On Propositional Encodings of Cooperative Path-Finding

The approach to solving cooperative-path finding (CPF) as propositional satisfiability (SAT) is revisited in this paper. An alternative encoding that exploits multi-valued state variables representing locations where a given agent resides is suggested. This encoding employs the ALL-DIFFERENT constraint to model the requirement that agents must not collide with each other. The use of suggested state variables also allowed us to incorporate certain heuristic reasoning to reduce the size of the propositional encoding of the problem. We show that our new domain-dependent encoding enables finding of optimal or near optimal solutions to CPFs in certain hard set-ups where A*-based techniques such as WHCA* fail to do so. Our finding is also that the ALL-DIFFERENT encoding can be solved faster than the existent encoding.