  In this paper, we study the problem of optimal multi-robot path planning
(MPP) on graphs. We propose two multiflow based integer linear programming
(ILP) models that computes minimum last arrival time and minimum total distance
solutions for our MPP formulation, respectively. The resulting algorithms from
these ILP models are complete and guaranteed to yield true optimal solutions.
In addition, our flexible framework can easily accommodate other variants of
the MPP problem. Focusing on the time optimal algorithm, we evaluate its
performance, both as a stand alone algorithm and as a generic heuristic for
quickly solving large problem instances. Computational results confirm the
effectiveness of our method.
