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Ch2 3-informed (heuristic) search

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Problem Solving by Searching Search Methods : informed (Heuristic) search
Using problem specific knowledge to aid searching ,[object Object],[object Object],Search everywhere!!
Using problem specific knowledge to aid searching ,[object Object],[object Object],[object Object],Search only in this subtree!! A B C E D F G H I J K L O M N
More formally, why heuristic functions work? ,[object Object],[object Object],[object Object]
Heuristic Functions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Approach 1: f Measures the Value of the Current State ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Approach 2: f Measures the Cost to the Goal ,[object Object],[object Object],[object Object],[object Object]
Approach 3: f measures the total cost of the solution path (Admissible Heuristic Functions) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Traditional informed search strategies ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Informed Search Strategies Best First Search
An implementation of Best First Search ,[object Object],[object Object],[object Object],[object Object]
Informed Search Strategies Greedy Search eval-fn : f(n) = h(n)
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search: Tree Search Start A
Greedy Search: Tree Search Start 75 118 140 [374] [329] [253] A B C E
Greedy Search: Tree Search 99 80 Start 75 118 140 [374] [329] [253] [193] [366] [178] A B C E F G A
Greedy Search: Tree Search 99 211 80 Start Goal 75 118 140 [374] [329] [253] [193] [366] [178] [0] [253] A B C E F I G A E
Greedy Search: Tree Search 99 211 80 Start Goal 75 118 140 [374] [329] [253] [193] [366] [178] [0] [253] Path cost(A-E-F-I) = 253 + 178 + 0 = 431 dist(A-E-F-I) = 140 + 99 + 211 = 450 A B C E F I G A E
Greedy Search: Optimal ? 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic dist(A-E-G-H-I) =140+80+97+101= 418 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search: Complete ? 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 ** C 250 D 244 E 253 F 178 G 193 H 98 I 0
Greedy Search: Tree Search Start A
Greedy Search: Tree Search Start 75 118 140 [374] [250] [253] A B C E
Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] A B C E D
Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] [250] Infinite Branch ! A B C E D C
Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] [250] [244] Infinite Branch ! A B C E D C D
Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] [250] [244] Infinite Branch ! A B C E D C D
Greedy Search: Time and Space Complexity ? 99 211 80 Start Goal 97 101 75 118 111 140 ,[object Object],[object Object],[object Object],[object Object],A B D C E F I G H
Informed Search Strategies A* Search eval-fn : f(n)=g(n)+h(n)
A* (A Star) ,[object Object],[object Object],[object Object]
A* (A Star) ,[object Object],[object Object],[object Object]
A* (A Star) g(n) h(n) f(n) = g(n)+h(n) n
A* Search f(n) = g(n) + h ( n ) g(n): is the exact cost to reach node n from the initial state. State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0 A B D C E F I 99 211 G H 80 Start Goal 97 101 75 118 111 140
A* Search: Tree Search Start A
A* Search: Tree Search Start 75 118 140 [393] [449] [447] A B C E
A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] A B C E F G
A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] 97 [415] A B C E F G H
A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] A B C E F I G H
A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] [450] A B C E F I G H I
A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] [450] A B C E F I G H I
A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] [450] A B C E F I G H I
A* with f() not Admissible h() overestimates the cost to reach the goal state
A* Search: h not admissible ! 99 211 80 Start Goal 97 101 75 118 111 f(n) = g(n) + h ( n ) – (H-I) Overestimated g(n): is the exact cost to reach node n from the initial state. 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 138 I 0
A* Search: Tree Search Start A
A* Search: Tree Search Start 75 118 140 [393] [449] [447] A B C E
A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] A B C E F G
A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] 97 [455] A B C E F G H
A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] A B C E F G H I
A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A B C E F G H I D
A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A B C E F G H I D
A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A B C E F G H I D
A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A* not optimal !!! A B C E F G H I D
A* Algorithm A* with systematic checking for repeated states …
A* Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
A* Search: Analysis 99 211 80 Start Goal 97 101 75 118 111 140 ,[object Object],[object Object],[object Object],[object Object],A B D C E F I G H
Informed Search Strategies Iterative Deepening A*
Iterative Deepening A*:IDA* ,[object Object],[object Object]
Consistent Heuristic ,[object Object],[object Object],N N’ h(N) h(N’) c(N,N’)
IDA* Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object]
8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=4 4 6
8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6
8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5
8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 5
8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 5 6
8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 6
8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6
8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5
8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7
8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7 5
8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7 5 5
8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7 5 5
When to Use Search Techniques ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Conclusions ,[object Object],[object Object]

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Ch2 3-informed (heuristic) search

  • 1. Problem Solving by Searching Search Methods : informed (Heuristic) search
  • 2.
  • 3.
  • 4.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10. Informed Search Strategies Best First Search
  • 11.
  • 12. Informed Search Strategies Greedy Search eval-fn : f(n) = h(n)
  • 13. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 14. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 15. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 16. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 17. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 18. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 19. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 20. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 21. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 22. Greedy Search 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 23. Greedy Search: Tree Search Start A
  • 24. Greedy Search: Tree Search Start 75 118 140 [374] [329] [253] A B C E
  • 25. Greedy Search: Tree Search 99 80 Start 75 118 140 [374] [329] [253] [193] [366] [178] A B C E F G A
  • 26. Greedy Search: Tree Search 99 211 80 Start Goal 75 118 140 [374] [329] [253] [193] [366] [178] [0] [253] A B C E F I G A E
  • 27. Greedy Search: Tree Search 99 211 80 Start Goal 75 118 140 [374] [329] [253] [193] [366] [178] [0] [253] Path cost(A-E-F-I) = 253 + 178 + 0 = 431 dist(A-E-F-I) = 140 + 99 + 211 = 450 A B C E F I G A E
  • 28. Greedy Search: Optimal ? 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic dist(A-E-G-H-I) =140+80+97+101= 418 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0
  • 29. Greedy Search: Complete ? 99 211 80 Start Goal 97 101 75 118 111 f(n) = h ( n ) = straight-line distance heuristic 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 ** C 250 D 244 E 253 F 178 G 193 H 98 I 0
  • 30. Greedy Search: Tree Search Start A
  • 31. Greedy Search: Tree Search Start 75 118 140 [374] [250] [253] A B C E
  • 32. Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] A B C E D
  • 33. Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] [250] Infinite Branch ! A B C E D C
  • 34. Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] [250] [244] Infinite Branch ! A B C E D C D
  • 35. Greedy Search: Tree Search 111 Start 75 118 140 [374] [250] [253] [244] [250] [244] Infinite Branch ! A B C E D C D
  • 36.
  • 37. Informed Search Strategies A* Search eval-fn : f(n)=g(n)+h(n)
  • 38.
  • 39.
  • 40. A* (A Star) g(n) h(n) f(n) = g(n)+h(n) n
  • 41. A* Search f(n) = g(n) + h ( n ) g(n): is the exact cost to reach node n from the initial state. State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 98 I 0 A B D C E F I 99 211 G H 80 Start Goal 97 101 75 118 111 140
  • 42. A* Search: Tree Search Start A
  • 43. A* Search: Tree Search Start 75 118 140 [393] [449] [447] A B C E
  • 44. A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] A B C E F G
  • 45. A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] 97 [415] A B C E F G H
  • 46. A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] A B C E F I G H
  • 47. A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] [450] A B C E F I G H I
  • 48. A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] [450] A B C E F I G H I
  • 49. A* Search: Tree Search 99 80 Start 97 101 75 118 140 [393] [449] [447] [417] [413] [415] Goal [418] [450] A B C E F I G H I
  • 50. A* with f() not Admissible h() overestimates the cost to reach the goal state
  • 51. A* Search: h not admissible ! 99 211 80 Start Goal 97 101 75 118 111 f(n) = g(n) + h ( n ) – (H-I) Overestimated g(n): is the exact cost to reach node n from the initial state. 140 A B D C E F I G H State Heuristic: h(n) A 366 B 374 C 329 D 244 E 253 F 178 G 193 H 138 I 0
  • 52. A* Search: Tree Search Start A
  • 53. A* Search: Tree Search Start 75 118 140 [393] [449] [447] A B C E
  • 54. A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] A B C E F G
  • 55. A* Search: Tree Search 99 80 Start 75 118 140 [393] [449] [447] [417] [413] 97 [455] A B C E F G H
  • 56. A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] A B C E F G H I
  • 57. A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A B C E F G H I D
  • 58. A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A B C E F G H I D
  • 59. A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A B C E F G H I D
  • 60. A* Search: Tree Search 99 80 Start 97 75 118 140 [393] [449] [447] [417] [413] [455] Goal [450] [473] A* not optimal !!! A B C E F G H I D
  • 61. A* Algorithm A* with systematic checking for repeated states …
  • 62.
  • 63.
  • 64. Informed Search Strategies Iterative Deepening A*
  • 65.
  • 66.
  • 67.
  • 68. 8-Puzzle f(N) = g(N) + h(N) with h(N) = number of misplaced tiles Cutoff=4 4 6
  • 69. 8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6
  • 70. 8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5
  • 71. 8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 5
  • 72. 8-Puzzle Cutoff=4 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 5 6
  • 73. 8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 6
  • 74. 8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6
  • 75. 8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5
  • 76. 8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7
  • 77. 8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7 5
  • 78. 8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7 5 5
  • 79. 8-Puzzle Cutoff=5 f(N) = g(N) + h(N) with h(N) = number of misplaced tiles 4 4 6 6 5 7 5 5
  • 80.
  • 81.