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Core-Boosted Linear Search for Incomplete MaxSAT

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11494))

Abstract

Maximum Satisfiability (MaxSAT), the optimisation extension of the well-known Boolean Satisfiability (SAT) problem, is a competitive approach for solving NP-hard problems encountered in various artificial intelligence and industrial domains. Due to its computational complexity, there is an inherent tradeoff between scalability and guarantee on solution quality in MaxSAT solving. Limitations on available computational resources in many practical applications motivate the development of complete any-time MaxSAT solvers, i.e. algorithms that compute optimal solutions while providing intermediate results. In this work, we propose core-boosted linear search, a generic search-strategy that combines two central approaches in modern MaxSAT solving, namely linear and core-guided algorithms. Our experimental evaluation on a prototype combining reimplementations of two state-of-the-art MaxSAT solvers, PMRES as the core-guided approach and LinSBPS as the linear algorithm, demonstrates that our core-boosted linear algorithm often outperforms its individual components and shows competitive and, on many domains, superior results when compared to other state-of-the-art solvers for incomplete MaxSAT solving.

The first author is financially supported by the University of Helsinki Doctoral Program in Computer Science and the Academy of Finland (grant 312662). We thank the University of Melbourne and the Melbourne School of Engineering Visiting Fellows scheme for supporting the visit of Jeremias Berg.

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Notes

  1. 1.

    A consequence of the metric we use is that the scores of the other solvers we report are lower than in the evaluation. Their relative ranking is however the same.

References

  1. Abramé, A., Habet, D.: AHMAXSAT: description and evaluation of a branch and bound MaxSAT solver. J. Satisf. Boolean Model. Comput. 9, 89–128 (2015)

    Google Scholar 

  2. Abramé, A., Habet, D.: Learning nobetter clauses in MaxSAT branch and bound solvers. In: Proceedings of the 28th International Conference on Tools with Artificial Intelligence, pp. 452–459. IEEE Computer Society (2016)

    Google Scholar 

  3. Achá, R.J.A., Nieuwenhuis, R.: Curriculum-based course timetabling with SAT and MaxSAT. Ann. Oper. Res. 218(1), 71–91 (2014)

    Article  MathSciNet  Google Scholar 

  4. Alviano, M., Dodaro, C., Ricca, F.: A MaxSAT algorithm using cardinality constraints of bounded size. In: Proceedings of IJCAI, pp. 2677–2683. AAAI Press (2015)

    Google Scholar 

  5. Ansótegui, C., Bonet, M.L., Levy, J.: Solving (Weighted) partial MaxSAT through satisfiability testing. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 427–440. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_39

    Chapter  MATH  Google Scholar 

  6. Ansótegui, C., Bonet, M., Levy, J.: SAT-based MaxSAT algorithms. Artif. Intell. 196, 77–105 (2013)

    Article  MathSciNet  Google Scholar 

  7. Ansótegui, C., Bonet, M.L., Gabàs, J., Levy, J.: Improving SAT-based weighted MaxSAT solvers. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33558-7_9

    Chapter  Google Scholar 

  8. Ansótegui, C., Didier, F., Gabàs, J.: Exploiting the structure of unsatisfiable cores in MaxSAT. In: Proceedings of IJCAI, pp. 283–289. AAAI Press (2015)

    Google Scholar 

  9. Ansótegui, C., Gabàs, J.: Wpm3: an (in)complete algorithm for weighted partial maxsat. Artif. Intell. 250, 37–57 (2017)

    Article  MathSciNet  Google Scholar 

  10. Argelich, J., Le Berre, D., Lynce, I., Marques-Silva, J., Rapicault, P.: Solving Linux upgradeability problems using Boolean optimization. In: Proceedings of LoCoCo. Electronic Proceedings in Theoretical Computer Science, vol. 29, pp. 11–22 (2010)

    Google Scholar 

  11. Asín, R., Nieuwenhuis, R., Oliveras, A., Rodríguez-Carbonell, E.: Cardinality networks and their applications. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 167–180. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02777-2_18

    Chapter  MATH  Google Scholar 

  12. Audemard, G., Simon, L.: Predicting learnt clauses quality in modern SAT solvers. In: Proceedings of IJCAI, pp. 399–404. Morgan Kaufmann Publishers Inc. (2009)

    Google Scholar 

  13. Bacchus, F., Narodytska, N.: Cores in core based MaxSat algorithms: an analysis. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 7–15. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_2

    Chapter  Google Scholar 

  14. Bacchus, F., Järvisalo, M., Martins, R., et al.: MaxSat evaluation 2018 (2018). https://maxsat-evaluations.github.io/2018/. Accessed 05 Sept 2018

  15. Berg, J., Järvisalo, M.: Cost-optimal constrained correlation clustering via weighted partial maximum satisfiability. Artif. Intell. 244, 110–143 (2017)

    Article  MathSciNet  Google Scholar 

  16. Berg, J., Järvisalo, M.: Weight-aware core extraction in SAT-based MaxSAT solving. In: Beck, J.C. (ed.) CP 2017. LNCS, vol. 10416, pp. 652–670. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66158-2_42

    Chapter  Google Scholar 

  17. Biere, A., Biere, A., Heule, M., van Maaren, H., Walsh, T.: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications., vol. 185. IOS Press, Amsterdam (2009)

    MATH  Google Scholar 

  18. Bjørner, N., Narodytska, N.: Maximum satisfiability using cores and correction sets. In: Proceedings of IJCAI, pp. 246–252. AAAI Press (2015)

    Google Scholar 

  19. Bunte, K., Järvisalo, M., Berg, J., Myllymäki, P., Peltonen, J., Kaski, S.: Optimal neighborhood preserving visualization by maximum satisfiability. In: Proceedings of AAAI, vol. 3, pp. 1694–1700. AAAI Press (2014)

    Google Scholar 

  20. Chen, Y., Safarpour, S., Marques-Silva, J., Veneris, A.: Automated design debugging with maximum satisfiability. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 29(11), 1804–1817 (2010)

    Article  Google Scholar 

  21. Davies, J., Bacchus, F.: Exploiting the power of mip solvers in MaxSAT. In: Järvisalo, M., Van Gelder, A. (eds.) SAT 2013. LNCS, vol. 7962, pp. 166–181. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39071-5_13

    Chapter  MATH  Google Scholar 

  22. Demirović, E., Musliu, N.: MaxSAT based large neighborhood search for high school timetabling. Comput. Oper. Res. 78, 172–180 (2017)

    Article  MathSciNet  Google Scholar 

  23. Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into SAT. J. Satisf. Boolean Model. Comput. 2(1–4), 1–26 (2006)

    MATH  Google Scholar 

  24. Guerra, J., Lynce, I.: Reasoning over biological networks using maximum satisfiability. In: Milano, M. (ed.) CP 2012. LNCS, pp. 941–956. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33558-7_67

    Chapter  Google Scholar 

  25. Heras, F., Morgado, A., Marques-Silva, J.: Core-guided binary search algorithms for maximum satisfiability. In: Proceedings of AAAI. AAAI Press (2011)

    Google Scholar 

  26. Hyttinen, A., Eberhardt, F., Järvisalo, M.: Constraint-based causal discovery: conflict resolution with answer set programming. In: Proceedings of UAI, pp. 340–349. AUAI Press (2014)

    Google Scholar 

  27. Joshi, S., Martins, R., Manquinho, V.: Generalized totalizer encoding for pseudo-boolean constraints. In: Pesant, G. (ed.) CP 2015. LNCS, vol. 9255, pp. 200–209. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23219-5_15

    Chapter  Google Scholar 

  28. Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: QMaxSat: a partial Max-Sat solver. J. Satisf. Boolean Model. Comput. 8, 95–100 (2012)

    MathSciNet  MATH  Google Scholar 

  29. Le Berre, D., Parrain, A.: The Sat4j library, release 2.2 system description. J. Satisf. Boolean Model. Comput. 7, 59–64 (2010)

    Google Scholar 

  30. Lei, Z., Cai, S.: Solving (weighted) partial MaxSat by dynamic local search for SAT. In: Proceedings of IJCAI, pp. 1346–1352 (2018)

    Google Scholar 

  31. Li, C.M., Manyà, F., Planes, J.: Exploiting unit propagation to compute lower bounds in branch and bound Max-SAT solvers. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 403–414. Springer, Heidelberg (2005). https://doi.org/10.1007/11564751_31

    Chapter  MATH  Google Scholar 

  32. Li, C.M., Manya, F., Planes, J.: New inference rules for MaxSAT. J. Artif. Intell. Res. 30(1), 321–359 (2007)

    Article  Google Scholar 

  33. Li, C.M., Quan, Z.: An efficient branch-and-bound algorithm based on MaxSAT for the maximum clique problem. In: Proceedings of AAAI, vol. 10, pp. 128–133. AAAI Press (2010)

    Google Scholar 

  34. Lin, H., Su, K., Li, C.M.: Within-problem learning for efficient lower bound computation in MaxSAT solving. In: Proceedings of AAAI, pp. 351–356. AAAI Press (2008)

    Google Scholar 

  35. Liu, Y.L., Li, C.M., He, K., Fan, Y.: Breaking cycle structure to improve lower bound for MaxSAT. In: Zhu, D., Bereg, S. (eds.) FAW 2016. LNCS, vol. 9711, pp. 111–124. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-39817-4_12

    Chapter  Google Scholar 

  36. Marques-Silva, J., Janota, M., Ignatiev, A., Morgado, A.: Efficient model based diagnosis with maximum satisfiability. In: Proceedings of IJCAI, pp. 1966–1972. AAAI Press (2015)

    Google Scholar 

  37. Marques-Silva, J., Argelich, J., Graça, A., Lynce, I.: Boolean lexicographic optimization: algorithms & applications. Ann. Math. Artif. Intell. 62(3–4), 317–343 (2011)

    Article  MathSciNet  Google Scholar 

  38. Marques-Silva, J., Planes, J.: On using unsatisfiability for solving maximum satisfiability. CoRR abs/0712.1097 (2007)

    Google Scholar 

  39. Marques-Silva, J., Sakallah, K.A.: GRASP - a new search algorithm for satisfiability. In: Proceedings of ICCAD, pp. 220–227. IEEE Computer Society (1996)

    Google Scholar 

  40. Martins, R., Manquinho, V., Lynce, I.: Open-WBO: a modular MaxSAT solver,. In: Sinz, C., Egly, U. (eds.) SAT 2014. LNCS, vol. 8561, pp. 438–445. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09284-3_33

    Chapter  Google Scholar 

  41. Morgado, A., Dodaro, C., Marques-Silva, J.: Core-duided MaxSAT with soft cardinality constraints. In: O’Sullivan, B. (ed.) CP 2014. LNCS, vol. 8656, pp. 564–573. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10428-7_41

    Chapter  Google Scholar 

  42. Morgado, A., Heras, F., Liffiton, M.H., Planes, J., Marques-Silva, J.: Iterative and core-guided maxsat solving: a survey and assessment. Constraints 18(4), 478–534 (2013)

    Article  MathSciNet  Google Scholar 

  43. Nadel, A., Ryvchin, V.: Efficient SAT solving under assumptions. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 242–255. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31612-8_19

    Chapter  MATH  Google Scholar 

  44. Narodytska, N., Bacchus, F.: Maximum satisfiability using core-guided MaxSAT resolution. In: Proceedings of AAAI, pp. 2717–2723. AAAI Press (2014)

    Google Scholar 

  45. Saikko, P., Berg, J., Järvisalo, M.: LMHS: a SAT-IP hybrid MaxSAT solver. In: Creignou, N., Le Berre, D. (eds.) SAT 2016. LNCS, vol. 9710, pp. 539–546. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40970-2_34

    Chapter  MATH  Google Scholar 

  46. Sinz, C.: Towards an optimal CNF encoding of boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005). https://doi.org/10.1007/11564751_73

    Chapter  MATH  Google Scholar 

  47. Tseitin, G.S.: On the complexity of derivation in propositional calculus. In: Siekmann, J.H., Wrightson, G. (eds.) Automation of Reasoning: 2: Classical Papers on Computational Logic 1967–1970. Symbolic Computation (Artificial Intelligence), pp. 466–483. Springer, Heidelberg (1983). https://doi.org/10.1007/978-3-642-81955-1_28

    Chapter  Google Scholar 

  48. Xing, Z., Zhang, W.: MaxSolver: an efficient exact algorithm for (weighted) maximum satisfiability. Artif. intell. 164(1–2), 47–80 (2005)

    Article  MathSciNet  Google Scholar 

  49. Zhang, L., Madigan, C.F., Moskewicz, M.H., Malik, S.: Efficient conflict-driven learning in a Boolean satisfiability solver. In: Proceedings of ICCAD, pp. 279–285. IEEE Computer Society (2001)

    Google Scholar 

  50. Zhang, X., Mangal, R., Grigore, R., Naik, M., Yang, H.: On abstraction refinement for program analyses in datalog. In: Proceedings of PLDI, PLDI 2014, pp. 239–248. ACM, New York (2014)

    Google Scholar 

  51. Zhu, C., Weissenbacher, G., Malik, S.: Post-silicon fault localisation using maximum satisfiability and backbones. In: Proceedings of FMCAD, pp. 63–66. FMCAD Inc. (2011)

    Google Scholar 

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Author information

Authors and Affiliations

  1. HIIT, Department of Computer Science, University of Helsinki, Helsinki, Finland

    Jeremias Berg

  2. University of Melbourne, Melbourne, Australia

    Emir Demirović

  3. Monash University, Melbourne, Australia

    Peter J. Stuckey

  4. Data61, CSIRO, Canberra, Australia

    Peter J. Stuckey

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  1. Jeremias Berg
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  2. Emir Demirović
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  3. Peter J. Stuckey
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Correspondence to Jeremias Berg .

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  1. Ecole Polytechnique de Montréal, Montréal, QC, Canada

    Louis-Martin Rousseau

  2. University of Western Macedonia, Kozani, Greece

    Kostas Stergiou

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Berg, J., Demirović, E., Stuckey, P.J. (2019). Core-Boosted Linear Search for Incomplete MaxSAT. In: Rousseau, LM., Stergiou, K. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2019. Lecture Notes in Computer Science(), vol 11494. Springer, Cham. https://doi.org/10.1007/978-3-030-19212-9_3

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