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 a 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.

多代理路径查找（MAPF）是一个具有挑战性的组合问题，它要求我们为协作代理团队规划无碰撞路径。在这项工作中，我们表明 MAPF 如此难以解决的一个原因是由于一种称为成对对称的现象，当两个代理有许多不同的路径到达其目标位置时就会发生这种情况，所有这些路径看起来都有希望，但每个组合它们中的一个会导致碰撞。我们确定了几类成对对称性，并表明每一种对称性在实践中都很常见，并且可以在可能的碰撞解决空间中产生指数爆炸，导致当前最先进（有界子）最优 MAPF 的运行时间无法接受算法。我们提出了多种推理技术，可以在对称性出现时有效地检测它们，并通过使用专门的约束来消除单个分支步骤中成对碰撞路径的所有排列来解决它们。我们在领先的最优 MAPF 算法 CBS 的上下文中实现了这些想法，并表明添加对称推理技术可以对其性能产生显着的积极影响——我们报告说节点扩展的数量减少了多达四个数量级规模和可扩展性增加多达 30 倍。这些收益使我们能够优化各种以前认为 CBS 无法实现的具有挑战性的 MAPF 实例。我们在领先的最优 MAPF 算法 CBS 的上下文中实现了这些想法，并表明添加对称推理技术可以对其性能产生显着的积极影响——我们报告说节点扩展的数量减少了多达四个数量级规模和可扩展性增加多达 30 倍。这些收益使我们能够优化各种以前认为 CBS 无法实现的具有挑战性的 MAPF 实例。我们在领先的最优 MAPF 算法 CBS 的上下文中实现了这些想法，并表明添加对称推理技术可以对其性能产生显着的积极影响——我们报告说节点扩展的数量减少了多达四个数量级规模和可扩展性增加多达 30 倍。这些收益使我们能够优化各种以前认为 CBS 无法实现的具有挑战性的 MAPF 实例。