AI_Session 8 A searching algorithm .pptx

AI_Session 8 A searching algorithm .pptx

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  ARTIFICAL INTELLIGENCE (R18 III(IISem)) Department of computer science and engineering (AI/ML) Session 8 by Asst.Prof.M.Gokilavani VITS 3/1/2023 Department of CSE (AI/ML) 1
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  TEXTBOOK: • Artificial IntelligenceA modern Approach, Third Edition, Stuart Russell and Peter Norvig, Pearson Education. REFERENCES: • Artificial Intelligence, 3rd Edn, E. Rich and K.Knight (TMH). • Artificial Intelligence, 3rd Edn, Patrick Henny Winston, Pearson Education. • Artificial Intelligence, Shivani Goel, Pearson Education. • Artificial Intelligence and Expert Systems- Patterson, Pearson Education. 3/1/2023 Department of CSE (AI/ML) 2
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  Topics covered insession 8 3/1/2023 Department of CSE (AI/ML) 3 • Problem solving by search-I: Introduction to AI, Intelligent Agents. • Problem solving by search-II: Problem solving agents, searching for solutions • Uniformed search strategies: BFS, Uniform cost search, DFS, Iterative deepening Depth-first search, Bidirectional search, • Informed ( Heuristic) search strategies: Greedy best-first search, A* search, Heuristic functions • Beyond classical search: Hill- climbing Search, Simulated annealing search, Local search in continuous spaces, Searching with non-deterministic Actions, searching with partial observations, online search agents and unknown environments.
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  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. • This is informed search technique also called as HEURISTIC search. This algo. Works using heuristic value. 3/1/2023 Department of CSE (AI/ML) 4
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  Working of A*Search algorithm 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- • Evaluation 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 3/1/2023 Department of CSE (AI/ML) 5
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  A* search 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. 3/1/2023 Department of CSE (AI/ML) 6
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  A* search Algorithm •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. 3/1/2023 Department of CSE (AI/ML) 7
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  Example with Solution Consider thefollowing 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. 3/1/2023 Department of CSE (AI/ML) 8
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  Step-01: • We startwith 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 3/1/2023 Department of CSE (AI/ML) 9
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  Step-02: • Node Gand 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 3/1/2023 Department of CSE (AI/ML) 10
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  Step-03: • Node Ican 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 3/1/2023 Department of CSE (AI/ML) 11
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  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. 3/1/2023 Department of CSE (AI/ML) 12
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  Shortest path forthe given tree 3/1/2023 Department of CSE (AI/ML) 13
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  Advantages of 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 3/1/2023 Department of CSE (AI/ML) 16
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  Topics to becovered in next session 9 • Beyond classical search: Hill- climbing Search 3/1/2023 Department of CSE (AI/ML) 17 Thank you!!!