Planning Optimal Paths for Multi-agent Systems on Graphs

For the problem of moving a set of agents on a connected graph with unit edge distance to agent-specific goal locations, free of collisions, we propose two multiflow based integer linear programming (ILP) models that find time optimal and distance optimal solutions, respectively. The resulting algorithms from our ILP models are complete and guaranteed to yield true optimal solutions. Focusing on the time optimal formulation, we evaluate its performance, both as a stand alone algorithm and as a generic heuristic for quickly solving large problem instances. The computational results confirm the effectiveness of our method.