Multi-Agent Path Finding with Deadlines
This addresses path planning for multiple agents with time constraints, an incremental extension of existing MAPF problems.
The authors formalized Multi-Agent Path Finding with Deadlines (MAPF-DL), a problem to maximize agents reaching goals within deadlines without collisions, proving it NP-hard. They developed two optimal algorithm classes (flow-based ILP and combinatorial search) that scale well and dominate in different scenarios.
We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.