finding optimal solutions to cooperative pathfinding problems trevor standley and rich korf computer...
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![Page 1: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/1.jpg)
Finding Optimal Solutions to Cooperative Pathfinding ProblemsTrevor Standley and Rich Korf
Computer Science Department
University of California, Los Angeles
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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
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Motivation
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Motivation
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My Formulation Gridworld pathfinding
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Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
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Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 8: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/8.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 9: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/9.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 10: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/10.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 11: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/11.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 12: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/12.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 13: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/13.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 14: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/14.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 15: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/15.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 16: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/16.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 17: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/17.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 18: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/18.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 19: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/19.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 20: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/20.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 21: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/21.jpg)
Related Work Centralized Approaches
Strengths: Typically complete, can be optimal
Weaknesses: Takes forever!
Decoupled Approaches Strengths: Fast
Weaknesses: Incomplete and suboptimal
![Page 22: Finding Optimal Solutions to Cooperative Pathfinding Problems Trevor Standley and Rich Korf Computer Science Department University of California, Los Angeles](https://reader036.vdocument.in/reader036/viewer/2022062519/5697bf8c1a28abf838c8bacf/html5/thumbnails/22.jpg)
Our Prior Work (Standley AAAI-10) Independence Detection
Empowers centralized algorithms.
Combines the strength of centralized and decentralized approaches.
Maintains optimality and completeness.
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Simple Independence DetectionFrom (Standley AAAI-10)
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Simple Independence Detection
1. Put each agent into its own group.
2. Plan paths for each group independently
3. Check for conflicts in new paths
4. Combine groups with conflicting paths
5. Repeat 2-4 until no conflicts
From (Standley AAAI-10)
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Simple Independence DetectionFrom (Standley AAAI-10)
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Simple Independence Detection Problem Are these agents independent?
From (Standley AAAI-10)
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Simple Independence Detection Problem Are these agents independent?
From (Standley AAAI-10)
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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
From (Standley AAAI-10)
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Best Independence Detection How can we make agent 2 take this path initially?
From (Standley AAAI-10)
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Best Independence Detection Try to avoid future conflicts
avoid the current paths of other agents.
From (Standley AAAI-10)
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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
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Reservation Tables
Illegal move table.
From (Standley AAAI-10)
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Reservation Tables
Illegal move table.
From (Standley AAAI-10)
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Reservation Tables
Illegal move table.
From (Standley AAAI-10)
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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
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Reservation Tables
Conflict avoidance table.
From (Standley AAAI-10)
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Reservation Tables
Conflict avoidance table.
From (Standley AAAI-10)
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Reservation Tables
Conflict avoidance table.
From (Standley AAAI-10)
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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.
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Complete Approximation Algorithms Modifications to the centralized algorithm
Expand nodes with fewest violations first
Use cost to break ties
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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
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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
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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.
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Simple Optimal Anytime Algorithm Problem The simple anytime algorithm suffers the cost of
unused and incomplete iterations.
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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.
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Optimal Anytime Algorithm Keep a lower bound for each group. When merging a group, add lower bounds
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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
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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.