Time Optimal Multi-Agent Path Planning on Graphs

Significant progress has been made in the area of multiagent path finding/planning in the past decade (Silver 2005; van den Berg et al. 2009; Standley 2010; Luna and Bekris 2011; Wang and Botea 2011). In this work, we introduce a multi-agent path planning problem similar to that of (Standley 2010) and aim at maximizing parallelism among the agents. That is, we seek a feasible plan that minimizes the time it takes the last agent to reach its goal. To solve the problem, we convert it into an equivalent multiflow problem, from which an integer linear programming (ILP) problem is readily obtained. Our algorithm is complete.