Improved Anonymous Multi-Agent Path Finding Algorithm

TL;DR

This paper tackles Anonymous MAPF (AMAPF) with the goal of minimizing makespan by assigning interchangeable agents to goals and computing collision-free paths. It sticks with the reduction-to-maximum-flow framework but introduces Bulk Search, which implicitly expands bulks of search states organized as connected-sequences, greatly reducing runtime and memory usage. Theoretical analysis proves completeness and substantial reduction in expansions, while experiments on the MovingAI MAPF benchmark show that the proposed flow-BS solver solves all tested instances within 30 seconds, outperforming the standard flow-based approach. The practical impact is a scalable, exact AMAPF solver that handles large maps and high agent counts more efficiently, with potential extensions to Min-Cost-Max-Flow and related MAPF variants.

Abstract

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.

Figures (7)

• Figure 1: Example of the flow network (left) for a $T$-steps AMAPF instance (right). Each line in the flow network represents the copies of a single vertex in the original AMAPF graph. The diagonal, solid horizontal, and dashed horizontal edges in the network denote move, wait, and restriction edges, respectively. In this example, the AMAPF instance has two start vertices $A,B$ and two goal vertices $C,D$, so the source node $s$ in the network is connected to the nodes $(A,0),(B,0)$ and the sink $g$ is connected to $(C,T'),(D,T')$. The example also shows the matching between the plans for the agents and the $s$-$g$ paths in the network (green and yellow edges).
• Figure 2: Example showing connected-sequences on the network. Yellow crossbars denote the connected-sequences on each vertex. Initially, we have the connected-sequences as shown in the upper figure. After a path (green one) is found and its edges are reversed, the connected-sequences are divided as shown in the lower figure.
• Figure 3: The (normalized) number of instances solved by a certain time cap.
• Figure 4: The number of expanded nodes with a different number of agents on different maps.
• Figure 5: The figure shows (for a specific map and a specific number of agents) how the number of expansions changes with the increasing values of $T$. Here $T_{min}$ denotes the optimal makespan.

Theorems & Definitions (1)

• Theorem 1