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A* Algorithm | A* Algorithm Example in AI

Artificial Intelligence

A* Algorithm-

 

  • A* Algorithm is one of the best and popular techniques used for path finding and graph traversals.
  • A lot of games and web-based maps use this algorithm for finding the shortest path efficiently.
  • It is essentially a best first search algorithm.

 

Working-

 

A* Algorithm works as-

  • It maintains a tree of paths originating at the start node.
  • It extends those paths one edge at a time.
  • It continues until its termination criterion is satisfied.

 

A* Algorithm extends the path that minimizes the following function-

f(n) = g(n) + h(n)

 

Here,

  • ‘n’ is the last node on the path
  • g(n) is the cost of the path from start node to node ‘n’
  • h(n) is a heuristic function that estimates cost of the cheapest path from node ‘n’ to the goal node

 

Algorithm-

 

  • The implementation of A* Algorithm involves maintaining two lists- OPEN and CLOSED.
  • OPEN contains those nodes that have been evaluated by the heuristic function but have not been expanded into successors yet.
  • CLOSED contains those nodes that have already been visited.

 

The algorithm is as follows-

 

Step-01:

 

  • Define a list OPEN.
  • Initially, OPEN consists solely of a single node, the start node S.

 

Step-02:

 

If the list is empty, return failure and exit.

 

Step-03:

 

  • Remove node n with the smallest value of f(n) from OPEN and move it to list CLOSED.
  • If node n is a goal state, return success and exit.

 

Step-04:

 

Expand node n.

 

Step-05:

 

  • If any successor to n is the goal node, return success and the solution by tracing the path from goal node to S.
  • Otherwise, go to Step-06.

 

Step-06:

 

For each successor node,

  • Apply the evaluation function f to the node.
  • If the node has not been in either list, add it to OPEN.

 

Step-07:

 

Go back to Step-02.

 

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PRACTICE PROBLEMS BASED ON A* ALGORITHM-

 

Problem-01:

 

Given an initial state of a 8-puzzle problem and final state to be reached-

 

 

Find the most cost-effective path to reach the final state from initial state using A* Algorithm.

Consider g(n) = Depth of node and h(n) = Number of misplaced tiles.

 

Solution-

 

  • A* Algorithm maintains a tree of paths originating at the initial state.
  • It extends those paths one edge at a time.
  • It continues until final state is reached.

 

 

Problem-02:

 

Consider the following graph-

 

 

The numbers written on edges represent the distance between the nodes.

The numbers written on nodes represent the heuristic value.

Find the most cost-effective path to reach from start state A to final state J using A* Algorithm.

 

Solution-

 

Step-01:

 

  • We start with node A.
  • Node B and Node F can be reached from node A.

 

A* Algorithm calculates f(B) and f(F).

  • f(B) = 6 + 8 = 14
  • f(F) = 3 + 6 = 9

 

Since f(F) < f(B), so it decides to go to node F.

 

Path- A → F

 

Step-02:

 

Node G and Node H can be reached from node F.

 

A* Algorithm calculates f(G) and f(H).

  • f(G) = (3+1) + 5 = 9
  • f(H) = (3+7) + 3 = 13

 

Since f(G) < f(H), so it decides to go to node G.

 

Path- A → F → G

 

Step-03:

 

Node I can be reached from node G.

 

A* Algorithm calculates f(I).

f(I) = (3+1+3) + 1 = 8

It decides to go to node I.

 

Path- A → F → G → I

 

Step-04:

 

Node E, Node H and Node J can be reached from node I.

 

A* Algorithm calculates f(E), f(H) and f(J).

  • f(E) = (3+1+3+5) + 3 = 15
  • f(H) = (3+1+3+2) + 3 = 12
  • f(J) = (3+1+3+3) + 0 = 10

 

Since f(J) is least, so it decides to go to node J.

 

Path- A → F → G → I → J

This is the required shortest path from node A to node J.

 

 

Important Note-

 

It is important to note that-

  • A* Algorithm is one of the best path finding algorithms.
  • But it does not produce the shortest path always.
  • This is because it heavily depends on heuristics.

 

To gain better understanding about A* Search Algorithm,

Watch this Video Lecture

 

Get more notes and other study material of Artificial Intelligence.

Watch video lectures by visiting our YouTube channel LearnVidFun.

Genetic Algorithm in AI | Operators | Working

Artificial Intelligence

Genetic Algorithm-

 

In Artificial Intelligence,

  • Genetic Algorithm is one of the heuristic algorithms.
  • They are used to solve optimization problems.
  • They are inspired by Darwin’s Theory of Evolution.
  • They are an intelligent exploitation of a random search.
  • Although randomized, Genetic Algorithms are by no means random.

 

Algorithm-

 

Genetic Algorithm works in the following steps-

 

Step-01:

 

  • Randomly generate a set of possible solutions to a problem.
  • Represent each solution as a fixed length character string.

 

Step-02:

 

Using a fitness function, test each possible solution against the problem to evaluate them.

 

Step-03:

 

  • Keep the best solutions.
  • Use best solutions to generate new possible solutions.

 

Step-04:

 

Repeat the previous two steps until-

  • Either an acceptable solution is found
  • Or until the algorithm has completed its iterations through a given number of cycles / generations.

 

Basic Operators-

 

The basic operators of Genetic Algorithm are-

 

1. Selection (Reproduction)-

 

  • It is the first operator applied on the population.
  • It selects the chromosomes from the population of parents to cross over and produce offspring.
  • It is based on evolution theory of “Survival of the fittest” given by Darwin.

 

There are many techniques for reproduction or selection operator such as-

  • Tournament selection
  • Ranked position selection
  • Steady state selection etc.

 

2. Cross Over-

 

  • Population gets enriched with better individuals after reproduction phase.
  • Then crossover operator is applied to the mating pool to create better strings.
  • Crossover operator makes clones of good strings but does not create new ones.
  • By recombining good individuals, the process is likely to create even better individuals.

 

3. Mutation-

 

  • Mutation is a background operator.
  • Mutation of a bit includes flipping it by changing 0 to 1 and vice-versa.
  • After crossover, the mutation operator subjects the strings to mutation.
  • It facilitates a sudden change in a gene within a chromosome.
  • Thus, it allows the algorithm to see for the solution far away from the current ones.
  • It guarantees that the search algorithm is not trapped on a local optimum.
  • Its purpose is to prevent premature convergence and maintain diversity within the population.

 

Flow Chart-

 

The following flowchart represents how a genetic algorithm works-

 

 

Advantages-

 

Genetic Algorithms offer the following advantages-

 

Point-01:

 

  • Genetic Algorithms are better than conventional AI.
  • This is because they are more robust.

 

Point-02:

 

  • They do not break easily unlike older AI systems.
  • They do not break easily even in the presence of reasonable noise or if the inputs get change slightly.

 

Point-03:

 

While performing search in multi modal state-space or large state-space,

  • Genetic algorithms has significant benefits over other typical search optimization techniques.

 

To gain better understanding about Genetic Algorithm & its Working,

Watch this Video Lecture

 

Get more notes and other study material of Artificial Intelligence.

Watch video lectures by visiting our YouTube channel LearnVidFun.