Pairwise Symmetry Reasoning for Multi-Agent Path Finding Search

TL;DR

This paper identifies pairwise symmetry as a key challenge in MAPF, and introduces reasoning techniques that significantly improve the efficiency and scalability of solving MAPF optimally.

Contribution

The paper presents novel symmetry reasoning methods integrated into CBS, drastically reducing search space and enabling optimal solutions for previously intractable MAPF instances.

Findings

Up to four orders of magnitude reduction in node expansions.

Up to thirty times increase in scalability.

Successful solving of challenging MAPF instances previously unsolvable.

Abstract

Multi-Agent Path Finding (MAPF) is a challenging combinatorial problem that asks us to plan collision-free paths for a team of cooperative agents. In this work, we show that one of the reasons why MAPF is so hard to solve is due to a phenomenon called pairwise symmetry, which occurs when two agents have many different paths to their target locations, all of which appear promising, but every combination of them results in a collision. We identify several classes of pairwise symmetries and show that each one arises commonly in practice and can produce an exponential explosion in the space of possible collision resolutions, leading to unacceptable runtimes for current state-of-the-art (bounded-sub)optimal MAPF algorithms. We propose a variety of reasoning techniques that detect the symmetries efficiently as they arise and resolve them by using specialized constraints to eliminate all permutations of pairwise colliding paths in a single branching step. We implement these ideas in the context of the leading optimal MAPF algorithm CBS and show that the addition of the symmetry reasoning techniques can have a dramatic positive effect on its performance - we report a reduction in the number of node expansions by up to four orders of magnitude and an increase in scalability by up to thirty times. These gains allow us to solve to optimality a variety of challenging MAPF instances previously considered out of reach for CBS.