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：我们考虑一个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，且每个目标顶点必须由某个智能体到达。该问题需要为目标分配智能体并找出无碰撞路径，我们致力于寻找具有最优完工时间的解决方案。解决该问题的一种成熟方法是将它简化为一种特殊类型的图搜索问题，即在由输入图诱导的辅助图上寻找最大流的问题。该辅助图的大小可能非常庞大，对其进行的搜索可能成为性能瓶颈。为此，我们提出了一种特定的搜索算法，该算法利用同时探索搜索空间中的批量状态而非逐一考虑独立状态的思想。即，我们隐式地将搜索状态的批量压缩、存储和扩展为单一状态，从而大幅降低运行时间和内存消耗。实验结果表明，由此产生的AMAPF求解器性能优于当前最先进的对比算法，并且能够在30秒内解决来自知名MovingAI基准测试的所有公开MAPF实例。