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P. Surynek. Time-Expanded Graph-Based Propositional Encodings for Makespan-Optimal Solving of Cooperative Path Finding Problems. *Annals of Mathematics and Artificial Intelligence, *81, (3-4), 329-375, 2017.

Abstract: This paper deals with solving cooperative pathfinding (CPF) problems in a makespan-optimal way. A feasible solution to the CPF problem lies in the moving of mobile agents where each agent has unique initial and goal positions. The abstraction adopted in CPF assumes that agents are discrete units that move over an undirected graph by traversing its edges. We focus specifically on makespan-optimal solutions to the CPF problem where the task is to generate solutions that are as short as possible in terms of the total number of time steps required for all agents to reach their goal positions. We demonstrate that reducing CPF to propositional satisfiability (SAT) represents a viable way to obtain makespan-optimal solutions. Several ways of encoding CPFs into propositional formulae are proposed and evaluated both theoretically and experimentally. Encodings based on the log and direct representations of decision variables are compared. The evaluation indicates that SAT-based solutions to CPF outperform the makespan-optimal versions of such search-based CPF solvers such as OD+ID,CBS, and ICTS in highly constrained scenarios (i.e., environments that are densely occupied by agents and where interactions among the agents are frequent). Moreover, the experiments clearly show that CPF encodings based on the direct representation of variables can be solved faster, although they are less space-efficient than log encodings.