Bidirectional Search: Is It For Me? Nathan R. Sturtevant Associate Professor University of Denver

Transcription

1 Bidirectional Search: Is It For Me? Nathan R. Sturtevant Associate Professor University of Denver

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4 practice, the most common heuristic es in the runtime distribution (looked during search) must be preserved. directional Pathmax (BPMX) is crucial ocal propagation of heuristic values and overy of lost information. with BPMX as well as combinations of EC and VC. Combinations with VC have the best performance (bold). Memory (A) (B) 0.5 (A) 0.25 (B) (C) 0.25 (B) (C) Collaborators C is most effective when the number alues in the PDB is just larger than the rest power of two. C can be effectively combined with VC. EC VC VC-bits Nodes 3.88M 3.88M 4.03M 10.39M 7.11M 7.11M 7.37M 30.43M 13.75M 13.74M 14.31M 30.48M Time Moving AI Lab Award DANIEL FELIX RITCHIE SCHOOL OF ENGINEERING & COMPUTER SCIENCE Sneha Sawlani Jingwei Chen University of Denver 4.63M 5.42M 5.19M Ariel Felner Robert Holte University of Alberta Sandra Zilles Eshed Shaham

5 Who am I? Designed and implemented pathfinding engine

6 Lecture Takeaways When should I use bidirectional search? What algorithm should I use for bidirectional search?

7 Pathfinding Architecture Optimizations by Steve Rabin & Nathan Sturtevant Bad Idea #2: Bidirectional Pathfinding

8 Optimal Bidirectional Search

9 Optimal Bidirectional Search!

10 Optimal Bidirectional Search! All states that could be expanded

11 Optimal Bidirectional Search! Choose a meeting point

12 Optimal Bidirectional Search! Expand up to that point forward

13 Optimal Bidirectional Search! Expand up to that point forward Expand up to that point backward

14 Demo

15 Explanation Perfect heuristic near goal Open space Symmetric

16 New Algorithm: NBS! NBS never expands more than 2x the states expanded by the best possible algorithm In our theoretical framework NBS does equal work in each direction

17 When should we use NBS?

18 Scenario 1: Weighted terrain

19 Weighted terrain Costly to look for alternate paths around weighted terrain

20 Scenario 2: Problem Asymmetry

21 Problem Asymmetry When forward is much more expensive than backwards 3x worse on average Also happens with weighted terrain

22 Scenario 3: Map Asymmetry

23 Map Asymmetry Common in city maps Dense regions of pathfinding nodes Bidirectional search will avoid the densest region

24 Scenario 4: Local Minima

25 ! Local Minima Many states look close, but aren t Could be fixed by a better heuristic

26 Testing in practice Web tool available for analysis

27 NBS Details

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30 A*

31 A* Put start onto priority queue

32 A* Put start onto priority queue While queue not empty / solution not found

33 A* Put start onto priority queue While queue not empty / solution not found Among all states on queue:

34 A* Put start onto priority queue While queue not empty / solution not found Among all states on queue: Select the state with lowest f-cost

35 A* Put start onto priority queue While queue not empty / solution not found Among all states on queue: Select the state with lowest f-cost Expand it

36 A*: f-cost start goal

37 A*: f-cost start goal

38 A*: f-cost cost-so-far (g-cost) start goal

39 A*: f-cost cost-so-far (g-cost) estimate to goal (h-cost) start goal

40 A*: f-cost cost-so-far (g-cost) estimate to goal (h-cost) start goal f-cost = g-cost + h-cost = estimated path length

41 A* Put start onto priority queue While queue not empty / solution not found Among all states on queue: Select the state with lowest f-cost Expand it

42 A* NBS! Put start onto priority queue While queue not empty / solution not found Among all states on queue: Select the state with lowest f-cost Expand it Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions, Jingwei Chen, Robert C. Holte, Sandra Zilles and Nathan R. Sturtevant, International Joint Conference on Artificial Intelligence (IJCAI), 2017

43 A* NBS! Put start/goal onto forward/backward priority queues While queue not empty / solution not found Among all states on queue: Select the state with lowest f-cost Expand it Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions, Jingwei Chen, Robert C. Holte, Sandra Zilles and Nathan R. Sturtevant, International Joint Conference on Artificial Intelligence (IJCAI), 2017

44 A* NBS! Put start/goal onto forward/backward priority queues While queues not empty / solution not found Among all states on queue: Select the state with lowest f-cost Expand it Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions, Jingwei Chen, Robert C. Holte, Sandra Zilles and Nathan R. Sturtevant, International Joint Conference on Artificial Intelligence (IJCAI), 2017

45 A* NBS! Put start/goal onto forward/backward priority queues While queues not empty / solution not found Among all states on queues: Select the state with lowest f-cost Expand it Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions, Jingwei Chen, Robert C. Holte, Sandra Zilles and Nathan R. Sturtevant, International Joint Conference on Artificial Intelligence (IJCAI), 2017

46 A* NBS! Put start/goal onto forward/backward priority queues While queues not empty / solution not found Among all states on queues: Select the pair with lowest lower bound Expand it Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions, Jingwei Chen, Robert C. Holte, Sandra Zilles and Nathan R. Sturtevant, International Joint Conference on Artificial Intelligence (IJCAI), 2017

47 A* NBS! Put start/goal onto forward/backward priority queues While queues not empty / solution not found Among all states on queues: Select the pair with lowest lower bound Expand both of them Front-to-End Bidirectional Heuristic Search with Near-Optimal Node Expansions, Jingwei Chen, Robert C. Holte, Sandra Zilles and Nathan R. Sturtevant, International Joint Conference on Artificial Intelligence (IJCAI), 2017

48 NBS: lower bound start goal

49 NBS: lower bound u v start goal

50 NBS: lower bound u v start goal

51 NBS: lower bound u v start goal

52 NBS: lower bound u v gf(u) start goal

53 NBS: lower bound u v gf(u) start h(u, goal) goal

54 NBS: lower bound u v gf(u) start h(u, goal) goal ff(u) = gf(u) + h(u, goal)

55 NBS: lower bound u v start goal

56 NBS: lower bound u v gb(v) start goal

57 NBS: lower bound u v gb(v) start h(start, v) goal

58 NBS: lower bound u v gb(v) start h(start, v) goal fb(v) = gb(v) + h(start, v)

59 NBS: lower bound! u v start goal

60 NBS: lower bound! u v gf(u) start goal

61 NBS: lower bound! u v gf(u) gb(v) start goal

62 NBS: lower bound! u v gf(u) gb(v) start goal gf(u) + gb(v)

63 NBS: lower bound! lb(u, v) =max(f F (u), f B (v), g F (u)+g B (v))

64 NBS Data Structure! Can efficiently find pair with minimum lower bound Filter by f-cost then by g-cost

65 NBS Data Structure! Can efficiently find pair with minimum lower bound Filter by f-cost then by g-cost Cannot just select by f-cost (A*) or g-cost (Dijkstra)

66 NBS Guarantee! NBS never expands more than 2x the states expanded by the best possible algorithm In our theoretical framework NBS does equal work in each direction

67 Suboptimal Solutions! Use weighted A* if path quality doesn t matter Terminate the search when the first solution is found in bidirectional search

68 Summary / Conclusions! Use NBS for bidirectional search May want bidirectional search for: Weighted terrain Problem Asymmetry Map Asymmetry Local Minima

69 Questions? Open-source implementation of NBS Demo from this lecture* Offline analyzer for analyzing pathfinding Technical reference papers Find me on