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Finding Optimal Solutions to Cooperative Pathfinding Problems

Finding Optimal Solutions to Cooperative Pathfinding Problems. Trevor Standley Computer Science Department University of California, Los Angeles http://cs.ucla.edu/~tstand/. Introduction. Pathfinding Problems A single agent must find a path from a start state to a goal state

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Finding Optimal Solutions to Cooperative Pathfinding Problems

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  1. Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley Computer Science Department University of California, Los Angeles http://cs.ucla.edu/~tstand/

  2. Introduction • Pathfinding Problems • A single agent must find a path from a start state to a goal state • Cooperative Pathfinding Problems • Multiple agents interact • Want to minimize the total cost

  3. Motivation

  4. Motivation

  5. Motivation

  6. My Formulation • Gridworld pathfinding

  7. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  8. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  9. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  10. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  11. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  12. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  13. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  14. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  15. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  16. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  17. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  18. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  19. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  20. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  21. Related Work • Centralized Approaches • Strengths: Typically complete, can be optimal • Weaknesses: Takes forever! • Decoupled Approaches • Strengths: Fast • Weaknesses: Incomplete and suboptimal

  22. The Standard Algorithm • The standard algorithm is A* • Centralized algorithm • There is a standard heuristic • State representation – A position for each agent • State space – Exponential in the number of agents • An operator – Complete assignment of moves to agents • One of {N; NE; E; SE; S; SW; W; NW; and wait} for each agent • Exponential in the number of agents • Obviously this algorithm is not taken seriously

  23. My algorithm • Optimal • Complete • Two main contributions • Operator decomposition • Independence detection

  24. Operator Decomposition • Intuition • Also a centralized algorithm • Still use A* • Change how operators are defined: only one agent moves at a time • Simple idea, tricky to get details right

  25. Operator Decomposition • Each operator assigns a move to a single agent • Assignments are made in a fixed order • Move assignments stored as part of the state representation

  26. Operator Decomposition • Example

  27. Operator Decomposition

  28. The Savings of Operator Decomposition

  29. Consequences of Operator Decomposition • Branching factor becomes polynomial • However, state space still exponential

  30. Simple Independence Detection

  31. Simple Independence Detection • Create a group for each agent • Plan paths for each group independently • Check for conflicts in new paths • Combine groups with conflicting paths • Repeat 2-4 until no conflicts

  32. Simple Independence Detection

  33. Simple Independence Detection Problem • Are these agents independent?

  34. Simple Independence Detection Problem • Are these agents independent?

  35. Better Independence Detection • When a conflict is detected between two groups, try to find an alternate path for one of the groups • If that fails try to find an alternate path for the other group • Only combine groups if no alternate path could be found

  36. Independence Detection • Which alternate paths are the best? • Only search for optimal paths • Paths can be found using operator decomposition • Find paths that will lead to fewest number of future conflicts • Operator decomposition can be modified to find optimal paths with few future conflicts

  37. My Algorithm • Uses decoupled planning where possible • Only uses centralized planning for non-independent subproblems • Calls operator decomposition as a subroutine to do the centralized planning

  38. Results • 10000 randomly generated problems with 2-60 agents

  39. Conclusions • Researchers have developed centralized and decoupled approaches for solving cooperative pathfinding problems • Operator decomposition is an improved centralized approach • Independence detection is a hybrid approach • Only uses centralized planning when necessary

  40. Acknowledgments • My advisor, Rich Korf. • Dawn Chen for editing, advice, and artwork

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