examples of problem solving agents

“ An agent with several immediate options of unknown value can decide what to do by first examining the future actions that eventually lead to states of known value ”

After Goal formulation and problem formulation, the agent has to look for a sequence of actions that reaches the goal. This process is called Search . A search algorithm takes a problem as input and returns a sequence of actions as output.

After the search phase, the agent has to carry out the actions that are recommended by the search algorithm. This final phase is called execution phase.

Formulate — Search — Execute

Thus the agent has a formulate, search and execute design to it.

Problems and Solutions

Before we get into more about problem formulating phase, we need to first understand what a problem is in terms of problem solving agents.

The problem can be defined formally in five components:

Initial State

Transition model.

The first component that describes the problem is the initial state that the agent starts in. For example, if a taxi agent needs to get to location(B) but the taxi is currently at location(A) then the initial state of the problem would be location(A).

The second component that describes the problem is a description of the possible actions available to the agent. Given a state s , Actions(s) returns the set of actions that can be executed in s. We say that each of these actions is applicable in s.

The third component is the description of what each action does which is called the transition model . It is specified by a function Result(s , a) that returns the state that results from doing action a in state s.

The initial state, actions and transition model together define the state space of a problem which is 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.

The goal test determines whether a given state is a goal state or not. Sometimes there is an explicit set of possible goal states and the test simply checks whether the given state is one of them. Sometimes the goal is specified by an abstract property rather than an explicitly enumerated set of states.

The last component of the problem is the path cost which is a function that assigns a numeric cost to each path. The problem solving agent chooses a cost function that reflects its own performance measure.

The solution to the problem is an action sequence that leads from initial state to goal state and the solution quality is measured by the path cost function. An optimal solution has the lowest path cost among all the solutions.

An Example Problem Formulation

Let us take the example of vacuum world that was introduced in the starting of this series, There is a vacuum cleaner agent and it can move left or right and its jump is to suck up the dirt from the floor.

The problem for vacuum world can be formulated as follows:

States: The state is determined by both the agent location and the dirt location. The agent is in one of two locations, each of which might or might not contain dirt. Therefore, there are 2 x 2 ² = 8 possible world states.

A larger environment would have n x 2 to the power of n states.

Initial State: Any state can be assigned as the initial state in this case.

Action: In this environment there are three actions, Move Left , Move Right , Suck up the dirt.

Transition Model: All the actions have expected effects, except for when the agent is in leftmost square and the action is Left , when the agent is in rightmost square and the action is Right and the square is clean when the action is to Suck.

Goal Test: Goal test checks whether all the squares are clean.

Path Cost: Each step costs 1, so the path cost is the number of steps in the path.

The vacuum world problem is a toy problem and involves only discrete locations, discrete dirt etc. Therefore, this problem is a Toy Problem . There are many Real-World Problems like the automated taxi world. Try to formulate problems of real world and see what would be the states be and what actions could be chosen etc.

In this article we have discussed mainly about problem formulation. In the next article of this series we will be discussing about finding solutions using Searching Methods .

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Problem Solving

Definitions.

Searching is one of the classic areas of AI.

A problem is a tuple $(S, s, A, \rho, G, P)$ where

Example: A water jug problem

You have a two-gallon jug and a one-gallon jug; neither have any measuring marks on them at all. Initially both are empty. You need to get exactly one gallon into the two-gallon jug. Formally:

A graphical view of the transition function (initial state shaded, goal states outlined bold):

And a tabular view:

To solve this problem, an agent would start at the initial state and explore the state space by following links until it arrived in a goal state. A solution to the water jug problem is a path from the initial state to a goal state .

Example solutions

There are an infinite number of solutions. Sometimes we are interested in the solution with the smallest path cost; more on this later.

Awww Man.... Why are we studying this?

Even if they’re not completely right, there are still zillions of problems that can be formulated in problem spaces, e.g.

Problem Types

State finding vs. action sequence finding.

A fundamental distinction:

Offline vs. Online Problems

In an online problem, the agent doesn’t even know what the state space is, and has to build a model of it as it acts. In an offline problem, percepts don’t matter at all. An agent can figure out the entire action sequence before doing anything at all .

Offline Example : Vacuum World with two rooms, cleaning always works, a square once cleaned stays clean. States are 1 – 8, goal states are 1 and 5.

Sensorless (Conformant) Problems

The agent doesn’t know where it is. We can use belief states (sets of states that the agent might be in). Example from above deterministic, static, single-agent vacuum world:

Note the goal states are 1 and 5. If a state 15 was reachable, it would be a goal too.

Contingency Problems

Contingency Problem: The agent doesn’t know what effect its actions will have. This could be due to the environment being partially observable, or because of another agent. Ways to handle this:

Example: Partially observable vacuum world (meaning you don’t know the status of the other square) in which sucking in a clean square may make it dirty.

Can also model contingency problems is with "AND-OR graphs".

Example: find a winning strategy for Nim if there are only five stones in one row left. You are player square. You win if it is player circle’s turn with zero stones left.

In general then, a solution is a subtree in which

If the tree has only OR nodes, then the solution is just a path.

Search Algorithms

Hey, we know what a problem is, what a problem space is, and even what a solution is, but how exactly do we search the space ? Well there are zillions of approaches:

Types of Problem Solving Tasks

Agents may be asked to be

An algorithm is

Search Trees

Example: The water jug problem with 4 and 3 gallon jugs. Cost is 1 point per gallon used when filling, 1 point to make a transfer, 5 points per gallon emptied (since it makes a mess). The search tree might start off like this:

Search trees have

The complexity of most search algorithms can be written as a function of one or more of $b$, $d$ and $m$.

In general though there may be more states than there are fundamental particles in the universe. But we need to find a solution. Usually is helpful to

An Introduction to Problem-Solving using Search Algorithms for Beginners

This article was published as a part of the Data Science Blogathon

In computer science, problem-solving refers to artificial intelligence techniques, including various techniques such as forming efficient algorithms, heuristics, and performing root cause analysis to find desirable solutions.

The basic crux of artificial intelligence is to solve problems just like humans.

Examples of Problems in Artificial Intelligence

In today’s fast-paced digitized world, artificial intelligence techniques are used widely to automate systems that can use the resource and time efficiently. Some of the well-known problems experienced in everyday life are games and puzzles. Using AI techniques, we can solve these problems efficiently. In this sense, some of the most common problems resolved by AI are

Problem solving techniques.

Properties of searching algorithms

Types of search algorithms

Uninformed search algorithms, comparison of various uninformed search algorithms, informed search algorithms, comparison of uninformed and informed search algorithms.

In artificial intelligence, problems can be solved by using searching algorithms, evolutionary computations, knowledge representations, etc.

In this article, I am going to discuss the various searching techniques that are used to solve a problem.

In general, searching is referred to as finding information one needs.

The process of problem-solving using searching consists of the following steps.

Let’s discuss some of the essential properties of search algorithms.

Properties of search algorithms

Completeness.

A search algorithm is said to be complete when it gives a solution or returns any solution for a given random input.

If a solution found is best (lowest path cost) among all the solutions identified, then that solution is said to be an optimal one.

Time complexity

The time taken by an algorithm to complete its task is called time complexity. If the algorithm completes a task in a lesser amount of time, then it is an efficient one.

Space complexity

It is the maximum storage or memory taken by the algorithm at any time while searching.

These properties are also used to compare the efficiency of the different types of searching algorithms.

Now let’s see the types of the search algorithm.

Based on the search problems, we can classify the search algorithm as

The uninformed search algorithm does not have any domain knowledge such as closeness, location of the goal state, etc. it behaves in a brute-force way. It only knows the information about how to traverse the given tree and how to find the goal state. This algorithm is also known as the Blind search algorithm or Brute -Force algorithm.

The uninformed search strategies are of six types.

Let’s discuss these six strategies one by one.

1. Breadth-first search

It is of the most common search strategies. It generally starts from the root node and examines the neighbor nodes and then moves to the next level. It uses First-in First-out (FIFO) strategy as it gives the shortest path to achieving the solution.

BFS is used where the given problem is very small and space complexity is not considered.

Now, consider the following tree.

Breadth-First search | Problem-Solving using AI

Source: Author

Here, let’s take node A as the start state and node F as the goal state.

The BFS algorithm starts with the start state and then goes to the next level and visits the node until it reaches the goal state.

In this example, it starts from A and then travel to the next level and visits B and C and then travel to the next level and visits D, E, F and G. Here, the goal state is defined as F. So, the traversal will stop at F.

The path of traversal is:

A —-> B —-> C —-> D —-> E —-> F

Let’s implement the same in python programming.

Python Code:

Advantages of BFS

Disadvantages of BFS

2. Depth-first search

The depth-first search uses Last-in, First-out (LIFO) strategy and hence it can be implemented by using stack. DFS uses backtracking. That is, it starts from the initial state and explores each path to its greatest depth before it moves to the next path.

DFS will follow

Root node —-> Left node —-> Right node

Now, consider the same example tree mentioned above.

Here, it starts from the start state A and then travels to B and then it goes to D. After reaching D, it backtracks to B. B is already visited, hence it goes to the next depth E and then backtracks to B. as it is already visited, it goes back to A. A is already visited. So, it goes to C and then to F. F is our goal state and it stops there.

A —-> B —-> D —-> E —-> C —-> F

The output path is as follows.

Advantages of DFS

Disadvantages of DFS

3. Depth-limited search

Depth-limited works similarly to depth-first search. The difference here is that depth-limited search has a pre-defined limit up to which it can traverse the nodes. Depth-limited search solves one of the drawbacks of DFS as it does not go to an infinite path.

DLS ends its traversal if any of the following conditions exits.

Standard Failure

It denotes that the given problem does not have any solutions.

Cut off Failure Value

It indicates that there is no solution for the problem within the given limit.

Now, consider the same example.

Let’s take A as the start node and C as the goal state and limit as 1.

The traversal first starts with node A and then goes to the next level 1 and the goal state C is there. It stops the traversal.

Depth-limited search example | Problem-Solving using AI

A —-> C

If we give C as the goal node and the limit as 0, the algorithm will not return any path as the goal node is not available within the given limit.

If we give the goal node as F and limit as 2, the path will be A, C, F.

Let’s implement DLS.

When we give C as goal node and 1 as limit the path will be as follows.

Advantages of DLS

It takes lesser memory when compared to other search techniques.

Disadvantages of DLS

4. Iterative deepening depth-first search

Iterative deepening depth-first search is a combination of depth-first search and breadth-first search. IDDFS find the best depth limit by gradually adding the limit until the defined goal state is reached.

Let me try to explain this with the same example tree.

Consider, A as the start node and E as the goal node. Let the maximum depth be 2.

The algorithm starts with A and goes to the next level and searches for E. If not found, it goes to the next level and finds E.

Iterative deepening depth-first search example

The path of traversal is

A —-> B —-> E

Let’s try to implement this.

The path generated is as follows.

Advantages of IDDFS

Disadvantages of IDDFS

It does all the works of the previous stage again and again.

5. Bidirectional search

The bidirectional search algorithm is completely different from all other search strategies. It executes two simultaneous searches called forward-search and backwards-search and reaches the goal state. Here, the graph is divided into two smaller sub-graphs. In one graph, the search is started from the initial start state and in the other graph, the search is started from the goal state. When these two nodes intersect each other, the search will be terminated.

Bidirectional search requires both start and goal start to be well defined and the branching factor to be the same in the two directions.

Consider the below graph.

Bidirectional Search Example | Problem-Solving using AI

Here, the start state is E and the goal state is G. In one sub-graph, the search starts from E and in the other, the search starts from G. E will go to B and then A. G will go to C and then A. Here, both the traversal meets at A and hence the traversal ends.

E —-> B —-> A —-> C —-> G

Let’s implement the same in Python.

The path is generated as follows.

Advantages of bidirectional search

Disadvantages of bidirectional search

6. Uniform cost search

Uniform cost search is considered the best search algorithm for a weighted graph or graph with costs. It searches the graph by giving maximum priority to the lowest cumulative cost. Uniform cost search can be implemented using a priority queue.

Consider the below graph where each node has a pre-defined cost.

Uniform Cost Search example | Problem-Solving using AI

Here, S is the start node and G is the goal node.

From S, G can be reached in the following ways.

Here, the path with the least cost is S, B, E, F, G.

Let’s implement UCS in Python.

The optimal output path is generated.

Advantages of UCS

This algorithm is optimal as the selection of paths is based on the lowest cost.

Disadvantages of UCS

The algorithm does not consider how many steps it goes to reach the lowest path. This may result in an infinite loop also.

Now, let me compare the six different uninformed search strategies based on the time complexity.

This is all about uninformed search algorithms.

Let’s take a look at informed search algorithms.

The informed search algorithm is also called heuristic search or directed search. In contrast to uninformed search algorithms, informed search algorithms require details such as distance to reach the goal, steps to reach the goal, cost of the paths which makes this algorithm more efficient.

Here, the goal state can be achieved by using the heuristic function.

The heuristic function is used to achieve the goal state with the lowest cost possible. This function estimates how close a state is to the goal.

Let’s discuss some of the informed search strategies.

1. Greedy best-first search algorithm

Greedy best-first search uses the properties of both depth-first search and breadth-first search. Greedy best-first search traverses the node by selecting the path which appears best at the moment. The closest path is selected by using the heuristic function.

Consider the below graph with the heuristic values.

Greedy best-first search algorithm example | Problem-Solving using AI

Here, A is the start node and H is the goal node.

Greedy best-first search first starts with A and then examines the next neighbour B and C. Here, the heuristics of B is 12 and C is 4. The best path at the moment is C and hence it goes to C. From C, it explores the neighbours F and G. the heuristics of F is 8 and G is 2. Hence it goes to G. From G, it goes to H whose heuristic is 0 which is also our goal state.

Path of traversal in Greedy best-first search algorithm | Problem-Solving using AI

A —-> C —-> G —-> H

Let’s try this with Python.

The output path with the lowest cost is generated.

The time complexity of Greedy best-first search is O(b m ) in worst cases.

Advantages of Greedy best-first search

Greedy best-first search is more efficient compared with breadth-first search and depth-first search.

Disadvantages of Greedy best-first search

Next, let’s discuss the other informed search algorithm called the A* search algorithm.

2. A* search algorithm

A* search algorithm is a combination of both uniform cost search and greedy best-first search algorithms. It uses the advantages of both with better memory usage. It uses a heuristic function to find the shortest path. A* search algorithm uses the sum of both the cost and heuristic of the node to find the best path.

Consider the following graph with the heuristics values as follows.

A* search example | Problem-Solving using AI

Let A be the start node and H be the goal node.

First, the algorithm will start with A. From A, it can go to B, C, H.

Note the point that A* search uses the sum of path cost and heuristics value to determine the path.

Here, from A to B, the sum of cost and heuristics is 1 + 3 = 4.

From A to C, it is 2 + 4 = 6.

From A to H, it is 7 + 0 = 7.

Here, the lowest cost is 4 and the path A to B is chosen. The other paths will be on hold.

Now, from B, it can go to D or E.

From A to B to D, the cost is 1 + 4 + 2 = 7.

From A to B to E, it is 1 + 6 + 6 = 13.

The lowest cost is 7. Path A to B to D is chosen and compared with other paths which are on hold.

Here, path A to C is of less cost. That is 6.

Hence, A to C is chosen and other paths are kept on hold.

From C, it can now go to F or G.

From A to C to F, the cost is 2 + 3 + 3 = 8.

From A to C to G, the cost is 2 + 2 + 1 = 5.

The lowest cost is 5 which is also lesser than other paths which are on hold. Hence, path A to G is chosen.

From G, it can go to H whose cost is 2 + 2 + 2 + 0 = 6.

Here, 6 is lesser than other paths cost which is on hold.

Also, H is our goal state. The algorithm will terminate here.

Path of traversal in A* | Problem-Solving using AI

Let’s try this in Python.

The output is given as

The time complexity of the A* search is O(b^d) where b is the branching factor.

Advantages of A* search algorithm

Disadvantages of A* search algorithm

Now, let’s compare uninformed and informed search strategies.

Uninformed search is also known as blind search whereas informed search is also called heuristics search. Uniformed search does not require much information. Informed search requires domain-specific details. Compared to uninformed search, informed search strategies are more efficient and the time complexity of uninformed search strategies is more. Informed search handles the problem better than blind search.

Search algorithms are used in games, stored databases, virtual search spaces, quantum computers, and so on. In this article, we have discussed some of the important search strategies and how to use them to solve the problems in AI and this is not the end. There are several algorithms to solve any problem. Nowadays, AI is growing rapidly and applies to many real-life problems. Keep learning! Keep practicing!

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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:

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

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 state space graph for the two-cell vacuum world.

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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COMMENTS

Problem Solving in Artificial Intelligence
The problem-solving agent performs precisely by defining problems and several solutions. So we can say that problem solving is a part of
Problem Solving Agent
Problem Solving Agent ... Example: Vacuum world, The effect of a suck action is random. There is no action sequence that can be calculated at planning time and is
Artificial Intelligence Series: Problem Solving Agents
Let us take the example of vacuum world that was introduced in the starting of this series, There is a vacuum cleaner agent and it can move left
Common Examples of Problem-Solving Agents
Slide 6 of 27.
Problem Solving
An agent that tries to come up with a sequence of actions that will bring the environment into a desired state. Search: The process of looking for such a
An Introduction to Problem-Solving using Search Algorithms for
The basic crux of artificial intelligence is to solve problems just like humans. Examples of Problems in Artificial Intelligence.
Problem solving agents
Define problem. Problem Solving Agents: A problem-solving agent is a goal-driven agent and. Well Defined Problems And Solutions A problem can be defined
Problem-Solving Agents
Artificial Intelligence – Intelligent Agents. Problem-Solving Agents. Subclass of goal-based agents goal formulation problem formulation example problems.
Problem Solving Agents in Artificial Intelligence
Initial State. 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)
Problem Solving Agents with Example Problems.
Artificial_intelligence #problem_solving_agents Hello Friends, In this video you are going to learn about : problem solving agents.