PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH - PowerPoint PPT Presentation

PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH Nathan R. Sturtevant, Canada CIFAR AI Chair, Amii, University of Alberta Shahaf Shperberg , Ben-Gurion University Ariel Felner , Ben-Gurion University Jingwei Chen, University of Alberta Moving AI Lab

BIDIRECTIONAL SEARCH Q: When does bidirectional (heuristic) search perform well? A: Performance of bidirectional search is positively correlated with the number of states that have heuristics that are both low and inaccurate. Caveat: Not enough time in talk to be completely precise.

BARKER AND KORF (2015) A strong heuristic expands a majority of the states in the first half of the search. BK2: Unidirectional search outperforms bidirectional search with a strong heuristic.

Start HOLTE ET AL (2017) MM is guaranteed to meet in the middle. If |FF| > |RN|, A* will expand more states than MM if the heuristic is weak, fewer if the heuristic is accurate. Goal

Start FF HOLTE ET AL (2017) MM is guaranteed to meet in the middle. If |FF| > |RN|, A* will expand more states than MM if the heuristic is weak, fewer if the heuristic is accurate. Goal

Start FF HOLTE ET AL (2017) MM is guaranteed to meet in the middle. If |FF| > |RN|, A* will expand more states than MM if the heuristic is weak, fewer if the heuristic is accurate. RN Goal

ECKERLE ET AL (2017) Front-to-end bidirectional search - admissible heuristic - not necessarily consistent Corresponds to finding a minimum vertex cover on a bipartite graph

ECKERLE ET AL (2017) Necessary expansions for a pair of states: f f (a) < C* f b (b) < C* g f (a) + g b (b) < C*

ECKERLE ET AL (2017) Necessary expansions for a pair of states: f f (a) < C* a f b (b) < C* g f (a) + g b (b) < C*

ECKERLE ET AL (2017) Necessary expansions for a pair of states: f f (a) < C* a b f b (b) < C* g f (a) + g b (b) < C*

ECKERLE ET AL (2017) Necessary expansions for a pair of states: ? f f (a) < C* a b f b (b) < C* g f (a) + g b (b) < C*

gF gB C* = 13 0 12 1 2 1 11 19 13 2 10 342 47 EXPLANATION 3 9 5,391 213 4 8 31,924 810 5 7 53,120 2,634 6 6 31,819 6,604 7 5 11,686 11,586 8 4 3,159 10,697 9 3 715 3,396 10 2 128 342 11 1 23 19 12 0 3 1

gF gB C* = 13 0 12 1 2 1 11 19 13 2 10 342 47 EXPLANATION 3 9 5,391 213 4 8 31,924 810 5 7 53,120 2,634 6 6 31,819 6,604 f f < C* 7 5 11,686 11,586 8 4 3,159 10,697 9 3 715 3,396 10 2 128 342 11 1 23 19 12 0 3 1

gF gB C* = 13 0 12 1 2 1 11 19 13 2 10 342 47 EXPLANATION 3 9 5,391 213 4 8 31,924 810 5 7 53,120 2,634 6 6 31,819 6,604 f f < C* f b < C* 7 5 11,686 11,586 8 4 3,159 10,697 9 3 715 3,396 10 2 128 342 11 1 23 19 12 0 3 1

gF gB C* = 13 0 12 1 2 1 11 19 13 2 10 342 47 EXPLANATION 3 9 5,391 213 g f (a) + g b (b) < C* 4 8 31,924 810 5 7 53,120 2,634 6 6 31,819 6,604 f f < C* f b < C* 7 5 11,686 11,586 8 4 3,159 10,697 9 3 715 3,396 10 2 128 342 11 1 23 19 12 0 3 1

gF gB C* = 13 0 12 1 2 1 11 19 13 2 10 342 47 EXPLANATION 3 9 5,391 213 4 8 31,924 810 5 7 53,120 2,634 6 6 31,819 6,604 f f < C* f b < C* 7 5 11,686 11,586 8 4 3,159 10,697 9 3 715 3,396 10 2 128 342 11 1 23 19 12 0 3 1

gF gB 36,364 C* = 13 0 12 1 2 36,363 1 11 19 13 36,369 2 10 342 47 EXPLANATION 36,664 3 9 5,391 213 41,842 4 8 31,924 810 72,956 5 7 53,120 2,634 123,442 6 6 31,819 6,604 148,657 7 5 11,686 11,586 148,757 8 4 3,159 10,697 141,219 9 3 715 3,396 138,538 10 2 128 342 138,324 11 1 23 19 138,328 12 0 3 1 138,330

gF gB C* = 12 0 11 1 3,749 1 10 18 4,371 RUBIK’S CUBE 2 9 237 4,273 7-TILE PDB 3 8 1,201 4,156 4 7 1,981 3,904 5 6 2,670 3,615 6 5 3,291 3,123 7 4 3,567 2,438 8 3 3,638 1,330 9 2 3,647 237 10 1 3,740 18 11 0 3,138 1

gF gB C* = 13 0 1 1 19 PANCAKE 2 259 GAP HEURISTIC 3 839 4 8 534 2 5 7 173 29 6 6 31 123 7 5 3 406 4 917 3 919 2 250 1 19 0 1

gF gB 2,666 C* = 13 0 12 1 0 2,667 1 11 19 0 2,686 PANCAKE 2 10 259 0 2,945 GAP HEURISTIC 3 9 839 0 3,784 4 8 534 2 4,316 5 7 173 29 4,460 6 6 31 123 4,368 7 5 3 406 3,965 8 4 0 917 3,048 9 3 0 919 2,129 10 2 0 250 1,879 11 1 0 19 1,860 12 0 0 1 1,859

PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH - PowerPoint PPT Presentation

PREDICTING THE EFFECTIVENESS OF BIDIRECTIONAL HEURISTIC SEARCH Nathan R. Sturtevant, Canada CIFAR AI Chair, Amii, University of Alberta Shahaf Shperberg , Ben-Gurion University Ariel Felner , Ben-Gurion University Jingwei Chen, University of

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