340 (2022).

Article MathSciNet Google Scholar

Mirjalili, S. & Mirjalili, S. Genetic algorithm. Evolut. Algorithms Neural Netw. Theory Appl. https://doi.org/10.1007/978-3-319-93025-1_4 (2019).

Price, K., Storn, R. M. & Lampinen, J. A. Differential Evolution: A Practical Approach to Global Optimization (Springer Science & Business Media, 2006).

Maheri, A., Jalili, S., Hosseinzadeh, Y., Khani, R. & Miryahyavi, M. A comprehensive survey on cultural algorithms. Swarm Evolut. Comput. https://doi.org/10.1016/j.swevo.2021.100846 (2021).

Simon, D. Biogeography-based optimization. IEEE Trans. Evolut. Comput. https://doi.org/10.1109/TEVC.2008.919004 (2008).

Tang, D., Dong, S., Jiang, Y., Li, H. & Huang, Y. Itgo: Invasive tumor growth optimization algorithm. Appl. Soft Comput. https://doi.org/10.1016/j.asoc.2015.07.045 (2015).

Rahman, C. M. & Rashid, T. A. A new evolutionary algorithm: Learner performance based behavior algorithm. Egypt. Inform. J. https://doi.org/10.1016/j.eij.2020.08.003 (2021).

Kennedy, J. & Eberhart, R. Particle swarm optimization. In Proc. of ICNN’95-international conference on neural networks , vol. 4, 1942–1948, https://doi.org/10.1109/ICNN.1995.488968 (1995).

Mirjalili, S., Mirjalili, S. M. & Lewis, A. Grey wolf optimizer. Adv. Eng. Softw. 69 , 46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007 (2014).

Chandran, V. & Mohapatra, P. Enhanced opposition-based grey wolf optimizer for global optimization and engineering design problems. Alex. Eng. J. 76 , 429–467. https://doi.org/10.1016/j.aej.2023.06.048 (2023).

Sarangi, P. & Mohapatra, P. Modified hybrid gwo-sca algorithm for solving optimization problems. Int. Conf. Data Anal. Comput. https://doi.org/10.1007/978-981-99-3432-4_10 (2022).

Dorigo, M., Maniezzo, V. & Colorni, A. Ant system: Optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. B (Cybern.) 26 , 29–41. https://doi.org/10.1109/3477.484436 (1996).

Article CAS PubMed Google Scholar

Mirjalili, S. & Lewis, A. The whale optimization algorithm. Adv. Eng. Softw. 95 , 51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008 (2016).

Kaur, S., Awasthi, L. K., Sangal, A. & Dhiman, G. Tunicate swarm algorithm: A new bio-inspired based metaheuristic paradigm for global optimization. Eng. Appl. Artif. Intell. 90 , 103541. https://doi.org/10.1016/j.engappai.2020.103541 (2020).

Hussien, A. G. et al. Crow search algorithm: Theory, recent advances, and applications. IEEE Access 8 , 173548–173565. https://doi.org/10.1109/ACCESS.2020.3024108 (2020).

Koohi, S. Z., Hamid, N. A. W. A., Othman, M. & Ibragimov, G. Raccoon optimization algorithm. IEEE Access 7 , 5383–5399. https://doi.org/10.1109/ACCESS.2018.2882568 (2018).

Gharehchopogh, F. S. Advances in tree seed algorithm: A comprehensive survey. Arch. Comput. Methods Eng. 29 , 3281–3304. https://doi.org/10.1007/s11831-021-09698-0 (2022).

Faramarzi, A., Heidarinejad, M., Mirjalili, S. & Gandomi, A. H. Marine predators algorithm: A nature-inspired metaheuristic. Expert Syst. Appl. 152 , 113377. https://doi.org/10.1016/j.eswa.2020.113377 (2020).

Braik, M., Sheta, A. & Al-Hiary, H. A novel meta-heuristic search algorithm for solving optimization problems: Capuchin search algorithm. Neural Comput. Appl. https://doi.org/10.1007/s00521-020-05145-6 (2021).

Braik, M. S. Chameleon swarm algorithm: A bio-inspired optimizer for solving engineering design problems. Expert Syst. Appl. https://doi.org/10.1016/j.eswa.2021.114685 (2021).

Abualigah, L. et al. Aquila optimizer: A novel meta-heuristic optimization algorithm. Comput. Ind. Eng. https://doi.org/10.1016/j.cie.2021.107250 (2021).

Mohapatra, P., Das, K. N. & Roy, S. A modified competitive swarm optimizer for large scale optimization problems. Appl. Soft Comput. 59 , 340–362. https://doi.org/10.1016/j.asoc.2017.05.060 (2017).

Sarangi, P. & Mohapatra, P. A novel cosine swarm algorithm for solving optimization problems. In Proc. of 7th International Conference on Harmony Search, Soft Computing and Applications: ICHSA 2022 , 427–434, https://doi.org/10.1007/978-981-19-2948-9_41 (2022).

Mohapatra, S. & Mohapatra, P. American zebra optimization algorithm for global optimization problems. Sci. Rep. 13 , 5211. https://doi.org/10.1038/s41598-023-31876-2 (2023).

Article ADS CAS PubMed PubMed Central Google Scholar

Sarangi, P. & Mohapatra, P. Evolved opposition-based mountain gazelle optimizer to solve optimization problems. J. King Saud Univ.-Comput. Inf. Sci. https://doi.org/10.1016/j.jksuci.2023.101812 (2023).

Mohapatra, S., Sarangi, P. & Mohapatra, P. An improvised grey wolf optimiser for global optimisation problems. Int. J. Math. Oper. Res. 26 , 263–281. https://doi.org/10.1504/IJMOR.2023.134490 (2023).

Gopi, S. & Mohapatra, P. Opposition-based learning cooking algorithm (olca) for solving global optimization and engineering problems. Int. J. Mod. Phys. C https://doi.org/10.1142/S0129183124500517 (2023).

Mohapatra, S. & Mohapatra, P. An improved golden jackal optimization algorithm using opposition-based learning for global optimization and engineering problems. Int. J. Comput. Intell. Syst. 16 , 147. https://doi.org/10.1007/s44196-023-00320-8 (2023).

Kumar, N., Kumar, R., Mohapatra, P. & Kumar, R. Modified competitive swarm technique for solving the economic load dispatch problem. J. Inf. Optim. Sci. 41 , 173–184. https://doi.org/10.1080/02522667.2020.1714184 (2020).

Huang, Z., Lin, Z., Zhu, Z. & Chen, J. An improved simulated annealing algorithm with excessive length penalty for fixed-outline floorplanning. IEEE Access 8 , 50911–50920. https://doi.org/10.1109/ACCESS.2020.2980135 (2020).

Eskandar, H., Sadollah, A., Bahreininejad, A. & Hamdi, M. Water cycle algorithm-a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput. Struct. 110 , 151–166. https://doi.org/10.1016/j.compstruc.2012.07.010 (2012).

Rashedi, E., Nezamabadi-Pour, H. & Saryazdi, S. Gsa: A gravitational search algorithm. Inf. Sci. 179 , 2232–2248. https://doi.org/10.1016/j.ins.2009.03.004 (2009).

Zhao, W., Wang, L. & Zhang, Z. Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl.-Based Syst. 163 , 283–304. https://doi.org/10.1016/j.knosys.2018.08.030 (2019).

Mirjalili, S., Mirjalili, S. M. & Hatamlou, A. Multi-verse optimizer: A nature-inspired algorithm for global optimization. Neural Comput. Appl. 27 , 495–513. https://doi.org/10.1007/s00521-015-1870-7 (2016).

Abedinpourshotorban, H., Shamsuddin, S. M., Beheshti, Z. & Jawawi, D. N. Electromagnetic field optimization: A physics-inspired metaheuristic optimization algorithm. Swarm Evolut. Comput. 26 , 8–22. https://doi.org/10.1016/j.swevo.2015.07.002 (2016).

Wei, Z., Huang, C., Wang, X., Han, T. & Li, Y. Nuclear reaction optimization: A novel and powerful physics-based algorithm for global optimization. IEEE Access 7 , 66084–66109. https://doi.org/10.1109/ACCESS.2019.2918406 (2019).

Kashan, A. H. A new metaheuristic for optimization: Optics inspired optimization (oio). Comput. Oper. Res. 55 , 99–125. https://doi.org/10.1016/j.cor.2014.10.011 (2015).

Faramarzi, A., Heidarinejad, M., Stephens, B. & Mirjalili, S. Equilibrium optimizer: A novel optimization algorithm. Knowl.-Based Syst. 191 , 105190. https://doi.org/10.1016/j.knosys.2019.105190 (2020).

Hashim, F. A., Hussain, K., Houssein, E. H., Mabrouk, M. S. & Al-Atabany, W. Archimedes optimization algorithm: A new metaheuristic algorithm for solving optimization problems. Appl. Intell. https://doi.org/10.1007/s10489-020-01893-z (2021).

Pereira, J. L. J. et al. Lichtenberg algorithm: A novel hybrid physics-based meta-heuristic for global optimization. Expert Syst. Appl. https://doi.org/10.1016/j.eswa.2020.114522 (2021).

Lam, A. Y. & Li, V. O. Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans. Evolut. Comput. 14 , 381–399 (2009).

Islam, M. R., Saifullah, C. K. & Mahmud, M. R. Chemical reaction optimization: Survey on variants. Evolut. Intell. 12 , 395–420. https://doi.org/10.1007/s12065-019-00246-1 (2019).

Alatas, B. Acroa: Artificial chemical reaction optimization algorithm for global optimization. Expert Syst. Appl. 38 , 13170–13180. https://doi.org/10.1016/j.eswa.2011.04.126 (2011).

Moghdani, R. & Salimifard, K. Volleyball premier league algorithm. Appl. Soft Comput. 64 , 161–185. https://doi.org/10.1016/j.asoc.2017.11.043 (2018).

Dehghani, M., Mardaneh, M., Guerrero, J. M., Malik, O. & Kumar, V. Football game based optimization: An application to solve energy commitment problem. Int. J. Intell. Eng. Syst. 13 , 514–523. https://doi.org/10.22266/ijies2020.1031.45 (2020).

Dehghani, M., Trojovská, E. & Trojovskỳ, P. A new human-based metaheuristic algorithm for solving optimization problems on the base of simulation of driving training process. Sci. Rep. 12 , 9924. https://doi.org/10.1038/s41598-022-14225-7 (2022).

Kaveh, A. & Kaveh, A. Tug of war optimization. Adv. Metaheur. Algorithms Opt. Des. Struct. https://doi.org/10.1007/978-3-030-59392-6_15 (2021).

Rao, R. V., Savsani, V. J. & Vakharia, D. Teaching-learning-based optimization: A novel method for constrained mechanical design optimization problems. Comput.-aided Des. 43 , 303–315. https://doi.org/10.1016/j.cad.2010.12.015 (2011).

Dehghani, M. et al. A new “doctor and patient’’ optimization algorithm: An application to energy commitment problem. Appl. Sci. 10 , 5791. https://doi.org/10.3390/app10175791 (2020).

Article CAS Google Scholar

Moosavi, S. H. S. & Bardsiri, V. K. Poor and rich optimization algorithm: A new human-based and multi populations algorithm. Eng. Appl. Artif. Intell. 86 , 165–181. https://doi.org/10.1016/j.engappai.2019.08.025 (2019).

Mousavirad, S. J. & Ebrahimpour-Komleh, H. Human mental search: A new population-based metaheuristic optimization algorithm. Appl. Intell. 47 , 850–887. https://doi.org/10.1007/s10489-017-0903-6 (2017).

Glover, F. Tabu search-part I. ORSA J. Comput. 1 , 190–206. https://doi.org/10.1287/ijoc.1.3.190 (1989).

Glover, F. Tabu search-part II. ORSA J. Comput. 2 , 4–32. https://doi.org/10.1287/ijoc.2.1.4 (1990).

Atashpaz-Gargari, E. & Lucas, C. Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. In 2007 IEEE Congress on Evolutionary Computation , 4661–4667, https://doi.org/10.1109/CEC.2007.4425083 (2007).

Kaveh, A. & Mahdavi, V. R. Colliding bodies optimization: A novel meta-heuristic method. Comput. Struct. 139 , 18–27. https://doi.org/10.1016/j.compstruc.2014.04.005 (2014).

Sadollah, A., Bahreininejad, A., Eskandar, H. & Hamdi, M. Mine blast algorithm: A new population based algorithm for solving constrained engineering optimization problems. Appl. Soft Comput. 13 , 2592–2612. https://doi.org/10.1016/j.asoc.2012.11.026 (2013).

Dai, C., Zhu, Y. & Chen, W. Seeker optimization algorithm. In Computational Intelligence and Security: International Conference, CIS. Guangzhou, China, November 3–6, 2006. Revised Selected Papers , 167–176. https://doi.org/10.1007/978-3-540-74377-4_18 (2006).

Eita, M. & Fahmy, M. Group counseling optimization: A novel approach. In Research and Development in Intelligent Systems XXVI: Incorporating Applications and Innovations in Intelligent Systems XVII (eds Eita, M. & Fahmy, M.) 195–208 (Springer, 2009). https://doi.org/10.1007/978-1-84882-983-1_14 .

Chapter Google Scholar

Eita, M. & Fahmy, M. Group counseling optimization. Appl. Soft Comput. 22 , 585–604. https://doi.org/10.1016/j.asoc.2014.03.043 (2014).

Geem, Z. W., Kim, J. H. & Loganathan, G. V. A new heuristic optimization algorithm: Harmony search. Simulation 76 , 60–68. https://doi.org/10.1177/003754970107600201 (2001).

Kashan, A. H. League championship algorithm (LCA): An algorithm for global optimization inspired by sport championships. Appl. Soft Comput. https://doi.org/10.1016/j.asoc.2013.12.005 (2014).

Al-Betar, M. A., Alyasseri, Z. A. A., Awadallah, M. A. & Abu Doush, I. Coronavirus herd immunity optimizer (chio). Neural Comput. Appl. 33 , 5011–5042. https://doi.org/10.1007/s00521-020-05296-6 (2021).

Article PubMed Google Scholar

Braik, M., Ryalat, M. H. & Al-Zoubi, H. A novel meta-heuristic algorithm for solving numerical optimization problems: Ali baba and the forty thieves. Neural Comput. Appl. https://doi.org/10.1007/s00521-021-06392-x (2022).

Sharma, S., Saha, A. K. & Lohar, G. Optimization of weight and cost of cantilever retaining wall by a hybrid metaheuristic algorithm. Eng. Comput. https://doi.org/10.1007/s00366-021-01294-x (2021).

Ang, K. M. et al. Modified teaching-learning-based optimization and applications in multi-response machining processes. Comput. Ind. Eng. 174 , 108719. https://doi.org/10.1016/j.cie.2022.108719 (2022).

Sharma, S., Saha, A. K., Majumder, A. & Nama, S. Mpboa-a novel hybrid butterfly optimization algorithm with symbiosis organisms search for global optimization and image segmentation. Multimed. Tools Appl. 80 , 12035–12076. https://doi.org/10.1007/s11042-020-10053-x (2021).

Jiyue, E., Liu, J. & Wan, Z. A novel adaptive algorithm of particle swarm optimization based on the human social learning intelligence. Swarm Evolut. Comput. 80 , 101336. https://doi.org/10.1016/j.swevo.2023.101336 (2023).

Bac, B. H. et al. Performance evaluation of nanotubular halloysites from weathered pegmatites in removing heavy metals from water through novel artificial intelligence-based models and human-based optimization algorithm. Chemosphere 282 , 131012. https://doi.org/10.1016/j.chemosphere.2021.131012 (2021).

Chakraborty, S., Sharma, S., Saha, A. K. & Saha, A. A novel improved whale optimization algorithm to solve numerical optimization and real-world applications. Artif. Intell. Rev. https://doi.org/10.1007/s10462-021-10114-z (2022).

Chakraborty, P., Sharma, S. & Saha, A. K. Convergence analysis of butterfly optimization algorithm. Soft Comput. 27 , 7245–7257. https://doi.org/10.1007/s00500-023-07920-8 (2023).

Sahoo, S. K., Sharma, S. & Saha, A. K. A novel variant of moth flame optimizer for higher dimensional optimization problems. J. Bionic Eng. https://doi.org/10.1007/s42235-023-00357-7 (2023).

Sharma, S., Khodadadi, N., Saha, A. K., Gharehchopogh, F. S. & Mirjalili, S. Non-dominated sorting advanced butterfly optimization algorithm for multi-objective problems. J. Bionic Eng. 20 , 819–843. https://doi.org/10.1007/s42235-022-00288-9 (2023).

Sharma, S., Chakraborty, S., Saha, A. K., Nama, S. & Sahoo, S. K. mlboa: A modified butterfly optimization algorithm with Lagrange interpolation for global optimization. J. Bionic Eng. 19 , 1161–1176. https://doi.org/10.1007/s42235-022-00175-3 (2022).

Mirjalili, S. et al. Salp swarm algorithm: A bio-inspired optimizer for engineering design problems. Adv. Eng. Softw. 114 , 163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002 (2017).

Chopra, N. & Ansari, M. M. Golden jackal optimization: A novel nature-inspired optimizer for engineering applications. Expert Syst. Appl. 198 , 116924. https://doi.org/10.1016/j.eswa.2022.116924 (2022).

Zhong, C., Li, G. & Meng, Z. Beluga whale optimization: A novel nature-inspired metaheuristic algorithm. Knowl.-Based Syst. 251 , 109215. https://doi.org/10.1016/j.knosys.2022.109215 (2022).

Heidari, A. A. et al. Harris hawks optimization: Algorithm and applications. Future Gen. Comput. Syst. 97 , 849–872. https://doi.org/10.1016/j.future.2019.02.028 (2019).

Abdollahzadeh, B., Gharehchopogh, F. S., Khodadadi, N. & Mirjalili, S. Mountain gazelle optimizer: A new nature-inspired metaheuristic algorithm for global optimization problems. Adv. Eng. Softw. 174 , 103282. https://doi.org/10.1016/j.advengsoft.2022.103282 (2022).

Seyyedabbasi, A. & Kiani, F. Sand cat swarm optimization: A nature-inspired algorithm to solve global optimization problems. Eng. Comput. https://doi.org/10.1007/s00366-022-01604-x (2022).

Faridmehr, I., Nehdi, M. L., Davoudkhani, I. F. & Poolad, A. Mountaineering team-based optimization: A novel human-based metaheuristic algorithm. Mathematics 11 , 1273. https://doi.org/10.3390/math11051273 (2023).

Wolpert, D. H. & Macready, W. G. No free lunch theorems for optimization. IEEE Trans. Evolut. Comput. 1 , 67–82. https://doi.org/10.1109/4235.585893 (1997).

Zhao, W., Wang, L. & Mirjalili, S. Artificial hummingbird algorithm: A new bio-inspired optimizer with its engineering applications. Comput. Methods Appl. Mech. Eng. 388 , 114194. https://doi.org/10.1016/j.cma.2021.114194 (2022).

Article ADS MathSciNet Google Scholar

Viktorin, A., Senkerik, R., Pluhacek, M., Kadavy, T. & Zamuda, A. Dish algorithm solving the CEC 2019 100-digit challenge. In 2019 IEEE Congress on Evolutionary Computation (CEC) (eds Viktorin, A. et al. ) 1–6 (IEEE, 2019).

Mohapatra, S. & Mohapatra, P. Fast random opposition-based learning golden jackal optimization algorithm. Knowl.-Based Syst. https://doi.org/10.1016/j.knosys.2023.110679 (2023).

Wang, X., Li, C., Zhu, J. & Meng, Q. L-shade-e: Ensemble of two differential evolution algorithms originating from l-shade. Inf. Sci. 552 , 201–219. https://doi.org/10.1016/j.ins.2020.11.055 (2021).

Hansen, N., Müller, S. D. & Koumoutsakos, P. Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolut. Comput. 11 , 1–18. https://doi.org/10.1162/106365603321828970 (2003).

Nadimi-Shahraki, M. H., Taghian, S. & Mirjalili, S. An improved grey wolf optimizer for solving engineering problems. Expert Syst. Appl. 166 , 113917. https://doi.org/10.1016/j.eswa.2020.113917 (2021).

Gopi, S. & Mohapatra, P. A modified whale optimisation algorithm to solve global optimisation problems. In Proc. of 7th International Conference on Harmony Search, Soft Computing and Applications: ICHSA 2022 , 465–477, https://doi.org/10.1007/978-981-19-2948-9_45 (2022).

Wilcoxon, F. Individual comparisons by ranking methods. In Breakthroughs in Statistics: Methodology and Distribution (ed. Wilcoxon, F.) 196–202 (Springer, 1992).

Friedman, M. The use of ranks to avoid the assumption of normality implicit in the analysis of variance. J. Am. Stat. Assoc. 32 , 675–701. https://doi.org/10.1080/01621459.1937.10503522 (1937).

Hodges, J. L. Jr. & Lehmann, E. L. Rank methods for combination of independent experiments in analysis of variance. In Selected Works of EL Lehmann (eds Hodges, J. L., Jr. & Lehmann, E. L.) 403–418 (Springer, 2011).

Arora, J. S. Introduction to Optimum Design (Elsevier, 2004).

Book Google Scholar

Coello, C. A. C. Use of a self-adaptive penalty approach for engineering optimization problems. Comput. Ind. 41 , 113–127. https://doi.org/10.1016/S0166-3615(99)00046-9 (2000).

Sattar, D. & Salim, R. A smart metaheuristic algorithm for solving engineering problems. Eng. Comput. 37 , 2389–2417. https://doi.org/10.1007/s00366-020-00951-x (2021).

Sandgren, E. Nonlinear integer and discrete programming in mechanical design. Int. Des. Eng. Tech. Conf. Comput. Inf. Eng. Conf. 26584 , 95–105. https://doi.org/10.1115/DETC1988-0012 (1988).

Chickermane, H. & Gea, H. C. Structural optimization using a new local approximation method. Int. J. Numer. Methods Eng. 39 , 829–846. https://doi.org/10.1002/(SICI)1097-0207(19960315)39:5/3C829::AID-NME884/3E3.0.CO;2-U (1996).

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Americans’ Dismal Views of the Nation’s Politics

1. the biggest problems and greatest strengths of the u.s. political system, table of contents.

The impact of partisan polarization
Persistent concerns over money in politics
Views of the parties and possible changes to the two-party system
Other important findings
Explore chapters of this report
In their own words: Americans on the political system’s biggest problems
In their own words: Americans on the political system’s biggest strengths
Are there clear solutions to the nation’s problems?
Evaluations of the political system
Trust in the federal government
Feelings toward the federal government
The relationship between the federal and state governments
Americans’ ratings of their House member, governor and local officials
Party favorability ratings
Most characterize their party positively
Quality of the parties’ ideas
Influence in congressional decision-making
Views on limiting the role of money in politics
Views on what kinds of activities can change the country for the better
How much can voting affect the future direction of the country?
Views of members of Congress
In their own words: Americans’ views of the major problems with today’s elected officials
How much do elected officials care about people like me?
What motivates people to run for office?
Quality of recent political candidates
In elections, is there usually at least one candidate who shares your views?
What the public sees as most important in political candidates
Impressions of the people who will be running for president in 2024
Views about presidential campaigns
How much of an impact does who is president have on your life?
Whose priorities should the president focus on?
How different are the Republican and Democratic parties?
Views of how well the parties represent people’s interests
What if there were more political parties?
Would more parties make solving problems easier or harder?
How likely is it that an independent candidate will become president?
Americans who feel unrepresented by the parties have highly negative views of the political system
Views of the Electoral College
Should the size of the U.S. House of Representatives change?
Senate seats and population size
Younger adults more supportive of structural changes
Politics in a single word or phrase: An outpouring of negative sentiments
Negative emotions prevail when Americans think about politics
Americans say the tone of political debate in the country has worsened
Which political topics get too much – and too little – attention?
Majority of Americans find it stressful to talk politics with people they disagree with
Acknowledgments

The public sees a number of specific problems with American politics. Partisan fighting, the high cost of political campaigns, and the outsize influence of special interests and lobbyists are each seen as characteristic of the U.S. political system by at least 84% of Americans.

Yet 63% also say that “ordinary Americans care about making the political system work well” is a good description of U.S. politics today. Still, when asked to describe a strength of the political system in their own words, more than half either say “nothing” (22%) or decline to give an answer (34%).

Americans view negative statements as better descriptions of the political system than positive ones

Chart shows widely shared criticisms of politics: Partisan fights, costly campaigns, influence of special interests

More than eight-in-ten adults say that each of the following is at least a somewhat good description of the U.S. political system today:

Republicans and Democrats are more focused on fighting each other than on solving problems (86%);
The cost of political campaigns makes it hard for good people to run for office (85%);
Special interest groups and lobbyists have too much say in what happens in politics (84%).

About six-in-ten (63%) think ordinary Americans want to make the political system work well. This is the rare positive sentiment that a majority views as a good descriptor of the political system.

Fewer than half of adults hold the view that the government deserves more credit than it gets: Majorities say that “the federal government does more for ordinary Americans than people give it credit for” (59%) and “Congress accomplishes more than people give it credit for” (65%) are both bad descriptions of the political system.

Nearly seven-in-ten adults express frustration with the availability of unbiased information about politics: 68% say the statement “it is easy to find unbiased information about what is happening in politics” is not a good description of the political system.

And just 22% of Americans say that political leaders facing consequences for acting unethically is a good description of the political system. They are more than three times as likely to say that this is a bad description (76% say this).

Many critiques of the political system are bipartisan

Partisans have similar views of many of the descriptions of the political system included in the survey.

Chart shows Partisans largely agree in views of many problems with the political system

Overwhelming majorities in both parties think there is too much partisan fighting, campaigns cost too much, and lobbyists and special interests have too much say in politics. And just 24% of Democrats and Democratic-leaning independents and 20% of Republicans and Republican leaners say that political leaders face consequences if they act unethically.

The widest partisan gap is over a description of the federal government. Democrats are roughly twice as likely as Republicans to say “the federal government does more for ordinary Americans than people give it credit for” (54% vs. 26%).

There is a narrower gap in views of Congress’ accomplishments: 37% of Democrats and 28% of Republicans say it accomplishes more than people give it credit for.

Democrats are also more likely to say, “It is easy to find unbiased information about what is happening in politics” (36% of Democrats and 25% of Republicans say this is a good description of the political system today), while Republicans are slightly more likely than Democrats to view ordinary Americans as wanting to make the political system work well (67% of Republicans and 61% of Democrats say this is a good description).

Chart shows roughly a third of Americans say ‘politicians’ are the biggest problem with the political system today

When asked to describe in their own words the biggest problem with the political system in the U.S. today, Americans point to a wide range of factors.

Negative characteristics attributed to politicians and political leaders are a common complaint: 31% of U.S. adults say politicians are the biggest problem with the system, including 15% who point to greed or corruption and 7% who cite dishonesty or a lack of trustworthiness.

The biggest problem, according to one woman in her 50s, is that politicians are “hiding the truth and fulfilling their own agendas.” Similarly, a man in his 30s says, “They don’t work for the people. They are too corrupt and busy filling their pockets.”

Explore more voices: The political system’s biggest problems

What do you see as the biggest problem with the political system in the U.S. today?

“An almost total lack of credibility and trust. Coupled with a media that’s so biased, that they’ve lost all objectivity.” –Man, 70s

“Lying about intentions or not following through with what elected officials said they would do.” –Woman, 20s

“Blind faith in political figures.” –Woman, 50s

“Our elected officials would rather play political games than serve the needs of their constituents.” –Woman, 50s

“Same politicians in office too long.” –Woman, 30s

“Extremism on both sides exploited by the mainstream media for ratings. It is making it impossible for both parties to work together.” –Man, 30s

“It has become too polarized. No one is willing to compromise or be moderate.” –Woman, 40s

“Too much money in politics coming from large corporations and special interest.” –Man, 30s

“The people have no say in important matters, we have NO representation at all. Our lawmakers are isolated and could care less what we want.” –Man, 60s

About two-in-ten adults cite deep divisions between the parties as the biggest problem with the U.S. political system, with respondents describing a lack of cooperation between the parties or among elected leaders in Washington.

“Both of the political parties are so busy trying to stop the other party, they are wasting their opportunities to solve the problems faced by our nation,” in the view of one man in his 70s.

Even as some blame polarization, others (10% of respondents) identify the other party as the system’s biggest problem. Some Republicans say that the biggest problem is “Democrats” while some Democrats simply say “Republicans.”

Smaller but substantial shares of adults name the media and political discourse (9%), the influence of money in politics (7%), government’s perceived failures (6%), specific policy areas and issues (6%) or problems with elections and voting (4%) as the biggest problem with the political system today.

Chart shows those who see strengths in the U.S. political system often cite constitutional principles, democratic values

Far fewer adults name a specific strength of the political system today when asked to describe the system’s biggest strength in their own words. More than half either say that the system lacks a biggest strength (22%) or decline to answer (34%). As one woman in her 60s writes, “I’m not seeing any strengths!”

Among those who do identify strengths of the U.S. political system, the structure of political institutions and the principles that define the constitutional order are named most frequently (by 12% of respondents). Many respondents specifically point to the Constitution itself or refer to the separation of powers or the checks and balances created by the Constitution.

A man in his 20s believes that the “separation of powers and federalism work pretty well,” while one in his 30s writes that the system’s greatest strength is “the checks and balances to make sure that monumental changes aren’t made unilaterally.”

Explore more voices: The political system’s biggest strengths

What do you see as the biggest strength of the U.S. political system today?

“Everyone getting a say; democracy.” –Woman, 40s

“The right to have your opinions heard.” –Man, 60s

“In spite of our differences, we are still a democracy, and I believe there are people within our government who still care and are interested in the betterment of our country.” –Woman, 50s

“The freedom of speech and religion” –Woman, 50s

“If we have fair, honest elections we can vote out the corruption and/or incompetent politicians.” –Man, 70s

“The Constitution.” –Man, 50s

“The checks and balances to control the power of any office. The voice of the people and the options to remove an official from office.” –Man, 60s

“New, younger voices in government.” –Woman, 40s

“If we can’t get more bipartisanship we’ll become weaker. Our biggest strength is our working together.” –Woman, 60s

“The way that every two years the people get to make their voice heard.” –Man, 30s

About one-in-ten (9%) refer to individual freedoms and related democratic values, while a similar share (8%) discuss the right to vote and the existence of free elections. A woman in her 70s echoes many similar comments when she points to “the possibility of change in upcoming elections.”

However, even some of the descriptions of positive characteristics of the system are couched in respondents’ doubts about the way the system is working today. One woman in her 50s adds a qualification to what she views as the system’s biggest strength, saying, “Theoretically every voter has a say.”

Smaller shares of the public point to the positive characteristics of some politicians (4%) or the positive characteristics of the American people (4%) as reasons for optimism.

The public remains roughly evenly split over whether there are clear solutions to the biggest issues facing the country. Half of Americans today say there are clear solutions to most of the big issues facing the country, while about as many (48%) say most big issues don’t have clear solutions.

Chart shows Americans are split over whether there are clear solutions to big national issues

There are relatively modest demographic and political differences in perceptions of whether the solutions to the nations’ problems are clear or not.

While both men and women are relatively divided on this question, women are 6 percentage points more likely to think the big issues facing the country don’t have clear solutions.

Race and ethnicity

While 43% of Hispanic adults and about half of Black (50%) and White (48%) adults say there aren’t clear solutions for most big issues, that rises to 62% among Asian adults.

Age differences on this question are modest, but those under 30 are slightly more likely than those 30 and older to say most big issues have clear solutions.

Partisanship and political engagement

Both Republicans and Democrats are relatively split on this question, though Republicans are slightly more likely to say there are clear solutions to most big issues.

Those with higher levels of political engagement are more likely to say there are clear solutions to most big issues facing the country.

About six-in-ten adults with high levels of political engagement (61%) say there are clear solutions to big issues today, compared with half of those with medium levels of engagement and 41% of those with lower engagement.

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10 Steps to Problem Solving for Engineers
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10 Steps to Problem Solving for Engineers

The stages of problem solving like a pro:

Triggering correlations

Recent Posts

Engineering Problem Solving ¶

Steps in solving ‘real world’ engineering problems ¶

Defining problems collaboratively ¶

How ‘good’ a solution do you need ¶

Steps in solving well-defined engineering process problems, including textbook problems ¶

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Problem Solving for New Engineers What Every Engineering Manager Wants You to Know

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An Engineer's Guide to Solving Problems Paperback – January 31, 2014

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1 Identifying Problems & Customer Needs

Why is it Critical to Define the Problem?

The Anatomy of an Engineering Problem

Are You Solving the Wrong Problem?

1.2 Addressing Customer Needs

1.3 Converting Customer Needs to Quantitative Metrics

Asking Questions

1.4 Textbook Problem Analogy to Engineering Design

1.5 Organizing the Needs via Kano Model Analysis

Categorizing Customer Needs with the Kano Model

Attractive Needs “Migrate” Over Time

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How to Solve Any Problem in Engineering in Three Basic Steps

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Student Approaches to Engineering Problem-Solving - School of Engineering Education - Purdue University

Student Approaches to Engineering Problem-Solving

Everyday Problem Solving in Engineering: Lessons for Engineering Educators

790 Citations

Engineering: The nature of problems

Introduction

Learning outcomes

1 Problems and innovation

1.2 Innovation by context

Box 1 Innovation by context – an example

1.3 Innovation by development

Box 2 Innovation by development – an example

1.4 Routine solutions

Box 3 Routine solution – examples

2 Where does the need arise?

Box 4 Meeting the liquid challenges

3 Needs and problems

4 Looking for solutions

4.2 From a need to a problem