Exact Anytime Multi-Agent Path Finding Using Branch-and-Cut-and-Price and Large Neighborhood Search

Given a set of agents on a grid, the multi-agent path finding problem aims to find a path that moves each agent from its given start location to its target location such that they do not collide and that the sum of arrival times is minimized. LNS2 is a state-of-the-art algorithm for anytime, suboptimal solving. It is an upper-bounding algorithm that repeatedly adjusts an existing solution and, being a local search, is oblivious to optimality. BCP is a state-of-the-art algorithm for exact solving. It is a lower-bounding tree search that attempts to tighten the lower bound until a solution appears. As BCP operates on the lower bound, the first solution it finds is optimal or nearly optimal, and therefore has poor anytime behavior. This paper proposes to tightly couple LNS2 and BCP to achieve better anytime, suboptimal solving while retaining the optimality guarantee of BCP. Experiments indicate that the combination achieves better anytime behavior than BCP in general and better suboptimal performance than LNS2 on congested maps.