A Star Algorithm in Artificial intelligence

A Star Algorithm in Artificial intelligence

• 1.
  A* Search Algorithm This is informed search technique also called as HEURISTIC search.  This algo. Works using heuristic value.  A*uses h(n)->Heuristic function & g(n)->Cost to reach the node ‘n’ from start state.  Find shortest path though search spaces.  Estimated Cost f(n)=g(n)+h(n)  A* gives Fast & Optimal result as compared with previous algorithms.  Space & Time Complexity of BFS is also O(V+E) where V is vertices and E is edges.
• 2.
  A* Search Algorithm 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
• 3.
  A* Search Algorithm Thealgorithm 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.
• 4.
  A* Search Algorithm 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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  A* Search Algorithm Examplewith Solution: 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
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  A* Search Algorithm Examplewith Solution: 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). Estimated Cost f(n)=g(n) +h(n) f(B) = 6 + 8 = 14 f(F) = 3 + 6 = 9 Since f(F) < f(B), so it decides to go to node F. ->Closed list(F) Path- A
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  A* Search Algorithm Examplewith Solution: Solution- 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. ->Closed list(G)
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  A* Search Algorithm Examplewith Solution: Solution- 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. ->Closed list(I)
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  A* Search Algorithm Examplewith Solution: Solution- 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. ->Closed list(J) Shortest Path- A → F → G → I →
• 10.
  A* Search Algorithm EXAMPLE-02
• 11.
  A* Search Algorithm Advantagesof BFS: A* Algorithm is one of the best path finding algorithms. It is Complete & Optimal Used to solve complex problems. Disadvantages of BFS: Requires more memory