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

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 University ICAPS 2020

• Problem definition • Background: • Conflict-based search • Rectangle symmetry Outline • Corridor symmetry • Target symmetry • Empirical evaluation New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 2 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Multi-Agent Path Finding (MAPF) 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 New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding [3] https://futureoflife.org/wp-content/uploads/2019/04/Why-ban-lethal-AI-1030x595.jpg Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig [4] https://theconversation.com/we-can-design-better-intersections-that-are-safer-for-all-users-92178

Multi-Agent Path Finding (MAPF) • Given: • A graph, and • A set of agents, each with a start location and a target location. 2 Start 1 1 Target 2 New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 4 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Multi-Agent Path Finding (MAPF) Actions: Collisions: • Move : move to a neighboring location. • Vertex collision : two agents stay at the same location at the same timestep. • Wait : wait at its current location. 1 2 • Edge collision : two agents traverse the same edge in opposite directions at the same timestep. 1 2 New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 5 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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. 2 Start 1 1 Target 2 New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 6 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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. New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 7 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

CBS A B C D 1 2 2 1 Agent 1 cannot Agent 2 cannot 3 1 be at location B2 be at location B2 at timestep 1. at timestep 1. 4 2 A B C D A B C D CBS 1 2 1 2 2 1 2 1 A* 3 1 3 1 4 2 4 2 Number of agents … … [Sharon et al, 2015] … … New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 8 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Rectangle symmetry [AAAI 2019] A B C D A B C D A B C D A B C D 1 s2 1 s2 1 s2 1 s2 2 2 2 2 2 s1 2 s1 2 s1 2 s1 1 1 1 1 3 g1 3 g1 3 g1 3 g1 1 1 1 1 4 g2 4 g2 4 g2 4 g2 2 2 2 2 New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 9 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Corridor Symmetry A B C D A B C D A B C D 1 1 1 Replan Replan Replan 2 2 2 2 2 2 2 2 2 Agent 1 Agent 1 Agent 1 … 3 3 3 4 4 4 1 1 1 1 1 1 5 5 5 Replan Replan Replan Agent 2 Agent 2 Agent 2 … … … New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 10 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Corridor Symmetry A B C D 1 2 2 2 (nodes are denoted by 3 the collision locations) 4 1 1 5 𝑙 Corridor length 3 5 7 9 11 13 … 2 𝑙+1 CBS nodes 16 64 256 1,024 4,096 16,384 … New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 11 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

A B C D 1 Corridor Symmetry 2 2 2 3 • Resolving corridor symmetry by range constraints 4 1 1 Agent 1 cannot be at location Agent 2 cannot be at location 5 D3 before or at timestep 7. A3 before or at timestep 7. A B C D A B C D 1 1 4 timesteps 2 2 2 2 2 2 3 3 4 4 1 1 1 1 4 timesteps 5 5 No collisions! No collisions! New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 12 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Target Symmetry A B C D E A B C D E A B C D E 1 1 1 Replan Replan Replan Agent 1 Agent 1 Agent 1 … 2 s1 2 s1 2 s1 1 2 2 1 1 2 2 1 1 2 2 1 3 g1 3 g1 3 g1 Replan Replan Replan Agent 2 Agent 2 Agent 2 … … … New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 13 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Target Symmetry A B C D E (nodes are denoted by 1 the collision locations) 2 s1 1 2 2 1 3 g1 New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 14 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Target Symmetry A B C D E 1 • Resolving target symmetry by length constraints 2 s1 1 2 2 1 3 g1 The length of Agent 2’s path ≤ 3 , which implies that Agent 1 cannot be The length of Agent 2’s path > 3 . x at location D3 at or after timestep 3. A B C D E A B C D E 1 1 2 s1 2 s1 1 2 2 1 1 2 2 1 3 g1 3 g1 No solutions! No collisions! New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 15 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

Empirical Results *Success rate = percentage of solved instances within one minute. New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 16 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig

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 . New Techniques for Pairwise Symmetry Breaking in Multi-Agent Path Finding 17 Jiaoyang Li, Graeme Gange, Daniel Harabor, Peter J. Stuckey, Hang Ma, and Sven Koenig