problem solving using search in ai

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• Chapter 3 Solving Problems by Searching
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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 \(f(n)=h(n)\) .

Search Algorithms in Artificial Intelligence

Search algorithms in artificial intelligence are significant because they provide solutions to many artificial intelligence-related issues. There are a variety of search algorithms in artificial intelligence. The importance and characteristics of search algorithms in AI are covered in this article. Additionally, it will categorize search algorithms in artificial intelligence and list the most often used ones.

Introduction

Search algorithms in AI are algorithms that aid in the resolution of search issues. A search issue comprises the search space, start, and goal state. By evaluating scenarios and alternatives, search algorithms in artificial intelligence assist AI agents in achieving the objective state.

The algorithms provide search solutions by transforming the initial state to the desired state. Therefore, AI machines and applications can only perform search functions and discover viable solutions with these algorithms.

AI agents make artificial intelligence easy. These agents carry out tasks to achieve a specific objective and plan actions that can lead to the intended outcome. The combination of these actions completes the given task. The AI agents discover the best solution by considering all alternatives or solutions. Search algorithms in artificial intelligence are used to find the best possible solutions for AI agents.

Problem-solving Agents

Building agents with rational behavior is the subject of artificial intelligence research. These agents often use a search algorithm in the background to complete their job. Search techniques are universal problem-solving approaches in Artificial Intelligence. Rational or problem-solving agents mostly use these search strategies or algorithms in AI to solve a particular problem and provide the best result. The goal-based agents are problem-solving agents that use atomic representation. We will learn about different problem-solving search algorithms in AI in this topic.

Search Algorithm Terminologies

• Search - Searching solves a search issue in a given space step by step. Three major factors can influence a search issue.
• Search Space - A search space is a collection of potential solutions a system may have.
• Start State - The jurisdiction where the agent starts the search.
• Goal test - A function that examines the current state and returns whether or not the goal state has been attained.
• Search tree - A Search tree is a tree representation of a search issue. The node at the root of the search tree corresponds to the initial condition.
• Actions - It describes all the steps, activities, or operations accessible to the agent.
• Transition model - It can be used to convey a description of what each action does.
• Path Cost - It is a function that gives a cost to each path.
• Solution - An action sequence connects the start node to the target node.
• Optimal Solution - If a solution has the lowest cost among all solutions, it is said to be the optimal answer.

Properties of Search Algorithms

The four important properties of search algorithms in artificial intelligence for comparing their efficiency are as follows:

• Completeness - A search algorithm is said to be complete if it guarantees to yield a solution for any random input if at least one solution exists.
• Optimality - A solution discovered for an algorithm is considered optimal if it is assumed to be the best solution (lowest path cost) among all other solutions.
• Time complexity - It measures how long an algorithm takes to complete its job.
• Space Complexity - The maximum storage space required during the search, as determined by the problem's complexity.

These characteristics often contrast the effectiveness of various search algorithms in artificial intelligence.

Importance of Search Algorithms in Artificial Intelligence

The following points explain how and why the search algorithms in AI are important:

• Solving problems : Using logical search mechanisms, including problem description, actions, and search space, search algorithms in artificial intelligence improve problem-solving. Applications for route planning, like Google Maps, are one real-world illustration of how search algorithms in AI are utilized to solve problems. These programs employ search algorithms to determine the quickest or shortest path between two locations.
• Search programming : Many AI activities can be coded in terms of searching, which improves the formulation of a given problem's solution.
• Goal-based agents : Goal-based agents' efficiency is improved through search algorithms in artificial intelligence. These agents look for the most optimal course of action that can offer the finest resolution to an issue to solve it.
• Support production systems : Search algorithms in artificial intelligence help production systems run. These systems help AI applications by using rules and methods for putting them into practice. Production systems use search algorithms in artificial intelligence to find the rules that can lead to the required action.
• Neural network systems : The neural network systems also use these algorithms. These computing systems comprise a hidden layer, an input layer, an output layer, and coupled nodes. Neural networks are used to execute many tasks in artificial intelligence. For example, the search for connection weights that will result in the required input-output mapping is improved by search algorithms in AI.

Types of Search Algorithms in AI

We can divide search algorithms in artificial intelligence into uninformed (Blind search) and informed (Heuristic search) algorithms based on the search issues.

Uninformed/Blind Search

The uninformed search needs domain information, such as proximity or goal location. It works by brute force because it only contains information on traversing the tree and identifying leaf and goal nodes.

Uninformed search is a method of searching a search tree without knowledge of the search space, such as initial state operators and tests for the objective, and is also known as blind search. It goes through each tree node until it reaches the target node. These algorithms are limited to producing successors and distinguishing between goal and non-goal states.

• Breadth-first search - This is a search method for a graph or tree data structure. It starts at the tree root or searches key and goes through the adjacent nodes in the current depth level before moving on to the nodes in the next depth level. It uses the queue data structure that works on the first in, first out (FIFO) concept. It is a complete algorithm as it returns a solution if a solution exists.

• Depth-first search - It is also an algorithm used to explore graph or tree data structures. It starts at the root node, as opposed to the breadth-first search. It goes through the branch nodes and then returns. It is implemented using a stack data structure that works on the concept of last in, first out (LIFO).

• Uniform cost search(UCS) - Unlike breadth-first and depth-first algorithms, uniform cost search considers the expense. When there are multiple paths to achieving the desired objective, the optimal solution of uniform cost algorithms is the one with the lowest cost. So uniform cost search will check the expense to go to the next node. It will choose the path with the least cost if there are multiple paths. Only finite states and the absence of loops with zero weights make UCS complete. Also, only when there are no negative costs is UCS optimum. It is similar to the breadth-first search if each transition's cost is the same.

• Iterative deepening depth-first search - It performs a depth-first search to level 1, then restarts, completes a depth-first search to level 2, and so on until the answer is found. It only generates a node once all the lower nodes have been produced. It only stores a node stack. The algorithm terminates at depth d when the goal node is found.

• Bidirectional search - It searches forward from the initial state and backward from the target state until they meet to identify a common state. The route from the initial state is joined to the path from the goal state. Each search only covers half of the entire path.

Informed Search

Informed search algorithms in AI use domain expertise. Problem information is accessible in an informed search, which can guide the search. As a result, informed search strategies are more likely to discover a solution than uninformed ones.

Heuristic search is another name for informed search. A heuristic is a method that, while not always guaranteed to find the best solution, is guaranteed to find a decent solution in a reasonable amount of time. An informed search can answer many complex problems that would be impossible to handle otherwise.

Greedy Search - The closest node to the target node is expanded in greedy search algorithms in AI. A heuristic function, h, determines the closeness factor (x). h(x) is a distance estimate between one node and the end or target node. The closer the node is to the endpoint, the smaller the h(x) value. When the greedy search looks for the best route to the target node, it will select nodes with the lowest possible values. This algorithm is implemented through the priority queue. It is not an optimal algorithm. It can get stuck in loops.

For example, imagine a simple game where the goal is to reach a specific location on a board. The player can move in any direction but walls are blocking some paths. In a greedy search approach, the player would always choose the direction that brings them closer to the goal, without considering the potential obstacles or the fact that some paths may lead to dead ends.

If the chosen path leads to a dead end or a loop, the algorithm will keep moving back and forth between the same nodes, without ever exploring other options. This can result in an infinite loop where the algorithm keeps repeating the same steps and fails to find a solution.

A * Search - A* Tree Search, known as A* Search, combines the strengths of uniform-cost search and greedy search. To find the best path from the starting state to the desired state, the A* search algorithm investigates all potential paths in a graph or grid. The algorithm calculates the cost of each potential move at each stage using the following two criteria:

• How much it costs to reach the present node?
• The approximate cost from the present node to the goal.

A heuristic function is used to determine the estimated cost and estimate the distance between the current node and the desired state. The acceptable nature of this heuristic function ensures that it never overestimates the actual cost of achieving the goal.

The path with the lowest overall cost is chosen after an A* search examines each potential route based on the sum of the actual cost and the estimated cost (i.e., the cost so far and the estimated cost-to-go). By doing this, the algorithm is guaranteed to always investigate the most promising path first, which is most likely to lead to the desired state.

• Search algorithms in AI are algorithms that aid in the resolution of search issues. A search issue comprises the search space, start, and goal state.
• These algorithms are essential because they aid in solving AI problems and support other systems, such as neural networks and manufacturing systems.
• Search algorithms in artificial intelligence define the problem (initial state, target state, state space, space cost, etc.) and then perform search operations to find the best solution to the given problem.
• Search algorithms in artificial intelligence are classified into two types: informed algorithms and uninformed algorithms. Breadth-first, depth-first, and uniform-cost algorithms are examples of informed algorithms. Greedy, A* tree and A* graph algorithms are examples of uninformed algorithms.
• Vehicle routing, nurse scheduling, record retrieval, and industrial processes are some of AI's most common uses of search algorithms.

Additional Resources

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Understanding AI search algorithms

Elastic Platform Team

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Artificial intelligence tools are everywhere, and it’s no mystery why. They can carry out a huge variety of tasks and find the solutions to many everyday problems. But these apps are only as good as their AI search algorithm.

In simple terms, an AI search algorithm is the decision-making formula an AI tool uses to find the optimal solution to your specific problem. Search algorithms may make trade-offs between speed, relevance, or another weighted factor. It takes into account the query’s constraints and goals and presents back what it has calculated to be the best solution.

In this post, we’ll go through:

The importance and applications of AI search algorithms

Elements of AI search algorithms

The different types of AI search algorithms

AI search algorithm use cases

The challenges and limitations when using AI search algorithms

By the end of this article, you’ll have a clear understanding of what they are and how you can use them in your AI tools.

What is a search algorithm in AI?

An AI search algorithm is the method for understanding natural language queries and finding relevant results by evaluating indexed data and documents. It does this by exploring a set of potential solutions in order to find the best answer or solution to the query it's given.

Imagine you’re building a chess application using artificial intelligence that predicts the best move to make next. In order to determine the optimal move, your AI search algorithm must evaluate the different options to decide which one is best. This means systematically assessing the position of each piece, evaluating every possible combination of moves, and calculating the tactic that gives you the best chance of winning.

Importance and applications of AI search algorithms

AI search algorithms play a vital role across a huge variety of fields. This ranges from computer science problem-solving to sophisticated decision-making in logistics. Their versatility makes them indispensable for tackling diverse challenges and solving important problems.

For example, NASA is able to analyze rover data from the Mars mission using the AI search algorithms in Elastic®. This enables them to unlock crucial insights and navigate complex challenges much quicker than they would if they had to analyze this data manually. And in the healthcare sector, AI search algorithms are being used to assist in medical diagnosis, treatment planning, and drug discovery. This leads to better diagnostic accuracy, more efficient treatment plans, and the development of new therapies.

These examples highlight the importance and potential, but applications of these algorithms extend far beyond just these use cases. Various fields such as finance, manufacturing, legal services, and more are already benefiting from this new ability to process huge amounts of data and make informed decisions. As it continues to evolve, AI algorithms will play an even more prominent role across every industry and have a huge impact on the world around us.

Each AI search algorithm can be broken down into four elements: states, actions, goals, and path costs. This framework of elements is how the algorithm can navigate complex problem spaces to find optimal solutions.

States are a snapshot of the problem at a particular point in time. They encapsulate all the relevant information about the problem at that moment, so the algorithm can assess the current situation. Think of it like a maze — every turn represents a different “state” in the maze. So by looking at the state, you know where the AI is in the algorithm. 

Actions are the possible transitions between the states. Staying with the maze metaphor, these actions are the available directions you can choose to go. By combining these actions, you can determine the different potential paths to travel through the maze. 

The goal is the ultimate objective of the search process. In search, this goal will be the best and most relevant answer to the initial query. This provides a clear direction for the algorithm, so its efforts are focused on finding the best results. In the maze example, the query “find the best route to escape the maze” would be the goal. 

Path costs are the trade-off between precision and recall for each step or action in the path toward answering the query. This cost represents the effort or resources required to make each particular move. The cost can then be used by the algorithm to prioritize efficient and resource-economic routes.

Types of AI search algorithms

Natural language processing (nlp) algorithms.

NLP algorithms are an essential part of search because they bridge the gap between human communication and machine understanding. This enables search AI to understand what is being asked of it and to deliver results that are relevant and contextual to the query.

Using NLP, the search results will be more aligned with the user's intent, and the algorithm will be able to handle complex queries by understanding more nuanced requests. This is because it can identify sentiment and understand the context, as well as personalize the search experience based on previous conversations with the user.

Word embeddings One of the ways an algorithm can work with words to find similarity is with word embeddings , where words and assets are represented as vectors . This is where it analyzes unstructured data like text and images and transforms them into a numeric value.

A popular example of this is Word2vec, an algorithm that learns word embeddings from a huge collection of written texts. It then analyzes the surrounding text to determine meaning and understand context. Another example is GloVe (Global Vectors for Word Representation), which is also trained to build connections between different words by mapping them depending on their semantic similarity.

Language models There are also language models that analyze large amounts of data in order to accurately predict the likelihood of what order words will appear. Or in simpler terms, they’re algorithms that allow the search AI to not just understand what we’re saying, but also be able to respond in a way that matches how humans communicate.

For example, BERT (Bidirectional Encoder Representations from Transformers) is a popular language model that’s able to understand complex and nuanced language, which can then be used for powerful semantic search and question answering.

k-nearest neighbors (kNN)

kNN is a simple but versatile AI search algorithm that’s used for identifying the closest data points (“k”) to a new data point. It then uses those “neighbors” to predict the class or value of the new data point. Or in simpler terms, it analyzes the new data and finds the existing data that matches it the closest.

This makes it great for ranking results by relevance, suggesting similar images or videos, or recommending products based on previous purchases. 

Although it is relatively simple and easy to understand, it can be an expensive algorithm to run. This is especially the case for large data sets, because it needs to calculate the distance between the new data points and all the existing data.

Approximate nearest neighbors (ANN)

An alternative to finding the closest match with kNN is to find a match that’s good enough for your specific needs. This is where approximate nearest neighbors algorithms excel. That’s because ANN algorithms look for data that is a very close match to the query, but not necessarily the closest one. So instead of painstakingly analyzing every bit of data, which can be time and resource-intensive, ANN will settle for something that’s not as close, but still “close enough” in relative terms.

The benefit of this is that you can create a much faster and more efficient similarity search. ANN achieves these “close enough” results by inferring semantic relationships between content and data.

For this approach to be worthwhile, though, you need to accept the trade-off with accuracy, as it doesn’t guarantee the closest result. ANN will be a great solution most of the time, but if you need to guarantee absolute accuracy, this might not be the best option for you.

Uninformed or blind search algorithms

Uninformed search algorithms (also known as blind search algorithms) do not know information about the search space. They solve the query systematically, with no guidance or domain-specific knowledge. They rely entirely on the existing structure of the search space to find the solution.

There are several different types of uninformed search algorithms, but the three most common are breadth-first search (BFS), depth-first search (DFS), and uniform cost search (UCS).

Informed or heuristic search algorithms

Informed search algorithms (also known as heuristic search algorithms) are a type of search that uses additional information and domain-specific knowledge to guide their searches. Unlike uninformed searches, they use heuristics, which are rules of thumb and estimates that help them prioritize paths and avoid unnecessary exploration.

There are a few different types of informed search algorithm, but the most common are greedy best-first search, A* search, and beam search.

Use cases of AI search algorithms

As we have already mentioned, AI search algorithms are being utilized across a wide range of industries to complete a variety of tasks. Here are just a few real-world examples where they’ve made a huge impact.

Informational retrieval : NLP search algorithms can enhance search results by understanding the context and tone of a query to retrieve more useful information.

Recommendations: kNN algorithms are often used to recommend products, movies, or music based on their preferences and past behavior.

Speech recognition: ANN algorithms are commonly used to recognize patterns in speech. This is useful in things like speech-to-text and language identification.

Medical diagnosis: AI search algorithms can help with speeding up medical diagnosis. For example, they can be trained on massive data sets of medical images and use image recognition to detect anomalies from photos, X-rays, CT scans, etc.

Pathfinding: Uninformed search algorithms can help find the shortest path between two points on a map or network. For example, determining the shortest delivery route for a driver.

Challenges and limitations of AI search algorithms

AI search algorithms might have revolutionized various industries with efficient problem-solving and decision-making, but they also create challenges and limitations. For a start, the computation complexity involved can make them extremely expensive to run. This is because they require huge amounts of processing, computational, and memory resources to carry out the search. This limits their effectiveness where there are constraints in place.

Another problem is that an informed search algorithm can only be as good as the heuristics it uses. If the heuristic function isn’t accurate, it can lead the algorithm down the wrong path and result in suboptimal or even incorrect solutions.

Also, AI search algorithms have generally been designed to solve specific types of problems like pathfinding and constraint satisfaction. This has been useful for certain tasks, but there are still limitations to the problem-solving scope, especially when solving more diverse problems. 

Decoding AI search for the future

AI search algorithms are important tools in solving complex modern problems across a wide range of fields. Their diversity and versatility make them indispensable for tasks like pathfinding, planning, and machine learning.

But while they are revolutionizing industries such as robotics, healthcare, and finance, there is still so much potential. The current limitations and challenges are also opportunities for future advancement. As research continues to enhance performance, AI search algorithms will continue to play an increasingly prominent role in solving real-world problems and changing the face of technology.

What you should do next

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OpenAI Announces a New AI Model, Code-Named Strawberry, That Solves Difficult Problems Step by Step

OpenAI made the last big breakthrough in artificial intelligence by increasing the size of its models to dizzying proportions, when it introduced GPT-4 last year. The company today announced a new advance that signals a shift in approach—a model that can “reason” logically through many difficult problems and is significantly smarter than existing AI without a major scale-up.

The new model, dubbed OpenAI o1, can solve problems that stump existing AI models, including OpenAI’s most powerful existing model, GPT-4o . Rather than summon up an answer in one step, as a large language model normally does, it reasons through the problem, effectively thinking out loud as a person might, before arriving at the right result.

“This is what we consider the new paradigm in these models,” Mira Murati , OpenAI’s chief technology officer, tells WIRED. “It is much better at tackling very complex reasoning tasks.”

The new model was code-named Strawberry within OpenAI, and it is not a successor to GPT-4o but rather a complement to it, the company says.

Murati says that OpenAI is currently building its next master model, GPT-5, which will be considerably larger than its predecessor. But while the company still believes that scale will help wring new abilities out of AI, GPT-5 is likely to also include the reasoning technology introduced today. “There are two paradigms,” Murati says. “The scaling paradigm and this new paradigm. We expect that we will bring them together.”

LLMs typically conjure their answers from huge neural networks fed vast quantities of training data. They can exhibit remarkable linguistic and logical abilities, but traditionally struggle with surprisingly simple problems such as rudimentary math questions that involve reasoning.

Murati says OpenAI o1 uses reinforcement learning, which involves giving a model positive feedback when it gets answers right and negative feedback when it does not, in order to improve its reasoning process. “The model sharpens its thinking and fine tunes the strategies that it uses to get to the answer,” she says. Reinforcement learning has enabled computers to play games with superhuman skill and do useful tasks like designing computer chips . The technique is also a key ingredient for turning an LLM into a useful and well-behaved chatbot.

Mark Chen, vice president of research at OpenAI, demonstrated the new model to WIRED, using it to solve several problems that its prior model, GPT-4o, cannot. These included an advanced chemistry question and the following mind-bending mathematical puzzle: “A princess is as old as the prince will be when the princess is twice as old as the prince was when the princess’s age was half the sum of their present age. What is the age of the prince and princess?” (The correct answer is that the prince is 30, and the princess is 40).

“The [new] model is learning to think for itself, rather than kind of trying to imitate the way humans would think,” as a conventional LLM does, Chen says.

OpenAI says its new model performs markedly better on a number of problem sets, including ones focused on coding, math, physics, biology, and chemistry. On the American Invitational Mathematics Examination (AIME), a test for math students, GPT-4o solved on average 12 percent of the problems while o1 got 83 percent right, according to the company.

The new model is slower than GPT-4o, and OpenAI says it does not always perform better—in part because, unlike GPT-4o, it cannot search the web and it is not multimodal, meaning it cannot parse images or audio.

Improving the reasoning capabilities of LLMs has been a hot topic in research circles for some time. Indeed, rivals are pursuing similar research lines. In July, Google announced AlphaProof , a project that combines language models with reinforcement learning for solving difficult math problems.

AlphaProof was able to learn how to reason over math problems by looking at correct answers. A key challenge with broadening this kind of learning is that there are not correct answers for everything a model might encounter. Chen says OpenAI has succeeded in building a reasoning system that is much more general. “I do think we have made some breakthroughs there; I think it is part of our edge,” Chen says. “It’s actually fairly good at reasoning across all domains.”

Noah Goodman , a professor at Stanford who has published work on improving the reasoning abilities of LLMs, says the key to more generalized training may involve using a “carefully prompted language model and handcrafted data” for training. He adds that being able to consistently trade the speed of results for greater accuracy would be a “nice advance.”

Yoon Kim , an assistant professor at MIT, says how LLMs solve problems currently remains somewhat mysterious, and even if they perform step-by-step reasoning there may be key differences from human intelligence. This could be crucial as the technology becomes more widely used. “These are systems that would be potentially making decisions that affect many, many people,” he says. “The larger question is, do we need to be confident about how a computational model is arriving at the decisions?”

The technique introduced by OpenAI today also may help ensure that AI models behave well. Murati says the new model has shown itself to be better at avoiding producing unpleasant or potentially harmful output by reasoning about the outcome of its actions. “If you think about teaching children, they learn much better to align to certain norms, behaviors, and values once they can reason about why they’re doing a certain thing,” she says.

Oren Etzioni , a professor emeritus at the University of Washington and a prominent AI expert, says it’s “essential to enable LLMs to engage in multi-step problem solving, use tools, and solve complex problems.” He adds, “Pure scale up will not deliver this.” Etzioni says, however, that there are further challenges ahead. “Even if reasoning were solved, we would still have the challenge of hallucination and factuality.”

OpenAI’s Chen says that the new reasoning approach developed by the company shows that advancing AI need not cost ungodly amounts of compute power. “One of the exciting things about the paradigm is we believe that it’ll allow us to ship intelligence cheaper,” he says, “and I think that really is the core mission of our company.”

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Solving the 8-Puzzle with A* and SimpleAI

Discover Heuristic-Based Problem Solving

Welcome to a comprehensive exploration into the world of Informed Search Heuristics with a captivating use case - the 8-Puzzle . Leveraging Python and its powerful libraries, we’ll delve into solving the 8-puzzle problem. This project covers:

• The basics of Informed Search Heuristics and their significance in artificial intelligence.
• Understanding the 8-Puzzle problem and its representation.
• The implementation of A* algorithm to solve the 8-Puzzle.
• The application of Manhattan Distance and Misplaced Tiles as heuristics in our problem.
• A detailed guide to coding the solution with Python .
• An in-depth analysis of the solution and the impact of different heuristics on the efficiency of the solution.

This insightful journey is beneficial for both AI beginners and seasoned researchers . The project offers a deep understanding of Informed Search Heuristics and their practical implementation in the 8-Puzzle problem .

Informed Search Heuristics

Informed Search Heuristics play a pivotal role in the domain of artificial intelligence. Heuristics are techniques that guide the search process towards more promising regions, thus reducing the search time. They are based on information (hence “informed”) that is available a priori and can provide an estimate to the solution from any given state.

Application in Artificial Intelligence

Heuristics are often used in path-finding problems, scheduling, and in the game industry. They are a cornerstone of the A* search algorithm, which combines the benefits of Breadth-First Search (completeness and optimality) and Depth-First Search (space-efficiency) and is used widely due to its effectiveness and efficiency. For instance, the paper ‘Search-Based Optimal Solvers for the Multi-Agent Pathfinding Problem: Summary and Challenges’ discusses various search-based techniques developed for optimally solving Multi-agent pathfinding (MAPF) under the sum-of-costs objective function 1 . Similarly, ‘Multi-Agent Pathfinding with Simultaneous Execution of Single-Agent Primitives’ proposes an algorithm for multi-agent pathfinding that utilizes single-agent primitives but allows all agents to move in parallel 2 . These examples illustrate the practical application and effectiveness of heuristics in solving complex problems.

The 8-Puzzle Problem

The 8-Puzzle problem is a puzzle that was invented and popularized by Noyes Palmer Chapman in the late 19th century. It consists of a 3x3 grid with eight numbered tiles and a blank space. The goal is to reach a specified goal state from a given start state by sliding the blank space up, down, left or right.

Visualizing the Program Flow and Execution

We have prepared a series of diagrams to provide a better understanding of the program flow and execution of our 8-puzzle solution, including the utilization of the A* Search Algorithm:

These diagrams help you visualize the flow of control and object, structure of the classes used, and the sequence of operations in our implementation to solve the 8-Puzzle problem.

GitHub Repository

For complete access to the code and resources associated with this project, visit our GitHub repository:

Interactive Document Preview

Immerse yourself in the 8-Puzzle project write-up with our interactive document preview. Navigate, zoom in, scroll through, and engage with the content freely.

To access the project write-up in PDF format for offline reading or printing, download from the link below.

By implementing Informed Search Heuristics and using the A* search algorithm, we’ve developed an efficient solution to the 8-Puzzle problem. This project demonstrates the efficacy of Informed Search Heuristics and A* in problem-solving tasks and provides valuable insights into their workings. As we delve deeper into the field of Artificial Intelligence, we can apply these concepts to other problem-solving tasks and real-world applications.

Join the Discussion

We welcome your thoughts, inquiries, and experiences related to the 8-Puzzle project! Engage in our Disqus forum below. Share your insights, ask questions, and connect with others passionate about Informed Search Heuristics and problem-solving.

Feel free to share your ideas or ask for help; we’re all in this together. Let’s build a vibrant community to discuss, learn, and explore the exciting world of Informed Search Heuristics and their application in problems like the 8-Puzzle.

Do provide us with feedback and share with us how we could make this write-up more beneficial for you! We are always eager to learn and improve.

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OpenAI unveils o1, a model that can fact-check itself

ChatGPT maker OpenAI has announced its next major product release: A generative AI model code-named Strawberry, officially called OpenAI o1.

To be more precise, o1 is actually a family of models. Two are available Thursday in ChatGPT and via OpenAI’s API: o1-preview and o1-mini, a smaller, more efficient model aimed at code generation.

You’ll have to be subscribed to ChatGPT Plus or Team to see o1 in the ChatGPT client. Enterprise and educational users will get access early next week.

Note that the o1 chatbot experience is fairly barebones at present. Unlike GPT-4o , o1’s forebear, o1 can’t browse the web or analyze files yet. The model does have image-analyzing features, but they’ve been disabled pending additional testing. And o1 is rate-limited; weekly limits are currently 30 messages for o1-preview and 50 for o1-mini.

In another downside, o1 is expensive . Very expensive. In the API, o1-preview is $15 per 1 million input tokens and $60 per 1 million output tokens. That’s 3x the cost versus GPT-4o for input and 4x the cost for output. (“Tokens” are bits of raw data; 1 million is equivalent to around 750,000 words.)

OpenAI says it plans to bring o1-mini access to all free users of ChatGPT but hasn’t set a release date. We’ll hold the company to it.

Chain of reasoning

OpenAI o1 avoids some of the reasoning pitfalls that normally trip up generative AI models because it can effectively fact-check itself by spending more time considering all parts of a question. What makes o1 “feel” qualitatively different from other generative AI models is its ability to “think” before responding to queries, according to OpenAI.

When given additional time to “think,” o1 can reason through a task holistically — planning ahead and performing a series of actions over an extended period of time that help the model arrive at an answer. This makes o1 well-suited for tasks that require synthesizing the results of multiple subtasks, like detecting privileged emails in an attorney’s inbox or brainstorming a product marketing strategy.

In a series of posts on X on Thursday, Noam Brown, a research scientist at OpenAI, said that “o1 is trained with reinforcement learning.” This teaches the system “to ‘think’ before responding via a private chain of thought” through rewards when o1 gets answers right and penalties when it does not, he said.

Brown alluded to the fact that OpenAI leveraged a new optimization algorithm and training dataset containing “reasoning data” and scientific literature specifically tailored for reasoning tasks. “The longer [o1] thinks, the better it does,” he said.

TechCrunch wasn’t offered the opportunity to test o1 before its debut; we’ll get our hands on it as soon as possible. But according to a person who did have access — Pablo Arredondo, VP at Thomson Reuters — o1 is better than OpenAI’s previous models (e.g., GPT-4o) at things like analyzing legal briefs and identifying solutions to problems in LSAT logic games.

“We saw it tackling more substantive, multi-faceted, analysis,” Arredondo told TechCrunch. “Our automated testing also showed gains against a wide range of simple tasks.”

In a qualifying exam for the International Mathematical Olympiad (IMO), a high school math competition, o1 correctly solved 83% of problems while GPT-4o only solved 13%, according to OpenAI. (That’s less impressive when you consider that Google DeepMind’s recent AI achieved a silver medal in an equivalent to the actual IMO contest.) OpenAI also says that o1 reached the 89th percentile of participants — better than DeepMind’s flagship system AlphaCode 2 , for what it’s worth — in the online programming challenge rounds known as Codeforces.

In general, o1 should perform better on problems in data analysis, science, and coding, OpenAI says. (GitHub, which tested o1 with its AI coding assistant GitHub Copilot , reports that the model is adept at optimizing algorithms and app code.) And, at least per OpenAI’s benchmarking, o1 improves over GPT-4o in its multilingual skills, especially in languages like Arabic and Korean.

Ethan Mollick, a professor of management at Wharton, wrote his impressions of o1 after using it for a month in a post on his personal blog. On a challenging crossword puzzle, o1 did well, he said — getting all the answers correct (despite hallucinating a new clue).

OpenAI o1 is not perfect

Now, there are drawbacks.

OpenAI o1 can be slower than other models, depending on the query. Arredondo says o1 can take over 10 seconds to answer some questions; it shows its progress by displaying a label for the current subtask it’s performing.

Given the unpredictable nature of generative AI models, o1 likely has other flaws and limitations. Brown admitted that o1 trips up on games of tic-tac-toe from time to time, for example. And in a technical paper , OpenAI said that it’s heard anecdotal feedback from testers that o1 tends to hallucinate (i.e., confidently make stuff up) more than GPT-4o — and less often admits when it doesn’t have the answer to a question.

“Errors and hallucinations still happen [with o1],” Mollick writes in his post. “It still isn’t flawless.”

We’ll no doubt learn more about the various issues in time, and once we have a chance to put o1 through the wringer ourselves.

Fierce competition

We’d be remiss if we didn’t point out that OpenAI is far from the only AI vendor investigating these types of reasoning methods to improve model factuality.

Google DeepMind researchers recently published a study showing that by essentially giving models more compute time and guidance to fulfill requests as they’re made, the performance of those models can be significantly improved without any additional tweaks.

Illustrating the fierceness of the competition, OpenAI said that it decided against showing o1’s raw “chains of thoughts” in ChatGPT partly due to “competitive advantage.” (Instead, the company opted to show “model-generated summaries” of the chains.)

OpenAI might be first out of the gate with o1. But assuming rivals soon follow suit with similar models, the company’s real test will be making o1 widely available — and for cheaper.

From there, we’ll see how quickly OpenAI can deliver upgraded versions of o1. The company says it aims to experiment with o1 models that reason for hours, days, or even weeks to further boost their reasoning capabilities.

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How AI Could Change Online Product Search and Discovery

The tech world is bent on making generative AI an everyday assistant to millions of customers. If it succeeds, it could have major implications for how shoppers find and buy products, including fashion and beauty.

On Monday, Apple announced that its newest phone, the iPhone 16, will incorporate generative AI models that power what it calls Apple Intelligence, a system aimed at helping users with personal tasks like writing emails, putting events in their calendar or whipping up just the right emoji for the group chat. These AI features are meant to be so integral to the phone that Apple built the device from the ground up around them. Apple will also let users access third-party tools, including ChatGPT thanks to a partnership with OpenAI.

The company is hurrying to catch up with the likes of Google, Microsoft and OpenAI as they pitch generative AI as the next big leap in technology. One area squarely in the crosshairs is online search.

A strength of the AI models underlying tools like ChatGPT is their ability to ingest large amounts of data and summarise it. The technology isn’t flawless. It doesn’t understand and retrieve information but rather uses probabilities to predict the next word in a sequence. Like any predictions, they’re not always correct. But with more data, the predictions can get better, and companies are training their models on just about the entire internet.

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The result is that users can ask a question and get an answer without having to do any searching themselves. “Let Google do the searching for you,” is how Google put it when it began rolling out AI overviews for search results to all US users earlier this year.

When it comes to shopping, that may be a service consumers welcome — if it ever becomes widespread.

In a report this year , IBM found that 86 percent of consumers who hadn’t yet tried AI for shopping wanted to see how the technology could help them research products or get product information.

Similarly, Kirsten Green, a founder and partner at Forerunner Ventures, a consumer-focused venture capital firm, argued in a talk in July that consumers today feel overburdened by the amount of information available to them and are prioritising technology that can sift through it for them, driving a shift in services from what she calls “access” to “edit.”

“As a result, we now see a refreshed desire for experts and services that edit the vastness of what’s available, present the best possible options instead of more options, and do things for us instead of enabling us to do it ourselves,” Green wrote in a post . AI, in her view, offers a solution.

What a move from “access” to “edit” with AI could look like is evident when searching for products online. Right now, for example, a Google search for “best men’s gym shorts” brings up the usual list of links to reviews. A user could just make a decision based on the first link, but more likely they’d end up clicking into a few links, reading the different opinions and coming up with a conclusion — on their own — as to what’s best.

The same question plugged into ChatGPT provides a very different response. It spits out a list of shorts numbered one through 10, with bullets underneath identifying key features, the uses they’re best for and “highlights” with distinguishing characteristics.

This format doesn’t only change how shoppers get information. It can also change the information they get.

ChatGPT’s list, for example, included Vuori’s Kore Shorts. But the style wasn’t mentioned within the top four links in the Google search. On the other hand, two of those links named Ten Thousand’s Interval Shorts as the best overall. They appeared in the fifth spot in ChatGPT’s list.

ChatGPT’s list isn’t actually meant to be a ranking. The site presents its results as “some of the top-rated gym shorts.” But the numbering could be misconstrued. If that happened, the shopper would think their best option was Nike’s Flex Stride Shorts, a specific style of Nike’s Flex shorts that wasn’t specifically mentioned in any of the top four links from Google.

By digesting the information for readers and presenting answers, the AI results arguably carry even more weight than any individual link or set of reviews, which means brands whose products appear in them could benefit greatly while those that don’t might suffer. It would make AI optimisation even more crucial than search-engine optimisation, and might lead to companies looking for ways to game the results.

As researchers recently demonstrated , there are ways to do that. By adding a “strategic text sequence” to a coffee maker’s product page, they were able to “significantly increase its likelihood of being listed as the [large language model’s] top recommendation.” The New York Times recently covered other ways AI can be manipulated, too.

AI developers are aware of these issues. Google said its AI overviews use its core systems for search ranking and quality, which already have protections against these types of tactics. But just as with SEO, it could lead to an endless battle between AI companies and those looking for the best placement in the AI’s answers.

For now, however, product searches using generative AI remain an edge case. While ChatGPT quickly became an object of fascination after its public release at the end of 2022, it remains a niche product. According to Pew Research Center, as of March 2024, just 23 percent of US adults had used ChatGPT. (Though among those aged 18 to 29, the number was 43 percent.) Even those who tried it may have done so once and never again.

Some companies, including Amazon and Shopify, do have AI-powered shopping chatbots , but they might only exist in the companies’ apps.

Apple’s new phone is likely to drive usage of ChatGPT, but it’s unclear whether Apple would ever route product searches to it. Siri currently responds to those questions with a Google search.

And while Google’s AI overviews kick in for gifting-specific questions, such as “best gifts for home cooks,” the company confirmed they aren’t yet triggered by a broad range of product queries. As for whether they might be rolled out to those searches in the future, Google said it had nothing to share.

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Marc Bain is Technology Correspondent at The Business of Fashion. He is based in New York and drives BoF’s coverage of technology and innovation, from start-ups to Big Tech.

• Technology : Artificial Intelligence

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Problem Solving in Artificial Intelligence

The reflex agent of AI directly maps states into action. Whenever these agents fail to operate in an environment where the state of mapping is too large and not easily performed by the agent, then the stated problem dissolves and sent to a problem-solving domain which breaks the large stored problem into the smaller storage area and resolves one by one. The final integrated action will be the desired outcomes.

On the basis of the problem and their working domain, different types of problem-solving agent defined and use at an atomic level without any internal state visible with a problem-solving algorithm. The problem-solving agent performs precisely by defining problems and several solutions. So we can say that problem solving is a part of artificial intelligence that encompasses a number of techniques such as a tree, B-tree, heuristic algorithms to solve a problem.  

We can also say that a problem-solving agent is a result-driven agent and always focuses on satisfying the goals.

There are basically three types of problem in artificial intelligence:

1. Ignorable: In which solution steps can be ignored.

2. Recoverable: In which solution steps can be undone.

3. Irrecoverable: Solution steps cannot be undo.

Steps problem-solving in AI: The problem of AI is directly associated with the nature of humans and their activities. So we need a number of finite steps to solve a problem which makes human easy works.

These are the following steps which require to solve a problem :

• Problem definition: Detailed specification of inputs and acceptable system solutions.
• Problem analysis: Analyse the problem thoroughly.
• Knowledge Representation: collect detailed information about the problem and define all possible techniques.
• Problem-solving: Selection of best techniques.

Components to formulate the associated problem: 

• Initial State: This state requires an initial state for the problem which starts the AI agent towards a specified goal. In this state new methods also initialize problem domain solving by a specific class.
• Action: This stage of problem formulation works with function with a specific class taken from the initial state and all possible actions done in this stage.
• Transition: This stage of problem formulation integrates the actual action done by the previous action stage and collects the final stage to forward it to their next stage.
• Goal test: This stage determines that the specified goal achieved by the integrated transition model or not, whenever the goal achieves stop the action and forward into the next stage to determines the cost to achieve the goal.  
• Path costing: This component of problem-solving numerical assigned what will be the cost to achieve the goal. It requires all hardware software and human working cost.

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