HEURISTIC SEARCH 4.0 Introduction 4.3 Using Heuristics I

HEURISTIC SEARCH 4.0 Introduction 4.3  Using Heuristics I

HEURISTIC SEARCH 4.0 Introduction 4.3

Using Heuristics I n Games 4.1 An Algorithm for Heuristic Search 4.4

Complexity Issues 4.2 Admissibility, Monotonicity, and Informedness

4.5 Epilogue and References 4.6

Exercises George F Luger ARTIFICIAL INTELLIGENCE 6th edition Structures and Strategies for Complex Problem Solving 1

Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.1 First three levels of the tic-tac-toe state space reduced by symmetry 2 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.2 The most wins heuristic applied to the first children in tic-tac-toe. 3 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.3 Heuristically reduced state space for tic-tac-toe.

4 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.4 The local maximum problem for hill-climbing with 3-level look ahead 5

Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.5 The initialization stage and first step in completing the array for character alignment using dynamic programming. 6 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.6 The completed array reflecting the maximum alignment information for the strings. 7 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.7 A completed backward component of the dynamic programming example giving one (of several possible) string alignments. 8 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.8 Initialization of minimum edit difference matrix between intention

and execution (adapted from Jurafsky and Martin, 2000). 9 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 10 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.9 Complete array of minimum edit difference between intention and execution (adapted from Jurafsky and Martin, 2000) (of several possible) string alignments. Intention ntention

delete I, cost 1 etention cost 2 replace n with e,

exention cost 2 replace t with x, exenution insert u, cost 1

11 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 12 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.10 Heuristic search of a hypothetical state space.

13 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 A trace of the execution of best_first_search for Figure 4.4 14

Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.11 Heuristic search of a hypothetical state space with open and closed states highlighted. 15 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.12 The start state, first moves, and goal state for an example-8 puzzle. 16 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.14 Three heuristics applied to states in the 8-puzzle.

17 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.15 The heuristic f applied to states in the 8-puzzle. 18

Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 The successive stages of open and closed that generate this graph are: 19 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.16 State space generated in heuristic search of the 8-puzzle graph. 20 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.17 Open and closed as they appear after the 3rd iteration of heuristic search

21 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 22 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

23 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 24 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.18

Comparison of state space searched using heuristic search with space searched by breadth-first search. The proportion of the graph searched heuristically is shaded. The optimal search selection is in bold. Heuristic used is f(n) = g(n) + h(n) where h(n) is tiles out of place. 25

Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.19 State space for a variant of nim. Each state partitions the seven matches into one or more piles. 26 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.20 Exhaustive minimax for the game of nim. Bold lines indicate forced win for MAX. Each node is marked with its derived value (0 or 1) under minimax. 27

Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.21 Minimax to a hypothetical state space. Leafstates show heuristic values; internal states show backed-up values. 28 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.22 Heuristic measuring conflict applied to states of tic-tac-toe. 29 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.23 Two-ply minimax applied to the opening move of tic-tac-toe, from

Nilsson (1971). 30 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.24 Two ply minimax, and one of two possible MAX second moves, from Nilsson (1971).

31 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.25 Two-ply minimax applied to Xs move near the end of the game, from Nilsson (1971).

32 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.26 Alpha-beta pruning applied to state space of Fig 4.21. States without numbers are not evaluated. 33

Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.27 Number of nodes generated as a function of branching factor, B, for various lengths, L, of solution paths. The relating equation is T = B(BL 1)/(B 1), adapted from Nilsson (1980).

34 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.28 Informal plot of cost of searching and cost of computing heuristic evaluation against informedness of heuristic, adapted from Nilsson (1980).

35 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.29 The sliding block puzzle. 36 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

Fig 4.30. 37 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009 Fig 4.31.

38 Luger: Artificial Intelligence, 6th edition. Pearson Education Limited, 2009

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