Makespan Optimal Solving of Cooperative Path-Finding

The problem of makespan optimal solving of cooperative path finding (CPF) is addressed in this paper. The task in CPF is to relocate a group of agents in a non-colliding way so that each agent eventually reaches its goal location from the given initial location. The abstraction adopted in this work assumes that agents are discrete items moving in an undirected graph by traversing edges. Makespan optimal solving of CPF means to generate solutions that are as short as possible in terms of the total number of time steps required for the execution of the solution. We show that reducing CPF to propositional satisfiability (SAT) represents a viable option for obtaining makespan optimal solutions. Several encodings of CPF into propositional formulae are suggested and experimentally evaluated. The evaluation indicates that SAT based CPF solving outperforms other makespan optimal methods significantly in highly constrained situations (environments that are densely occupied by agents).