Template Matching and Decision Diagrams for Multi-agent Path Finding

We propose a polyhedral cutting plane procedure for computing a lower bound on the optimal solution to multi-agent path finding (MAPF) problems. We obtain our cuts by projecting the polytope representing the solutions to MAPF to lower dimensions. A novel feature of our approach is that the projection polytopes we used to derive the cuts can be viewed as 'templates'. By translating these templates spatio-temporally, we obtain different projections, and so the cut generation scheme is reminiscent of the template matching technique from image processing. We use decision diagrams to compactly represent the templates and to perform the cut generation. To obtain the lower bound, we embed our cut generation procedure into a Lagrangian Relax-and-Cut scheme. We incorporate our lower bounds as a node evaluation function in a conflict-based search procedure, and experimentally evaluate its effectiveness.