Optimal Target Assignment and Path Finding for Teams of Agents

TL;DR

This paper introduces an optimal hierarchical algorithm, CBM, for solving the TAPF problem, which involves assigning agents to targets and planning collision-free paths in known terrains, applicable to large-scale multi-agent systems.

Contribution

The paper presents CBM, a novel hierarchical algorithm that optimally solves TAPF by combining min-cost flow and conflict-based search techniques, scalable to large agent teams.

Findings

CBM is proven correct, complete, and optimal.

CBM scales to dozens of teams and hundreds of agents.

Effective in simulated warehouse environments.

Abstract

We study the TAPF (combined target-assignment and path-finding) problem for teams of agents in known terrain, which generalizes both the anonymous and non-anonymous multi-agent path-finding problems. Each of the teams is given the same number of targets as there are agents in the team. Each agent has to move to exactly one target given to its team such that all targets are visited. The TAPF problem is to first assign agents to targets and then plan collision-free paths for the agents to their targets in a way such that the makespan is minimized. We present the CBM (Conflict-Based Min-Cost-Flow) algorithm, a hierarchical algorithm that solves TAPF instances optimally by combining ideas from anonymous and non-anonymous multi-agent path-finding algorithms. On the low level, CBM uses a min-cost max-flow algorithm on a time-expanded network to assign all agents in a single team to targets and plan their paths. On the high level, CBM uses conflict-based search to resolve collisions among agents in different teams. Theoretically, we prove that CBM is correct, complete and optimal. Experimentally, we show the scalability of CBM to TAPF instances with dozens of teams and hundreds of agents and adapt it to a simulated warehouse system.