1 / 48

Finding Optimal Solutions to Cooperative Pathfinding Problems

Finding Optimal Solutions to Cooperative Pathfinding Problems. Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles. Introduction. Pathfinding Problems A single agent must find a path from a start state to a goal state

neona
Download Presentation

Finding Optimal Solutions to Cooperative Pathfinding Problems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standleyand Rich Korf Computer Science Department University of California, Los Angeles

  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. My Formulation • Gridworld pathfinding

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

  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. Our Prior Work (Standley AAAI-10) • Independence Detection • Empowers centralized algorithms. • Combines the strength of centralized and decentralized approaches. • Maintains optimality and completeness.

  23. From (Standley AAAI-10) Simple Independence Detection

  24. From (Standley AAAI-10) Simple Independence Detection • Put each agent into its own group. • Plan paths for each group independently • Check for conflicts in new paths • Combine groups with conflicting paths • Repeat 2-4 until no conflicts

  25. From (Standley AAAI-10) Simple Independence Detection

  26. From (Standley AAAI-10) Simple Independence Detection Problem • Are these agents independent?

  27. From (Standley AAAI-10) Simple Independence Detection Problem • Are these agents independent?

  28. From (Standley AAAI-10) Better Independence Detection • When a conflict is detected between two groups, try to find an alternative path for one of the groups • If that fails try to find an alternate path for the other group • Only as a last resort do we combine the groups

  29. From (Standley AAAI-10) Best Independence Detection • How can we make agent 2 take this path initially?

  30. From (Standley AAAI-10) Best Independence Detection • Try to avoid future conflicts • avoid the current paths of other agents.

  31. Reservation Tables • Illegal move table • Contains all the ways alternative paths could result in a conflict with the currently conflicting group. • Consider such moves illegal. • Conflict avoidance table • Contains all the ways alternative paths could result in a conflict with any other group • Keep track of conflict avoidance table violations and

  32. From (Standley AAAI-10) Reservation Tables Illegal move table.

  33. From (Standley AAAI-10) Reservation Tables Illegal move table.

  34. From (Standley AAAI-10) Reservation Tables Illegal move table.

  35. Reservation Tables • Illegal move table • Contains all the ways alternative paths could result in a conflict with the currently conflicting group. • Consider such moves illegal. • Conflict avoidance table • Contains all the ways alternative paths could result in a conflict with any other group • Keep track of conflict avoidance table violations

  36. From (Standley AAAI-10) Reservation Tables Conflict avoidance table.

  37. From (Standley AAAI-10) Reservation Tables Conflict avoidance table.

  38. From (Standley AAAI-10) Reservation Tables Conflict avoidance table.

  39. Complete Approximation Algorithms • Our previous work maintained optimality by: • Only accepting alternate paths if they have the same cost as original paths. • Coupling independence detection with an optimal centralized algorithm. • We recognize in our current work that we can drop these two constraints.

  40. Complete Approximation Algorithms • Modifications to the centralized algorithm • Expand nodes with fewest violations first • Use cost to break ties

  41. When to drop these constraints • Always • Leads to a fast and complete algorithm • When doing so avoids the creation of groups containing more than x agents • Leads to a slower but still fast algorithm • Produces higher quality paths

  42. Parameterized Approximation • Maximum group size parameter x • Drop constraints to avoid creating groups larger than x. • x =1 : always drop the constraints. • x = ∞ : never drop the constraints (optimal) • The algorithm is complete for any choice of x

  43. Simple Optimal Anytime Algorithm • Run the parameterized approximation with x = 1. • Then run the parameterized approximation with x = 2. • … • When we run out of time, we return the best solution found by any run.

  44. Simple Optimal Anytime Algorithm Problem • The simple anytime algorithm suffers the cost of unused and incomplete iterations.

  45. Optimal Anytime Algorithm Problem • Keep paths and groupings from previous iterations when possible. • Keep track of groups that might not have optimal paths. • Fix these paths one at a time starting with the easiest.

  46. Optimal Anytime Algorithm • Keep a lower bound for each group. • When merging a group, add lower bounds

  47. Optimal Anytime Algorithm • Update best path many times within an iteration. • Whenever the solution is conflict free we update the best solution found. • When lower bound equals cost, we’re done

  48. Results • Our coarsest approximation is complete, has competitive running time, and produces superior solutions. • As an optimal algorithm, our anytime algorithm is competitive with our previous state-of-the-art. • If our anytime algorithm is terminated early, it often returns an optimal path.

More Related