We consider an Anonymous Multi-Agent Path-Finding (AMAPF) problem where the set of agents is confined to a graph, a set of goal vertices is given and each of these vertices has to be reached by some agent. The problem is to find an assignment of the goals to the agents as well as the collision-free paths, and we are interested in finding the solution with the optimal makespan. A well-established approach to solve this problem is to reduce it to a special type of a graph search problem, i.e. to the problem of finding a maximum flow on an auxiliary graph induced by the input one. The size of the former graph may be very large and the search on it may become a bottleneck. To this end, we suggest a specific search algorithm that leverages the idea of exploring the search space not through considering separate search states but rather bulks of them simultaneously. That is, we implicitly compress, store and expand bulks of the search states as single states, which results in high reduction in runtime and memory. Empirically, the resultant AMAPF solver demonstrates superior performance compared to the state-of-the-art competitor and is able to solve all publicly available MAPF instances from the well-known MovingAI benchmark in less than 30 seconds.

翻译：本文考虑匿名多智能体路径规划（AMAPF）问题，其中智能体集合被限制在一个图上，给定一组目标顶点，且每个顶点需由某个智能体到达。该问题需要找到一个目标到智能体的分配方案以及无冲突路径，我们关注于寻找具有最优完工时间的解决方案。解决该问题的一个成熟方法是将其转化为一种特殊类型的图搜索问题，即在一个由输入图诱导的辅助图上寻找最大流问题。该辅助图的规模可能非常大，导致在其上的搜索成为瓶颈。为此，我们提出一种特定的搜索算法，该算法通过同时探索搜索空间的整体块而非单独考虑搜索状态，隐式压缩、存储和扩展搜索状态的块作为单一状态，从而大幅降低运行时间和内存消耗。实验结果表明，所提出的AMAPF求解器性能优于当前最先进的对比方法，能够在30秒内解决所有来自著名MovingAI基准的公开MAPF实例。