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.

翻译：多机构路径定位(MAPF)是一个具有挑战性的组合问题,它要求我们为合作剂团队规划无碰撞路径。在这项工作中,我们表明MAPF如此难以解决的原因之一是所谓的双向对称现象,这种现象发生时,两个物剂有许多通往目标地点的不同路径,所有这些路径似乎都充满希望,但每种组合都会导致碰撞。我们确定几类双向对称,并表明每种对称在实际中都常见,并可在可能的碰撞分辨率空间中产生指数性爆炸,导致目前最先进的(受限制的)最佳MAPF算法无法令人接受的运行时间。我们建议了各种推理技术,在它们出现时能够有效地检测对称,并通过使用专门限制来消除双向对齐交错路径在一个分支步骤中发生碰撞。我们在最佳MAPFC CBS计算中采用这些想法,并表明附加的对称性推理技术可以在目前最先进的(受约束的)亚值上产生惊人的积极效果。我们提出了各种推理技术,在前期可以使CFFFS 增长到最具有挑战性的程度。