New Mechanisms in Flex Distribution for Bounded Suboptimal Multi-Agent Path Finding

Multi-Agent Path Finding (MAPF) is the problem of finding a set of collision-free paths, one for each agent in a shared environment. Its objective is to minimize the sum of path costs (SOC), where the path cost of each agent is defined as the travel time from its start location to its target location. Explicit Estimation Conflict-Based Search (EECBS) is the leading algorithm for bounded-suboptimal MAPF, with the SOC of the solution being at most a user-specified factor $w$ away from optimal. EECBS maintains sets of paths and a lower bound $LB$ on the optimal SOC. Then, it iteratively selects a set of paths whose SOC is at most $w \cdot LB$ and introduces constraints to resolve collisions. For each path in a set, EECBS maintains a lower bound on its optimal path that satisfies constraints. By finding an individually bounded-suboptimal path with cost at most a threshold of $w$ times its lower bound, EECBS guarantees to find a bounded-suboptimal solution. To speed up EECBS, previous work uses flex distribution to increase the threshold. Though EECBS with flex distribution guarantees to find a bounded-suboptimal solution, increasing the thresholds may push the SOC beyond $w \cdot LB$, forcing EECBS to switch among different sets of paths instead of resolving collisions on a particular set of paths, and thus reducing efficiency. To address this issue, we propose Conflict-Based Flex Distribution that distributes flex in proportion to the number of collisions. We also estimate the delays needed to satisfy constraints and propose Delay-Based Flex Distribution. On top of that, we propose Mixed-Strategy Flex Distribution, combining both in a hierarchical framework. We prove that EECBS with our new flex distribution mechanisms is complete and bounded-suboptimal. Our experiments show that our approaches outperform the original (greedy) flex distribution.