Multi-Agent Path Finding with Deadlines: Preliminary Results
This addresses path planning for multiple agents under time constraints, but it is preliminary and incremental, building on existing MAPF methods.
The authors tackled the problem of multi-agent path finding with deadlines (MAPF-DL), aiming to maximize agents reaching goals within deadlines without collisions, and showed it is NP-hard and presented an optimal algorithm based on a flow reduction and integer linear programming.
We formalize the problem of 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 a given deadline, without colliding with each other. We first show that the MAPF-DL problem is NP-hard to solve optimally. We then present an optimal MAPF-DL algorithm based on a reduction of the MAPF-DL problem to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network.