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Time-expanded graph-based propositional encodings for makespan-optimal solving of cooperative path finding problems

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Abstract

This paper deals with solving cooperative path finding (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.

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Acknowledgments

This work has been supported by an AIRC project commissioned by the New Energy and Industrial Technology Development Organization Japan (NEDO) and the Czech-Israeli cooperation project number 8G15027. The author would like to thank the research team at Ben Gurion University, Israel led by Ariel Felner and Roni Stern and the student members of the team, Guni Sharon and Eli Boyarski, for providing the source code needed to conduct the present experiments.

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  1. National Institute of Advanced Industrial Science and Technology (AIST), AIRC, 2-3-26, Aomi, Koto-ku, Tokyo, 135-0064, Japan

    Pavel Surynek

  2. Department of Theoretical Computer Science and Mathematical Logic, Charles University, Malostranské nàmìstì 25, Praha 1, 118 00, Czechia

    Pavel Surynek

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Correspondence to Pavel Surynek.

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Submitted to Annals on Mathematics and Artificial Intelligence on April 15, 2016. Reviews received on June 26, 2016. Major revision submitted on October 28, 2016. Reviews received on March 21, 2017. Minor revision submitted on May 20, 2017.

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Surynek, P. Time-expanded graph-based propositional encodings for makespan-optimal solving of cooperative path finding problems. Ann Math Artif Intell 81, 329–375 (2017). https://doi.org/10.1007/s10472-017-9560-z

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