Improving Problem Decomposition and Regulation in Distributed Multi-Agent Path Finder (DMAPF)

Abstract

Distributed Multi-Agent Path Finder (DMAPF) is a novel distributed algorithm to solve the Multi-Agent Path Finding (MAPF) problem, where the objective is to find a sequence of movements for agents to reach their assigned locations without colliding with obstacles, which include other agents. The idea of DMAPF is to decompose a given MAPF problem into smaller sub-problems, then solve them in parallel. It has been shown that DMAPF can achieve higher scalability compared to centralized methods. This paper addresses two problems in the previous works. First, the previous works only divide problem maps in a simple, rectangular manner. This can create sub-problems with unbalanced numbers of locations in their maps when the shape of the original map is not rectangular or when the obstacles are not uniformly distributed. Having sub-problems that vary in sizes diminishes the effectiveness of parallelism. Second, the idea of DMAPF is to have agents move across sub-problems until they reach the sub-problems that contain their goals, but the previous works do not have a mechanism to regulate the number of agents residing in the sub-problems, thus it may fail to find the solution when a sub-problem is overcrowded. To mitigate the problems, we introduce (i) a method to decompose MAPF problems with balanced numbers of vertices; and (ii) a mechanism to regulate the number of agents in sub-problems. We also improve the performance of the Answer Set Programming (ASP) encoding, that was used in previous DMAPF implementations to solve MAPF sub-problem instances, by eliminating unnecessary parameters. The results show that the new solver scales better and is more efficient than the previous versions.