AI3391 Session 10 A searching algorithm.pptx
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This document covers the A* algorithm in artificial intelligence, detailing its functioning as a best-first search method for pathfinding and graph traversal. It explains the algorithm's evaluation function, the maintenance of open and closed lists, and provides a step-by-step example demonstrating how to find the shortest path using the A* algorithm. Additionally, it addresses the advantages and disadvantages of the algorithm in problem-solving contexts.
AI3391 Session 10 A searching algorithm.pptx
- 1. AI3391 ARTIFICAL INTELLIGENCE (II YEAR (III Sem)) Department of Artificial Intelligence and Data Science Session 10 by Asst.Prof.M.Gokilavani NIET 11/14/2023 Department of AI & DS 1
- 2. TEXTBOOK: • Artificial Intelligence A 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. 11/14/2023 Department of CSE (AI/ML) 2
- 3. Topics covered in session 10 11/14/2023 Department of AI & DS 3 Unit II: Problem Solving • Heuristic search Strategies • Heuristic function • Local search and optimization problems • Local search in continuous space • Search with non deterministic actions • Search in partial observation environments • Online search agents and unknown environment
- 4. 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. 11/14/2023 Department of CSE (AI/ML) 4
- 5. 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 11/14/2023 Department of CSE (AI/ML) 5
- 6. 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. 11/14/2023 Department of CSE (AI/ML) 6
- 7. 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. 11/14/2023 Department of CSE (AI/ML) 7
- 8. Example with 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 from start state A to final state J using A* Algorithm. 11/14/2023 Department of CSE (AI/ML) 8
- 9. 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 11/14/2023 Department of CSE (AI/ML) 9
- 10. 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 11/14/2023 Department of CSE (AI/ML) 10
- 11. 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 11/14/2023 Department of CSE (AI/ML) 11
- 12. 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. 11/14/2023 Department of CSE (AI/ML) 12
- 13. Shortest path for the given tree 11/14/2023 Department of CSE (AI/ML) 13
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- 15. 11/14/2023 Department of CSE (AI/ML) 15
- 16. 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 11/14/2023 Department of CSE (AI/ML) 16
- 17. Topics to be covered in next session 11 • Beyond classical search: Hill- climbing Search 11/14/2023 Department of CSE (AI/ML) 17 Thank you!!!