New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path - - PowerPoint PPT Presentation

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path - - PowerPoint PPT Presentation

Dec 13, 2022 367 likes •558 views

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li 1 , Graeme Gange 2 , Daniel Harabor 2 , Peter J. Stuckey 2 , Hang Ma 3 , and Sven Koenig 1 1 University of Southern California 2 Monash University 3 Simon Fraser

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding

Jiaoyang Li1, Graeme Gange2, Daniel Harabor2, Peter J. Stuckey2, Hang Ma3, and Sven Koenig1

1University of Southern California 2Monash University 3Simon Fraser University

ICAPS 2020

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SLIDE 2

Outline

  • Problem definition
  • Background:
  • Conflict-based search
  • Rectangle symmetry
  • Corridor symmetry
  • Target symmetry
  • Empirical evaluation

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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SLIDE 3

Figure and video sources: [1] https://www.youtube.com/watch?v=8gy5tYVR-28&t=30s [2] https://en.wikipedia.org/wiki/Cossacks:_European_Wars#/media/File:3_cossacks_european_wars.JPG [3] https://futureoflife.org/wp-content/uploads/2019/04/Why-ban-lethal-AI-1030x595.jpg [4] https://theconversation.com/we-can-design-better-intersections-that-are-safer-for-all-users-92178

Multi-Agent Path Finding (MAPF)

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Multi-Agent Path Finding (MAPF)

  • Given:
  • A graph, and
  • A set of agents, each with a start location and a target location.

1 2 1 2

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Start Target

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Multi-Agent Path Finding (MAPF)

Actions:

  • Move: move to a neighboring location.
  • Wait: wait at its current location.

Collisions:

  • Vertex collision: two agents stay at the

same location at the same timestep.

  • Edge collision: two agents traverse the

same edge in opposite directions at the same timestep.

2 1 2 1

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Multi-Agent Path Finding (MAPF)

  • Given:
  • A graph, and
  • A set of agents, each with a start location and a goal location.
  • Goal:
  • Find collision-free paths for all agents, and
  • Minimize the sum of their travel times.

1 2 1 2

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Start Target

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Multi-Agent Path Finding (MAPF)

  • There are many optimal MAPF algorithms, such as
  • Search-based algorithms,
  • ILP-based algorithms,
  • SAT-based algorithms, and
  • CP-based algorithms.
  • Most of the state-of-the-art variants of optimal MAPF algorithms (e.g., CBSH, BCP,

SMT-CBS, lazy-CBS) deploy a strategy of planning paths individually first and resolving collisions afterward.

  • Collision symmetries can lead to unacceptable runtimes if undetected.

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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SLIDE 8

A B C D 1 2 3 4

1 1 2 2

A B C D 1 2 3 4

1 1 2 2

… …

A B C D 1 2 3 4

1 1 2 2

… …

CBS

Agent 1 cannot be at location B2 at timestep 1. Agent 2 cannot be at location B2 at timestep 1.

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[Sharon et al, 2015]

A* CBS

Number of agents New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Rectangle symmetry [AAAI 2019]

A B C D 1 s2 2 s1 3 g1 4 g2 A B C D 1 s2 2 s1 3 g1 4 g2 A B C D 1 s2 2 s1 3 g1 4 g2 A B C D 1 s2 2 s1 3 g1 4 g2

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Corridor Symmetry

A B C D 1 2 3 4 5

1 1 2 2

A B C D 1 2 3 4 5

1 1 2 2

A B C D 1 2 3 4 5

1 1 2 2

…

10

… … …

Replan Agent 1 Replan Agent 1 Replan Agent 1 Replan Agent 2 Replan Agent 2 Replan Agent 2

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Corridor Symmetry

A B C D 1 2 3 4 5

1 1 2 2

Corridor length 3 5 7 9 11 13 … 𝑙 CBS nodes 16 64 256 1,024 4,096 16,384 … 2𝑙+1

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(nodes are denoted by the collision locations)

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Corridor Symmetry

  • Resolving corridor symmetry by

range constraints

Agent 1 cannot be at location D3 before or at timestep 7. Agent 2 cannot be at location A3 before or at timestep 7. No collisions! No collisions! A B C D 1 2 3 4 5

1 1 2 2

A B C D 1 2 3 4 5

1 1 2 2

A B C D 1 2 3 4 5

1 1 2 2

4 timesteps 4 timesteps

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Target Symmetry

A B C D E 1 2 s1 3 g1

1 1 2 2

A B C D E 1 2 s1 3 g1

1 1 2 2

A B C D E 1 2 s1 3 g1

1 1 2 2

13

… … … …

Replan Agent 1 Replan Agent 1 Replan Agent 1 Replan Agent 2 Replan Agent 2 Replan Agent 2

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Target Symmetry

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A B C D E 1 2 s1 3 g1

1 1 2 2

(nodes are denoted by the collision locations)

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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SLIDE 15

Target Symmetry

  • Resolving target symmetry by

length constraints

The length of Agent 2’s path ≤ 3, The length of Agent 2’s path > 3. No solutions! No collisions! A B C D E 1 2 s1 3 g1

1 1 2 2

A B C D E 1 2 s1 3 g1

1 1 2 2

A B C D E 1 2 s1 3 g1

1 1 2 2

x

which implies that Agent 1 cannot be at location D3 at or after timestep 3.

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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Empirical Results

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*Success rate = percentage of solved instances within one minute.

New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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SLIDE 17

Summary

  • Corridor symmetry arises when two agents attempt to pass through the same

narrow corridor in opposite directions.

  • Target symmetry arises when the shortest path of one agent passes through the

target location of a second agent after the second agent has already arrived at it.

  • We propose to use range and length constraints to eliminate corridor and target

symmetries in a single branching step.

  • We experimentally show that our techniques can, in some cases, more than double

the success rate of CBS and reduce its runtime by one order of magnitude.

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New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig