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：我们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中，给定一组目标顶点，每个顶点需由某个智能体到达。该问题需要确定目标到智能体的分配方案以及无碰撞路径，且我们旨在寻找具有最优完工时间的解。解决该问题的一种成熟方法是通过将其转化为一种特殊的图搜索问题，即在由输入图诱导的辅助图上寻找最大流问题。前者的图规模可能非常庞大，其搜索过程可能成为瓶颈。为此，我们提出一种特定搜索算法，该算法利用探索搜索空间的思想——不是通过考虑单个搜索状态，而是同时批量处理它们。即，我们隐式地将批量搜索状态压缩、存储并展开为单个状态，从而大幅减少运行时间和内存消耗。实验结果表明，所提出的AMAPF求解器在性能上优于当前最先进的竞争者，能够在30秒内解决公开的MovingAI基准中所有已知的MAPF实例。