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Using the method of conditional expectations to supply an improved starting point for CCLS

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Abstract

This paper proposes to combine the method of conditional expectations (MOCE, also known as Johnson’s Algorithm) with the state-of-the-art heuristic configuration checking local search (CCLS), to solve maximum satisfiability (Max Sat) instances. First, MOCE is used to find an outstanding assignment, and then CCLS explores the solution space, starting at this assignment. This combined heuristic, which we call MOCE–CCLS, is shown to provide a significant improvement over each of its parts: MOCE and CCLS. An additional contribution of this paper is the results of a comprehensive comparative evaluation of MOCE–CCLS versus CCLS on various benchmarks. On random benchmarks, the combined heuristic reduces the number of unsatisfied clauses by up to tens of percents. On Max Sat 2016 and 2021 public competition benchmarks, which include crafted and industrial instances also, MOCE–CCLS outperforms CCLS as well. To provide an empirical basis to the above result, this work further explores the correlation between the quality of initial assignments provided to CCLS and that of the corresponding final assignments. Empirical results show that the correlation is significant and long-lasting. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics.

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Acknowledgements

We thank Shaowei Cai for providing us access to the original authors’ implementation of the CCLS solver used in Max Sat Evaluation 2016, and André Abramé for providing us access to the abrame-habet benchmark used (partially) in that evaluation. We thank Gregory Gutin for his helpful comments on this paper. We also thank the anonymous referees for their useful comments and beneficial suggestions. This research was partially supported by the Milken Families Foundation Chair in Mathematics and by the Israeli Council for Higher Education (CHE) via Data Science Research Center, Ben-Gurion University of the Negev.

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  1. Departments of Mathematics and of Computer Science, Ben-Gurion University, 84105, Beer Sheva, Israel

    Daniel Berend

  2. Department of Computer Science, Jerusalem College of Technology, 91160, Jerusalem, Israel

    Shahar Golan

  3. Department of Software Engineering, Shamoon College of Engineering, 8410802, Beer Sheva, Israel

    Yochai Twitto

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  1. Daniel Berend
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A preliminary version (Berend and Twitto 2020) of this work has been presented at the 18th International Symposium on Experimental Algorithms (SEA 2020). The contribution of this elaborated paper is mainly on the practical solving side. We performed a comprehensive empirical evaluation of the combined solver MOCE–CCLS on all the benchmarks from the Max Sat Evaluation of 2016 and 2021 to assess and establish its usability as a state-of-the-art solver for Max Sat.

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Berend, D., Golan, S. & Twitto, Y. Using the method of conditional expectations to supply an improved starting point for CCLS. J Comb Optim 44, 3711–3734 (2022). https://doi.org/10.1007/s10878-022-00907-5

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