Optimal Target Assignment and Path Finding for Teams of Agents

We study the TAPF (combined target-assignment and pathfinding) problem for teams of agents in known terrain, which generalizes both the anonymous and non-anonymous multiagent 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 collisionfree paths for the agents to their targets in a way such that the makespan is minimized. We present the CBM (ConflictBased Min-Cost-Flow) algorithm, a hierarchical algorithm that solves TAPF instances optimally by combining ideas from anonymous and non-anonymous multi-agent pathfinding algorithms. On the low level, CBM uses a mincost 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.