Informed Search by the artificial intelligence
- 2. Outline • Best-first search • Greedy best-first search • A* search
- 3. Search Heuristics A heuristic is: A function that estimates how close a state is to a goal Designed for a particular search problem Examples: Manhattan distance, Euclidean distance for pathing 10 5 11.2
- 5. Best-first search • Idea: use an evaluation function f(n) for each node • estimate of "desirability" Expand most desirable unexpanded node • Implementation: Order the nodes in fringe in decreasing order of desirability
- 6. Best-first search A T S Z 118 140 75
- 7. Best-first search A T S Z O 118 140 75 71
- 8. Best-first search A T S Z S O 118 140 75 71 151
- 9. Best-first search A T S Z S R F O 118 140 75 71 151 90 80
- 10. Best-first search A T S Z C S R F O P 118 140 75 71 151 90 80 97 146
- 11. Best-first search A T S Z C S R F O P C B 118 140 75 71 151 90 80 97 146 138 101
- 12. Best-first search A T S Z C S R F O P C B 118 140 75 71 151 90 80 97 146 138 101
- 14. Properties of Best First Search • Complete? No – can get stuck in loops • Optimal? No
- 15. Difference between Uniform Cost Search and Best First Search • Uniform-cost search is uninformed search • It doesn't use any domain knowledge. • It expands the least cost node, and it does so in every direction because no information about the goal is provided. • Best-first search is informed search • It uses a heuristic function to estimate how close the current state is to the goal.
- 16. Greedy best-first search • Evaluation function f(n) = h(n) (heuristic) = estimate of cost from n to goal • e.g., hSLD(n) = straight-line distance from n to Bucharest • Greedy best-first search expands the node that appears to be closest to goal
- 17. Greedy best-first search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 18. Greedy best-first search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 19. Greedy best-first search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 20. Greedy best-first search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 21. Greedy best-first search (DIY)
- 22. Properties of greedy best-first search • Complete? No – can get stuck in loops • Optimal? No
- 23. A* search • Idea: avoid expanding paths that are already expensive • Evaluation function f(n) = g(n) + h(n) • g(n) = cost so far to reach n • h(n) = estimated cost from n to goal • f(n) = estimated total cost of path through n to goal
- 24. A* search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 25. A* search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 26. A* search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 27. A* search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 28. A* search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 29. A* search example A 366 B 0 C 160 D 242 E 161 F 176 G 77 H 151 I 226 L 244 M 241 N 234 O 380 P 100 R 193 S 253 T 329 U 80 V 199 Z 374
- 30. Admissible heuristics • A heuristic h(n) is admissible if for every node n, h(n) ≤ h*(n), where h*(n) is the true cost to reach the goal state from n. • An admissible heuristic never overestimates the cost to reach the goal, i.e., it is optimistic • Example: hSLD(n) (never overestimates the actual road distance) • Theorem: If h(n) is admissible, A* using TREE-SEARCH is optimal
- 31. Properties of A* • Complete? Yes (unless there are infinitely many nodes with f ≤ f(G) ) • Space? Keeps all nodes in memory • Optimal? Yes
- 32. A* search (DIY)
- 33. Video of Demo Contours UCS Empty
- 34. Video of Demo Contours (Empty) -- Greedy
- 35. Video of Demo Contours (Empty) – A*
- 36. Video of Demo Contours UCS Pacman Small Maze
- 37. Video of Demo Contours Greedy (Pacman Small Maze)
- 38. Video of Demo Contours (Pacman Small Maze) – A*
Editor's Notes
- #23: Not complete since going for Iasi to Fagaas > the algorithm will never find the solution Iasi-> Vaslui -> Urziceni -> Bucharest -> Fagaras
- #31: Conditions for optimality: Admissibility and consistency Consistency (monotonocity) is slightly stronger than admissibility Every consistent heuristic is also admissible.