steps involved in problem solving agent

Problem Solving Agents in Artificial Intelligence

In this post, we will talk about Problem Solving agents in Artificial Intelligence, which are sort of goal-based agents. Because the straight mapping from states to actions of a basic reflex agent is too vast to retain for a complex environment, we utilize goal-based agents that may consider future actions and the desirability of outcomes.

You Will Learn

Problem Solving Agents

Problem Solving Agents decide what to do by finding a sequence of actions that leads to a desirable state or solution.

An agent may need to plan when the best course of action is not immediately visible. They may need to think through a series of moves that will lead them to their goal state. Such an agent is known as a problem solving agent , and the computation it does is known as a search .

The problem solving agent follows this four phase problem solving process:

• Goal Formulation: This is the first and most basic phase in problem solving. It arranges specific steps to establish a target/goal that demands some activity to reach it. AI agents are now used to formulate goals.
• Problem Formulation: It is one of the fundamental steps in problem-solving that determines what action should be taken to reach the goal.
• Search: After the Goal and Problem Formulation, the agent simulates sequences of actions and has to look for a sequence of actions that reaches the goal. This process is called search, and the sequence is called a solution . The agent might have to simulate multiple sequences that do not reach the goal, but eventually, it will find a solution, or it will find that no solution is possible. A search algorithm takes a problem as input and outputs a sequence of actions.
• Execution: After the search phase, the agent can now execute the actions that are recommended by the search algorithm, one at a time. This final stage is known as the execution phase.

Problems and Solution

Before we move into the problem formulation phase, we must first define a problem in terms of problem solving agents.

A formal definition of a problem consists of five components:

Initial State

Transition model.

It is the agent’s starting state or initial step towards its goal. For example, if a taxi agent needs to travel to a location(B), but the taxi is already at location(A), the problem’s initial state would be the location (A).

It is a description of the possible actions that the agent can take. Given a state s, Actions ( s ) returns the actions that can be executed in s. Each of these actions is said to be appropriate in s.

It describes what each action does. It is specified by a function Result ( s, a ) that returns the state that results from doing action an in state s.

The initial state, actions, and transition model together define the state space of a problem, a set of all states reachable from the initial state by any sequence of actions. The state space forms a graph in which the nodes are states, and the links between the nodes are actions.

It determines if the given state is a goal state. Sometimes there is an explicit list of potential goal states, and the test merely verifies whether the provided state is one of them. The goal is sometimes expressed via an abstract attribute rather than an explicitly enumerated set of conditions.

It assigns a numerical cost to each path that leads to the goal. The problem solving agents choose a cost function that matches its performance measure. Remember that the optimal solution has the lowest path cost of all the solutions .

Example Problems

The problem solving approach has been used in a wide range of work contexts. There are two kinds of problem approaches

• Standardized/ Toy Problem: Its purpose is to demonstrate or practice various problem solving techniques. It can be described concisely and precisely, making it appropriate as a benchmark for academics to compare the performance of algorithms.
• Real-world Problems: It is real-world problems that need solutions. It does not rely on descriptions, unlike a toy problem, yet we can have a basic description of the issue.

Some Standardized/Toy Problems

Vacuum world problem.

Let us take a vacuum cleaner agent and it can move left or right and its jump is to suck up the dirt from the floor.

The vacuum world’s problem can be stated as follows:

States: A world state specifies which objects are housed in which cells. The objects in the vacuum world are the agent and any dirt. The agent can be in either of the two cells in the simple two-cell version, and each call can include dirt or not, therefore there are 2×2×2 = 8 states. A vacuum environment with n cells has n×2 n states in general.

Initial State: Any state can be specified as the starting point.

Actions: We defined three actions in the two-cell world: sucking, moving left, and moving right. More movement activities are required in a two-dimensional multi-cell world.

Transition Model: Suck cleans the agent’s cell of any filth; Forward moves the agent one cell forward in the direction it is facing unless it meets a wall, in which case the action has no effect. Backward moves the agent in the opposite direction, whilst TurnRight and TurnLeft rotate it by 90°.

Goal States: The states in which every cell is clean.

Action Cost: Each action costs 1.

8 Puzzle Problem

In a sliding-tile puzzle , a number of tiles (sometimes called blocks or pieces) are arranged in a grid with one or more blank spaces so that some of the tiles can slide into the blank space. One variant is the Rush Hour puzzle, in which cars and trucks slide around a 6 x 6 grid in an attempt to free a car from the traffic jam. Perhaps the best-known variant is the 8- puzzle (see Figure below ), which consists of a 3 x 3 grid with eight numbered tiles and one blank space, and the 15-puzzle on a 4 x 4  grid. The object is to reach a specified goal state, such as the one shown on the right of the figure. The standard formulation of the 8 puzzles is as follows:

STATES : A state description specifies the location of each of the tiles.

INITIAL STATE : Any state can be designated as the initial state. (Note that a parity property partitions the state space—any given goal can be reached from exactly half of the possible initial states.)

ACTIONS : While in the physical world it is a tile that slides, the simplest way of describing action is to think of the blank space moving Left , Right , Up , or Down . If the blank is at an edge or corner then not all actions will be applicable.

TRANSITION MODEL : Maps a state and action to a resulting state; for example, if we apply Left to the start state in the Figure below, the resulting state has the 5 and the blank switched.

GOAL STATE :  It identifies whether we have reached the correct goal state. Although any state could be the goal, we typically specify a state with the numbers in order, as in the Figure above.

ACTION COST : Each action costs 1.

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Problem-Solving Agents In Artificial Intelligence

In artificial intelligence, a problem-solving agent refers to a type of intelligent agent designed to address and solve complex problems or tasks in its environment. These agents are a fundamental concept in AI and are used in various applications, from game-playing algorithms to robotics and decision-making systems. Here are some key characteristics and components of a problem-solving agent:

• Perception : Problem-solving agents typically have the ability to perceive or sense their environment. They can gather information about the current state of the world, often through sensors, cameras, or other data sources.
• Knowledge Base : These agents often possess some form of knowledge or representation of the problem domain. This knowledge can be encoded in various ways, such as rules, facts, or models, depending on the specific problem.
• Reasoning : Problem-solving agents employ reasoning mechanisms to make decisions and select actions based on their perception and knowledge. This involves processing information, making inferences, and selecting the best course of action.
• Planning : For many complex problems, problem-solving agents engage in planning. They consider different sequences of actions to achieve their goals and decide on the most suitable action plan.
• Actuation : After determining the best course of action, problem-solving agents take actions to interact with their environment. This can involve physical actions in the case of robotics or making decisions in more abstract problem-solving domains.
• Feedback : Problem-solving agents often receive feedback from their environment, which they use to adjust their actions and refine their problem-solving strategies. This feedback loop helps them adapt to changing conditions and improve their performance.
• Learning : Some problem-solving agents incorporate machine learning techniques to improve their performance over time. They can learn from experience, adapt their strategies, and become more efficient at solving similar problems in the future.

Problem-solving agents can vary greatly in complexity, from simple algorithms that solve straightforward puzzles to highly sophisticated AI systems that tackle complex, real-world problems. The design and implementation of problem-solving agents depend on the specific problem domain and the goals of the AI application.

Hello, I’m Hridhya Manoj. I’m passionate about technology and its ever-evolving landscape. With a deep love for writing and a curious mind, I enjoy translating complex concepts into understandable, engaging content. Let’s explore the world of tech together

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What is the problem-solving agent in artificial intelligence?

Are you curious to know how machines can solve complex problems, just like humans? Enter the world of artificial intelligence and meet one of its most critical players- the Problem-Solving Agent. In this blog post, we’ll explore what a problem-solving agent is, how it works in AI systems and some exciting real-world applications that showcase its potential. So, buckle up for an insightful journey into the fascinating world of AI problem solvers!

Problem-solving in artificial intelligence can be quite complex, requiring the use of multiple algorithms and data structures. One critical player is the Problem-Solving Agent, which helps machines find solutions to problems. In this blog post, we’ll explore what a problem-solving agent is, how it works in AI systems and some exciting real-world applications that showcase its potential. So, buckle up for an insightful journey into the fascinating world of AI problem solvers!

Table of Contents

What is Problem Solving Agent?

Problem-solving in artificial intelligence is the process of finding a solution to a problem. There are many different types of problems that can be solved, and the methods used will depend on the specific problem. The most common type of problem is finding a solution to a maze or navigation puzzle.

Other types of problems include identifying patterns, predicting outcomes, and determining solutions to systems of equations. Each type of problem has its own set of techniques and tools that can be used to solve it.

There are three main steps in problem-solving in artificial intelligence:

1) understanding the problem: This step involves understanding the specifics of the problem and figuring out what needs to be done to solve it.

2) generating possible solutions: This step involves coming up with as many possible solutions as possible based on information about the problem and what you know about how computers work.

3) choosing a solution: This step involves deciding which solution is best based on what you know about the problem and your options for solving it.

Types of Problem-Solving Agents

Problem-solving agents are a type of artificial intelligence that helps automate problem-solving. They can be used to solve problems in natural language, algebra, calculus, statistics, and machine learning.

There are three types of problem-solving agents: propositional, predicate, and automata. Propositional problem-solving agents can understand simple statements like “draw a line between A and B” or “find the maximum value of x.” Predicate problem-solving agents can understand more complex statements like “find the shortest path between two points” or “find all pairs of snakes in a jar.” Automata is the simplest form of problem-solving agent and can only understand sequences of symbols like “draw a square.”

Classification of Problem-Solving Agents

Problem-solving agents can be classified as general problem solvers or domain-specific problem solvers. General problem solvers can solve a wide range of problems, while domain-specific problem solvers are better suited for solving specific types of problems.

General problem solvers include AI programs that are designed to solve general artificial intelligence (AI) problems such as learning how to navigate a 3D environment or playing games. Domain-specific problem solvers include programs that have been specifically tailored to solve certain types of problems, such as photo editing or medical diagnosis.

Both general and domain-specific problem-solving agents can be used in conjunction with other AI tools, including natural language processing (NLP) algorithms and machine learning models. By combining these tools, we can achieve more effective and efficient outcomes in our data analysis and machine learning processes.

Applications of Problem-Solving Agents

Problem-solving agents can be used in a number of different ways in artificial intelligence. They can be used to help find solutions to specific problems or tasks, or they can be used to generalize a problem and find potential solutions. In either case, the problem-solving agent is able to understand complex instructions and carry out specific tasks.

Problem-solving is an essential skill for any artificial intelligence developer. With AI becoming more prevalent in our lives, it’s important that we have a good understanding of how to approach and solve problems. In this article, we’ll discuss some common problem-solving techniques and provide you with tips on how to apply them when developing AI applications. By applying these techniques systematically, you can build robust AI solutions that work correctly and meet the needs of your users.

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Understanding Problem Solving Agents in Artificial Intelligence

Have you ever wondered how artificial intelligence systems are able to solve complex problems? Problem solving agents play a key role in AI, using algorithms and strategies to find solutions to a variety of challenges.

Problem-solving agents in artificial intelligence are a type of agent that are designed to solve complex problems in their environment. They are a core concept in AI and are used in everything from games like chess to self-driving cars.

In this blog, we will explore problem solving agents in artificial intelligence, types of problem solving agents in AI, real-world applications, and many more.

Table of Contents

What is problem solving agents in artificial intelligence, type 1: simple reflex agents, type 2: model-based agents, type 3: goal-based agents, 2. knowledge base, 3. reasoning engine, 4. actuators, gaming agents, virtual assistants, recommendation systems, scheduling and planning.

A Problem-Solving Agent is a special computer program in Artificial Intelligence. It can perceive the world around it through sensors. Sensors help it gather information.

The agent processes this information using its knowledge base. A knowledge base is like the agent’s brain. It stores facts and rules. Using its knowledge, the agent can reason about the best actions. It can then take those actions to achieve goals.

In simple words, a Problem-Solving Agent observes its environment. It understands the situation. Then it figures out how to solve problems or finish tasks.

These agents use smart algorithms. The algorithms allow them to think and act like humans. Problem-solving agents are very important in AI. They help tackle complex challenges efficiently.

Types of Problem Solving Agents in AI

There are different types of Problem Solving Agents in AI. Each type works in its own way. Below are the different types of problem solving agents in AI:

Simple Reflex Agents are the most basic kind. They simply react to the current situation they perceive. They don’t consider the past or future.

For example, a room thermostat is a Simple Reflex Agent. It turns the heat on or off based only on the current room temperature.

Model-based agents are more advanced. They create an internal model of their environment. This model helps them track how the world changes over time.

Using this model, they can plan ahead for future situations. Self-driving cars use Model-Based Agents to predict how traffic will flow.

Goal-based agents are the most sophisticated type. They can set their own goals and figure out sequences of actions to achieve those goals.

These agents constantly update their knowledge as they pursue their goals. Virtual assistants like Siri or Alexa are examples of Goal-Based Agents assisting us with various tasks.

Each type has its own strengths based on the problem they need to solve. Simple problems may just need Reflex Agents, while complex challenges require more advanced Model-Based or Goal-Based Agents.

Components of a Problem Solving Agent in AI

A Problem Solving Agent has several key components that work together. Let’s break them down:

Sensors are like the agent’s eyes and ears. They collect information from the environment around the agent. For example, a robot’s camera and motion sensors act as sensors.

The Knowledge Base stores all the facts, rules, and information the agent knows. It’s like the agent’s brain full of knowledge. This knowledge helps the agent understand its environment and make decisions.

The Reasoning Engine is the thinking part of the agent. It processes the information from sensors using the knowledge base. The reasoning engine then figures out the best action to take based on the current situation.

Finally, Actuators are like the agent’s hands and limbs. They carry out the actions decided by the reasoning engine. For a robot, wheels and robotic arms would be its actuators.

All these components work seamlessly together. Sensors gather data, the knowledge base provides context, the reasoning engine makes a plan, and actuators implement that plan in the real world.

Real-world Applications of Problem Solving Agents in AI

Problem Solving Agents are not just theoretical concepts. They are actively used in many real-world applications today. Let’s look at some examples:

Problem solving agents are widely used in gaming applications. They can analyze the current game state, consider possible future moves, and make the optimal play. This allows them to beat human players in complex games like chess or go.

Robots in factories and warehouses heavily rely on problem solving agents. These agents perceive the environment around the robot using sensors. They then plan efficient paths and control the robot’s movements and actions accordingly.

Smart home devices like Alexa or Google Home use goal-based problem solving agents. They can understand your requests, look up relevant information from their knowledge base, and provide useful responses to assist you.

Online retailers suggest products you may like based on recommendations from problem solving agents. These agents analyze your past purchases and preferences to make personalized product suggestions.

Scheduling apps help plan your day efficiently using problem solving techniques. The agents consider your appointments, priorities, and travel time to optimize your daily schedule.

Self-Driving Cars One of the most advanced applications is self-driving cars. Their problem solving agents continuously monitor surroundings, predict the movements of other vehicles and objects, and navigate roads safely without human intervention.

In conclusion, Problem solving agents are at the heart of artificial intelligence, mimicking human-like reasoning and decision-making. From gaming to robotics, virtual assistants to self-driving cars, these intelligent agents are already transforming our world. As researchers continue pushing the boundaries, problem solving agents will become even more advanced and ubiquitous in the future. Exciting times lie ahead as we unlock the full potential of this remarkable technology.

Ajay Rathod loves talking about artificial intelligence (AI). He thinks AI is super cool and wants everyone to understand it better. Ajay has been working with computers for a long time and knows a lot about AI. He wants to share his knowledge with you so you can learn too!

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How does an agent formulate a problem?

In artificial intelligence (AI) and machine learning, an agent is an entity that perceives its environment, processes information and acts upon that environment to achieve specific goals. The process by which an agent formulates a problem is critical, as it lays the foundation for the agent’s decision-making and problem-solving capabilities.

This article explores the steps and considerations involved in problem formulation by an intelligent agent.

Table of Content

Understanding Problem Formulation

Example: problem formulation for a package delivery by an autonomous drone, step 1: define the initial state, step 2: define actions and transition model, step 3: define the goal state and objective function, importance of problem formulation, challenges in problem formulation.

Problem formulation is the process by which an agent defines the task it needs to solve. This involves specifying the initial state, goal state, actions, constraints, and the criteria for evaluating solutions. Effective problem formulation is crucial for the success of the agent in finding optimal or satisfactory solutions.

Steps in Problem Formulation

• Example: In a navigation problem, the initial state could be the agent’s starting location on a map.
• Example: For the navigation problem, the goal state is the destination location.
• Example: In a robot navigation scenario, actions could include moving forward, turning left, or turning right.
• Example: In a game, the transition model would include the rules that specify how the game state changes based on the player’s moves.
• Example: For a delivery drone, constraints might include battery life, weight capacity, and no-fly zones.
• Example: In route planning, the cost function could represent the distance traveled, time taken, or energy consumed.
• Example: For a puzzle-solving agent, success criteria could be the completion of the puzzle within the shortest time or the fewest moves.

We will demonstrate how to formulate the problem of package delivery by an autonomous drone, implementing the concepts in Python code. The drone needs to navigate from an initial location to a customer’s location while avoiding no-fly zones and managing its battery life.

The initial state includes the drone’s starting location and its battery level.

We create a Drone class with an initializer ( __init__ method) that sets the initial location, battery level, no-fly zones, and goal location.

The drone can take various actions such as taking off, landing, and moving in different directions. The transition model updates the drone’s state based on the action taken.

The takeoff , land , and move methods define how the drone’s state changes with each action. The transition_model method uses these actions to update the drone’s state.

The goal state is the customer’s location. The objective function evaluates the drone’s performance based on whether it reaches the goal and the remaining battery life.

The objective_function method returns a high score if the drone reaches the goal and otherwise returns the remaining battery level.

Complete Implementation

Now let’s put the problem formulation for a package delivery by an autonomous drone into practice:

We instantiate a Drone , execute a sequence of actions, and print the final location, battery level, and objective function score.

Effective problem formulation is essential because:

• Clarity : It provides a clear understanding of the problem, making it easier to devise a solution.
• Efficiency : Proper formulation can significantly reduce the computational resources required to solve the problem.
• Optimal Solutions : It helps in finding the most optimal or satisfactory solution by accurately defining the goals and constraints.
• Incomplete Information : The agent may not have access to all the necessary information about the environment.
• Dynamic Environments : The environment may change unpredictably, requiring the agent to adapt its problem formulation.
• Complex Constraints : Managing and incorporating complex constraints can be challenging.

A key step in artificial intelligence is problem formulation, which has a big influence on how well an agent completes its duties. An agent may efficiently traverse its environment and accomplish desired results by providing precise definitions for the starting state, actions, target state, restrictions, transition model, and objective function. By using a structured approach, the agent is guaranteed to be able to tackle complicated issues methodically and make well-informed judgments that result in effective and efficient solutions. The examples given show how issue formulation is used in a variety of contexts, underscoring its adaptability and significance in the area of artificial intelligence. Problem formulation techniques will continue to be essential to creating intelligent agents that can solve an ever-expanding array of problems as AI develops.

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Chapter 3 Solving Problems by Searching 

When the correct action to take is not immediately obvious, an agent may need to plan ahead : to consider a sequence of actions that form a path to a goal state. Such an agent is called a problem-solving agent , and the computational process it undertakes is called search .

Problem-solving agents use atomic representations, that is, states of the world are considered as wholes, with no internal structure visible to the problem-solving algorithms. Agents that use factored or structured representations of states are called planning agents .

We distinguish between informed algorithms, in which the agent can estimate how far it is from the goal, and uninformed algorithms, where no such estimate is available.

3.1 Problem-Solving Agents 

If the agent has no additional information—that is, if the environment is unknown —then the agent can do no better than to execute one of the actions at random. For now, we assume that our agents always have access to information about the world. With that information, the agent can follow this four-phase problem-solving process:

GOAL FORMULATION : Goals organize behavior by limiting the objectives and hence the actions to be considered.

PROBLEM FORMULATION : The agent devises a description of the states and actions necessary to reach the goal—an abstract model of the relevant part of the world.

SEARCH : Before taking any action in the real world, the agent simulates sequences of actions in its model, searching until it finds a sequence of actions that reaches the goal. Such a sequence is called a solution .

EXECUTION : The agent can now execute the actions in the solution, one at a time.

It is an important property that in a fully observable, deterministic, known environment, the solution to any problem is a fixed sequence of actions . The open-loop system means that ignoring the percepts breaks the loop between agent and environment. If there is a chance that the model is incorrect, or the environment is nondeterministic, then the agent would be safer using a closed-loop approach that monitors the percepts.

In partially observable or nondeterministic environments, a solution would be a branching strategy that recommends different future actions depending on what percepts arrive.

3.1.1 Search problems and solutions 

A search problem can be defined formally as follows:

A set of possible states that the environment can be in. We call this the state space .

The initial state that the agent starts in.

A set of one or more goal states . We can account for all three of these possibilities by specifying an \(Is\-Goal\) method for a problem.

The actions available to the agent. Given a state \(s\) , \(Actions(s)\) returns a finite set of actions that can be executed in \(s\) . We say that each of these actions is applicable in \(s\) .

A transition model , which describes what each action does. \(Result(s,a)\) returns the state that results from doing action \(a\) in state \(s\) .

An action cost function , denote by \(Action\-Cost(s,a,s\pr)\) when we are programming or \(c(s,a,s\pr)\) when we are doing math, that gives the numeric cost of applying action \(a\) in state \(s\) to reach state \(s\pr\) .

A sequence of actions forms a path , and a solution is a path from the initial state to a goal state. We assume that action costs are additive; that is, the total cost of a path is the sum of the individual action costs. An optimal solution has the lowest path cost among all solutions.

The state space can be represented as a graph in which the vertices are states and the directed edges between them are actions.

3.1.2 Formulating problems 

The process of removing detail from a representation is called abstraction . The abstraction is valid if we can elaborate any abstract solution into a solution in the more detailed world. The abstraction is useful if carrying out each of the actions in the solution is easier than the original problem.

3.2 Example Problems 

A standardized problem is intended to illustrate or exercise various problem-solving methods. It can be given a concise, exact description and hence is suitable as a benchmark for researchers to compare the performance of algorithms. A real-world problem , such as robot navigation, is one whose solutions people actually use, and whose formulation is idiosyncratic, not standardized, because, for example, each robot has different sensors that produce different data.

3.2.1 Standardized problems 

A grid world problem is a two-dimensional rectangular array of square cells in which agents can move from cell to cell.

Vacuum world

Sokoban puzzle

Sliding-tile puzzle

3.2.2 Real-world problems 

Route-finding problem

Touring problems

Trveling salesperson problem (TSP)

VLSI layout problem

Robot navigation

Automatic assembly sequencing

3.3 Search Algorithms 

A search algorithm takes a search problem as input and returns a solution, or an indication of failure. We consider algorithms that superimpose a search tree over the state-space graph, forming various paths from the initial state, trying to find a path that reaches a goal state. Each node in the search tree corresponds to a state in the state space and the edges in the search tree correspond to actions. The root of the tree corresponds to the initial state of the problem.

The state space describes the (possibly infinite) set of states in the world, and the actions that allow transitions from one state to another. The search tree describes paths between these states, reaching towards the goal. The search tree may have multiple paths to (and thus multiple nodes for) any given state, but each node in the tree has a unique path back to the root (as in all trees).

The frontier separates two regions of the state-space graph: an interior region where every state has been expanded, and an exterior region of states that have not yet been reached.

3.3.1 Best-first search 

In best-first search we choose a node, \(n\) , with minimum value of some evaluation function , \(f(n)\) .

3.3.2 Search data structures 

A node in the tree is represented by a data structure with four components

\(node.State\) : the state to which the node corresponds;

\(node.Parent\) : the node in the tree that generated this node;

\(node.Action\) : the action that was applied to the parent’s state to generate this node;

\(node.Path\-Cost\) : the total cost of the path from the initial state to this node. In mathematical formulas, we use \(g(node)\) as a synonym for \(Path\-Cost\) .

Following the \(PARENT\) pointers back from a node allows us to recover the states and actions along the path to that node. Doing this from a goal node gives us the solution.

We need a data structure to store the frontier . The appropriate choice is a queue of some kind, because the operations on a frontier are:

\(Is\-Empty(frontier)\) returns true only if there are no nodes in the frontier.

\(Pop(frontier)\) removes the top node from the frontier and returns it.

\(Top(frontier)\) returns (but does not remove) the top node of the frontier.

\(Add(node, frontier)\) inserts node into its proper place in the queue.

Three kinds of queues are used in search algorithms:

A priority queue first pops the node with the minimum cost according to some evaluation function, \(f\) . It is used in best-first search.

A FIFO queue or first-in-first-out queue first pops the node that was added to the queue first; we shall see it is used in breadth-first search.

A LIFO queue or last-in-first-out queue (also known as a stack ) pops first the most recently added node; we shall see it is used in depth-first search.

3.3.3 Redundant paths 

A cycle is a special case of a redundant path .

As the saying goes, algorithms that cannot remember the past are doomed to repeat it . There are three approaches to this issue.

First, we can remember all previously reached states (as best-first search does), allowing us to detect all redundant paths, and keep only the best path to each state.

Second, we can not worry about repeating the past. We call a search algorithm a graph search if it checks for redundant paths and a tree-like search if it does not check.

Third, we can compromise and check for cycles, but not for redundant paths in general.

3.3.4 Measuring problem-solving performance 

COMPLETENESS : Is the algorithm guaranteed to find a solution when there is one, and to correctly report failure when there is not?

COST OPTIMALITY : Does it find a solution with the lowest path cost of all solutions?

TIME COMPLEXITY : How long does it take to find a solution?

SPACE COMPLEXITY : How much memory is needed to perform the search?

To be complete, a search algorithm must be systematic in the way it explores an infinite state space, making sure it can eventually reach any state that is connected to the initial state.

In theoretical computer science, the typical measure of time and space complexity is the size of the state-space graph, \(|V|+|E|\) , where \(|V|\) is the number of vertices (state nodes) of the graph and \(|E|\) is the number of edges (distinct state/action pairs). For an implicit state space, complexity can be measured in terms of \(d\) , the depth or number of actions in an optimal solution; \(m\) , the maximum number of actions in any path; and \(b\) , the branching factor or number of successors of a node that need to be considered.

3.4 Uninformed Search Strategies 

3.4.1 breadth-first search .

When all actions have the same cost, an appropriate strategy is breadth-first search , in which the root node is expanded first, then all the successors of the root node are expanded next, then their successors, and so on.

Breadth-first search always finds a solution with a minimal number of actions, because when it is generating nodes at depth \(d\) , it has already generated all the nodes at depth \(d-1\) , so if one of them were a solution, it would have been found.

All the nodes remain in memory, so both time and space complexity are \(O(b^d)\) . The memory requirements are a bigger problem for breadth-first search than the execution time . In general, exponential-complexity search problems cannot be solved by uninformed search for any but the smallest instances .

3.4.2 Dijkstra’s algorithm or uniform-cost search 

When actions have different costs, an obvious choice is to use best-first search where the evaluation function is the cost of the path from the root to the current node. This is called Dijkstra’s algorithm by the theoretical computer science community, and uniform-cost search by the AI community.

The complexity of uniform-cost search is characterized in terms of \(C^*\) , the cost of the optimal solution, and \(\epsilon\) , a lower bound on the cost of each action, with \(\epsilon>0\) . Then the algorithm’s worst-case time and space complexity is \(O(b^{1+\lfloor C^*/\epsilon\rfloor})\) , which can be much greater than \(b^d\) .

When all action costs are equal, \(b^{1+\lfloor C^*/\epsilon\rfloor}\) is just \(b^{d+1}\) , and uniform-cost search is similar to breadth-first search.

3.4.3 Depth-first search and the problem of memory 

Depth-first search always expands the deepest node in the frontier first. It could be implemented as a call to \(Best\-First\-Search\) where the evaluation function \(f\) is the negative of the depth.

For problems where a tree-like search is feasible, depth-first search has much smaller needs for memory. A depth-first tree-like search takes time proportional to the number of states, and has memory complexity of only \(O(bm)\) , where \(b\) is the branching factor and \(m\) is the maximum depth of the tree.

A variant of depth-first search called backtracking search uses even less memory.

3.4.4 Depth-limited and iterative deepening search 

To keep depth-first search from wandering down an infinite path, we can use depth-limited search , a version of depth-first search in which we supply a depth limit, \(l\) , and treat all nodes at depth \(l\) as if they had no successors. The time complexity is \(O(b^l)\) and the space complexity is \(O(bl)\)

Iterative deepening search solves the problem of picking a good value for \(l\) by trying all values: first 0, then 1, then 2, and so on—until either a solution is found, or the depth- limited search returns the failure value rather than the cutoff value.

Its memory requirements are modest: \(O(bd)\) when there is a solution, or \(O(bm)\) on finite state spaces with no solution. The time complexity is \(O(bd)\) when there is a solution, or \(O(bm)\) when there is none.

In general, iterative deepening is the preferred uninformed search method when the search state space is larger than can fit in memory and the depth of the solution is not known .

3.4.5 Bidirectional search 

An alternative approach called bidirectional search simultaneously searches forward from the initial state and backwards from the goal state(s), hoping that the two searches will meet.

3.4.6 Comparing uninformed search algorithms 

3.5 Informed (Heuristic) Search Strategies 

An informed search strategy uses domain–specific hints about the location of goals to find colutions more efficiently than an uninformed strategy. The hints come in the form of a heuristic function , denoted \(h(n)\) :

\(h(n)\) = estimated cost of the cheapest path from the state at node \(n\) to a goal state.

3.5.1 Greedy best-first search 

Greedy best-first search is a form of best-first search that expands first the node with the lowest \(h(n)\) value—the node that appears to be closest to the goal—on the grounds that this is likely to lead to a solution quickly. So the evaluation function \(f(n)=h(n)\) .

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Home » Machine Learning/Artificial Intelligence

Problem Solving in Artificial Intelligence

In this tutorial, you will study about the problem-solving approach in Artificial Intelligence. You will learn how an agent tackles the problem and what steps are involved in solving it? By Monika Sharma Last updated : April 12, 2023

Problem Solving in AI

The aim of Artificial Intelligence is to develop a system which can solve the various problems on its own. But the challenge is, to understand a problem, a system must predict and convert the problem in its understandable form. That is, when an agent confronts a problem, it should first sense the problem, and this information that the agent gets through the sensing should be converted into machine-understandable form. For this, a particular sequence should be followed by the agent in which a particular format for the representation of agent's knowledge is defined and each time a problem arises, the agent can follow that particular approach to find a solution to it .

Types of Problems in AI

The types of problems in artificial intelligence are:

1. Ignorable Problems

In ignorable problems, the solution steps can be ignored.

2. Recoverable Problems

In recoverable problems, the solution steps which you have already implemented can be undone.

3. Irrecoverable Problems

In irrecoverable problems, the solution steps which you have already implemented cannot be undone.

Steps for Problem Solving in AI

The steps involved in solving a problem (by an agent based on Artificial Intelligence ) are:

1. Define a problem

Whenever a problem arises, the agent must first define a problem to an extent so that a particular state space can be represented through it. Analyzing and defining the problem is a very important step because if the problem is understood something which is different than the actual problem, then the whole problem-solving process by the agent is of no use.

2. Form the state space

Convert the problem statement into state space. A state space is the collection of all the possible valid states that an agent can reside in. But here, all the possible states are chosen which can exist according to the current problem. The rest are ignored while dealing with this particular problem.

3. Gather knowledge

collect and isolate the knowledge which is required by the agent to solve the current problem. This knowledge gathering is done from both the pre-embedded knowledge in the system and the knowledge it has gathered through the past experiences in solving the same type of problem earlier.

4. Planning-(Decide data structure and control strategy)

A problem may not always be an isolated problem. It may contain various related problems as well or some related areas where the decision made with respect to the current problem can affect those areas. So, a well-suited data structure and a relevant control strategy must be decided before attempting to solve the problem.

5. Applying and executing

After all the gathering of knowledge and planning the strategies, the knowledge should be applied and the plans should be executed in a systematic way so s to reach the goal state in the most efficient and fruitful manner.

Components to Formulate the Associated Problem

• Initial State
• Path Costing

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AI Problem Solving Process

Artificial Intelligence aims at making such systems which are capable of solving various problems on its own. AI Problem solving is a process where an AI agent tries to reach a goal with an intention to find the solution to a certain problem.

When a new problem is solved by the AI process, the AI agent maps the problem States into action. If the problem is too large and cannot be mapped directly by the agent, then the agent splits the problem domain into sub problems. It now solves the sub problems separately and then it clubs the results so obtained in order to get to the solution for the whole problem.

Based on the type of problem, different agents employ different techniques like trees, heuristics, b-trees etc. to reach to the solution of the problem. Such agents are also referred to as problem solving agents.

Problem solving agents are goal based agents which work with an aim to reach the goal with an apt solution for the problem.

Examples of problems in AI

AI is being used widely in order to reduce the time and effort required to solve the problems and increase the efficiency in the applied area. AI has been applied in the following areas efficiently:

• Boolean Formulas
• N Queens Problem
• Travelling Salesman Problem (or touring problem, here the objective is to find the shortest distance possible from a starting point to a destination.)
• Cell Layout
• Channel Routing
• Protein Design (the objective here is to find a sequence of amino acids which fold into 3D proteins which help in curing some diseases.)
• Tower of Hanoi
• Water Jug Problem

AI Problem Solving – The Steps Involved

Solving any kind of problem requires certain systematic steps to be followed. Similar is the case with solving problems by AI agents. Have a look at the flowchart below. This flowchart shows the basic steps which are followed by any of the AI agents in order to solve any problem in an AI environment.

Let us now discuss the above steps taken in order to solve a problem by the AI agents.

• Goal Formulation –In this step as soon as a problem arises, the agent sets a goal or a target. This requires the agent to promptly analyse and define the problem. This is a crucial step as if the goal for the problem is wrongly formulated then all the steps taken in order to reach the goal would be of no use.
• Defining Initial State –In order for an agent to start solving the problem, it needs to start from a state. The first state from where the agent starts working is referred to as the initial state.
• Gather Knowledge –Now the agent gathers information and uses the information required by it to solve the problem. This knowledge will be gathered with past experiences as well as current learnings.
• Planning the Transitions –Some problems are small and so these can be solved easily. But most of the times problems will be such where proper planning and execution is needed. Hence this requires proper data structures and control strategies well in advance.

Here the problem is divided into sub problems. The results of the various actions taken in solving the previous sub problem are forwarded to the next sub problem and the combined effect of the sub problems leads to the final solution. This requires proper planning and execution of transitions.

• Calculating the Cost of Path taken –Whenever an agent takes a path in order to solve a problem it allots a numeric value (or cost) to that path. These values are then evaluated using a cost function. The evaluated result is hence used in the agent’s performance measure. The solution which is reached with the minimum or lowest cost of path is termed as an optimal solution .

Measuring Performance in Problem Solving

Performance measure is one of the important things in AI problem solving which defines the worth of the algorithm used to solve the problem. There are four ways in which the performance of an algorithm is measured. These are as follows:

• Completeness – Completeness measures the algorithms guarantee to find the solution for the problem if there exists any solution for it.
• Optimality – This measure is used in order to measure the search strategies which find an optimal solution to the given problem.
• Time Complexity – This measures the amount of time the algorithm takes in order to reach till the solution for the given problem.
• Space Complexity – This is the measure which is used to determine the amount of space (in memory) which the algorithm requires in order to perform the search.

The complexity of an algorithm depends on various factors like: maximum number of successors also known as branching factor, depth or shallowness of the goal state, and the maximum length of any path in the state space representation.