Break Loops: A Divide-and-Conquer Framework for Multi-Agent Path Finding for Large Agents Without Compromising Solvability

Background: Multi-Agent Path Finding (MAPF) has been widely studied in recent years. However, the computational cost of solving MAPF and MAPF for large agents (LA-MAPF) grows exponentially as the number of agents increases. This challenge is particularly severe for LA-MAPF, primarily due to the increased overhead of conflict detection between geometric agents. Objectives: To reduce the computational cost of solving MAPF and LA-MAPF problems, a general method is needed that can accelerate a variety of MAPF algorithms. Methods: We propose a framework that decomposes an LA-MAPFproblem into multiple subproblems, which are solved independently to reduce computational costs. The framework is general and compatible with various MAPF algorithms (e.g., CBS or LaCAM). The decomposition of an LA-MAPF problem is formulated as a combinatorial optimization problem and solved using neighborhood search. To handle unsolvable subproblems generated during decomposition, we introduce a solvability safeguard mechanism that merges subproblems until all are solvable. Results: Our experiments demonstrate the performance of the framework across various mapsasthenumberofagentsincreases, showing substantial acceleration of both MAPF and LA-MAPF methods. Specifically, after applying Break Loops, the average runtime of CBS and LA-CBS is reduced from 49.0 s to 6.8 s and from 54.0 s to 18.65 s, respectively; LaCAM and LA-LaCAM are reduced from 9.5 s to 7.0 s and from 52.9 s to 16.2 s, respectively. The success rate of CBS and LA-CBS increases from 0.27 to 0.98 and from 0.11 to 0.72, respectively; LaCAM and LA-LaCAM increase from 0.85 to 0.97 and from 0.10 to 0.77, respectively. Conclusions: Our results show that incorporating Break Loops into MAPF and LA-MAPF methods significantly reduces computational costs and improves success rates. These f indings demonstrate that solving MAPF problems can be accelerated by decomposing them into subproblems. To facilitate further research, we have made the source code for the framework publicly available at https://github.com/JoeYao-bit/LayeredMAPF/tree/main/algorithm/LA-MAPF.