The Cost of Classical Multi-Agent Path Finding

2026-10-07

AI Summary

This study addresses the limitation of classical Multi-Agent Path Finding (MAPF), where discrete-time assumptions constrain solution quality, while the computational overhead of continuous-time planning remains unclear. To investigate this, we quantitatively evaluate the performance discrepancies between discrete- and continuous-time MAPF across diverse topological structures through comparative experiments employing continuous-time planning and multi-agent path search algorithms. Our findings reveal that expanding the action space, rather than adopting continuous time per se, is the critical factor in enhancing solution quality. Experimental results demonstrate up to a 17% improvement in open maps, whereas high-resolution discrete approaches yield only a marginal 3% gain. These insights provide a substantial theoretical foundation for future MAPF algorithm design.

Abstract

Multi-Agent Path Finding (MAPF) is the problem of planning conflict-free paths for multiple agents in a shared space, each from its start to its goal. Classical MAPF has been the dominant formulation for many years, with its assumptions of discrete time and graph-based conflicts presumably easing the search for solutions. These assumptions limit the physical environments and agents for which a solution is truly collision-free, and also place an upper bound on solution quality that no algorithmic improvements can lift. This work investigates how much solution quality, and in what contexts, the classical MAPF formulation forfeits. Continuous-time MAPF (MAPF$_R$) relaxes these assumptions, making it a natural counter-formulation to compare against across various agent counts and sizes, and graph connectedness, topologies, and resolutions. We find that continuous time and agent shape consideration are worth relatively little on their own; their value comes from enabling an expanded range of move actions, on average improving solution quality by at least $5\%$ on narrow and constrained maps and $17\%$ on maps with open spaces. In some cases, the improvements exceed $20\%$. Doubling the map resolution with classical MAPF recovers less than $3\%$, meaning that little of what is forfeited can be bought back through more compute. This work therefore provides insight on when classical MAPF is a reasonable simplification, and when MAPF$_R$ unlocks significantly higher-quality solutions.

Problem

• Multi-Agent Path Finding
• Classical MAPF
• Continuous-time MAPF
• Solution Quality
• Path Planning

Innovation

• Multi-Agent Path Finding
• Continuous-time MAPF
• Solution quality
• Agent shape
• Graph resolution