Map Connectivity and Empirical Hardness of Grid-based Multi-Agent Pathfinding Problem

Published: 12 Feb 2024, Last Modified: 06 Mar 2024ICAPS 2024EveryoneRevisionsBibTeXCC BY 4.0
Keywords: Multi-Agent Path Planning, Empirical Hardness
TL;DR: An empirical study on the relationship between map connectivity and the empirical hardness of multi-agent pathfinding (MAPF) problem
Abstract: We present an empirical study of the relationship between map connectivity and the empirical hardness of the multi-agent pathfinding~(MAPF) problem. By analyzing the second smallest eigenvalue~(commonly known as $\lambda_2$) of the normalized Laplacian matrix of different maps, our initial study indicates that maps with smaller $\lambda_2$ tend to create more challenging instances when agents are generated uniformly randomly. Additionally, we introduce a map generator based on Quality Diversity~(QD) that is capable of producing maps with specified $\lambda_2$ ranges, offering a possible way for generating challenging MAPF instances. Despite the absence of a strict monotonic correlation with $\lambda_2$ and the empirical hardness of MAPF, this study serves as a valuable initial investigation for gaining a deeper understanding of what makes a MAPF instance hard to solve.
Primary Keywords: Multi-Agent Planning
Category: Short
Student: Graduate
Supplemtary Material: pdf
Submission Number: 139
Loading