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An effective variable selection heuristic in SLS for weighted Max-2-SAT

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Abstract

Stochastic local search (SLS) is an appealing method for solving the maximum satisfiability (Max-SAT) problem. This paper proposes a new variable selection heuristic for Max-SAT local search algorithms, which works particularly well for weighted Max-2-SAT instances. Evolving from the recent configuration checking strategy, this new heuristic works in three levels and is called CCTriplex. According to the CCTriplex heuristic, a variable that is both decreasing and configuration changed has the higher priority to be flipped than a decreasing variable, which in turn has the higher priority than a configuration changed variable. The CCTriplex heuristic is used to develop a new SLS algorithm for weighted Max-2-SAT called CCMaxSAT. We evaluate CCMaxSAT on random benchmarks with different densities, and the hand crafted Frb benchmark, as well as weighted Max-2-SAT instances encoded from MaxCut, MaxClique and sports scheduling problems. Compared with the state-of-the-art SLS solver for weighted Max-2-SAT called ITS and the best SLS solver in Max-SAT Evaluation 2012 namely ubcsat-IRoTS, as well as the famous complete solver wMaxSATz, our algorithm CCMaxSAT shows rather good performance on all the benchmarks.

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Notes

  1. http://www.proin.ktu.lt/~gintaras/wmax2sat.html.

  2. http://ubcsat.dtompkins.com/downloads.

  3. http://home.mis.u-picardie.fr/~cli/EnglishPage.html.

  4. ftp://dimacs.rutgers.edu/pub/challenge/satisfiability/cotributed/selman/.

  5. http://www.nlsde.buaa.edu.cn/~kexu/benchmarks/max-sat-benchmarks.htm.

  6. http://maxsat.ia.udl.cat:81/12/benchmarks/index.html.

  7. ftp://dimacs.rutgers.edu/pub/challenges.

  8. http://www-or.amp.i.kyoto-u.ac.jp/~yagiura/sat/max2sat/.

  9. www.shaoweicai.net/MaxSAT.html.

  10. http://www-or.amp.i.kyoto-u.ac.jp/~yagiura/sat/max2sat/.

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Acknowledgments

We would like to thank the anonymous reviewers for their valuable comments, which helped to improve the quality of this article. This work is supported by China National 973 project 2014CB340301, ARC Future Fellowship FT0991785, and National Natural Science Foundation of China 61370072 and 61472369.

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Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Shaowei Cai

  2. Key Laboratory of High Confidence Software Technologies, Peking University, Beijing, China

    Zhong Jie

  3. Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, Australia

    Kaile Su

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  1. Shaowei Cai
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  2. Zhong Jie
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  3. Kaile Su
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Correspondence to Shaowei Cai.

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Cai, S., Jie, Z. & Su, K. An effective variable selection heuristic in SLS for weighted Max-2-SAT. J Heuristics 21, 433–456 (2015). https://doi.org/10.1007/s10732-015-9284-3

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