Multi-Agent Path Finding with Deadlines: Preliminary Results

TL;DR

This paper formalizes the multi-agent path finding problem with deadlines, proving its NP-hardness and proposing an optimal solution based on flow reduction and integer linear programming.

Contribution

It introduces the MAPF-DL problem, proves its NP-hardness, and develops an optimal algorithm using flow reduction and ILP formulation.

Findings

MAPF-DL is NP-hard to solve optimally.

An optimal algorithm for MAPF-DL is proposed.

The algorithm is based on flow reduction and ILP.

Abstract

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.