Abstract
In the last few years, there has been a significant effort in designing and developing efficient Weighted MaxSAT solvers. We study in detail the WPM1 algorithm identifying some weaknesses and proposing solutions to mitigate them. Basically, WPM1 is based on iteratively calling a SAT solver and adding blocking variables and cardinality constraints to relax the unsatisfiable cores returned by the SAT solver. We firstly identify and study how to break the symmetries introduced by the blocking variables and cardinality constraints. Secondly, we study how to prioritize the discovery of higher quality cores. We present an extensive experimental investigation comparing the new algorithm with state-of-the-art solvers showing that our approach makes WPM1 much more competitive.
This research has been partially founded by the CICYT research projects TASSAT (TIN2010-20967-C04-01/03/04) and ARINF (TIN2009-14704-C03-01).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Ansótegui, C., Bonet, M.L., Levy, J.: A new algorithm for weighted partial MaxSAT. In: AAAI 2010 (2010)
Ansótegui, C., Manyà, F.: Mapping Problems with Finite-Domain Variables to Problems with Boolean Variables. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 1–15. Springer, Heidelberg (2005)
Argelich, J., Li, C.M., Manyà, F., Planes, J.: MaxSAT evaluations (2006, 2007, 2008, 2009, 2010, 2011), http://www.maxsat.udl.cat
Berre, D.L.: SAT4J, a satisfiability library for java (2006), http://www.sat4j.org
Biere, A.: PicoSAT essentials. Journal on Satisfiability 4, 75–97 (2008)
Bonet, M.L., Levy, J., Manyà, F.: Resolution for Max-SAT. Artif. Intell. 171(8-9), 606–618 (2007)
Davies, J., Bacchus, F.: Solving MAXSAT by Solving a Sequence of Simpler SAT Instances. In: Lee, J. (ed.) CP 2011. LNCS, vol. 6876, pp. 225–239. Springer, Heidelberg (2011)
Fu, Z., Malik, S.: On Solving the Partial MAX-SAT Problem. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 252–265. Springer, Heidelberg (2006)
Heras, F., Larrosa, J., Oliveras, A.: MiniMaxSat: A New Weighted Max-SAT Solver. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 41–55. Springer, Heidelberg (2007)
Heras, F., Morgado, A., Marques-Silva, J.: Core-guided binary search algorithms for maximum satisfiability. In: AAAI 2011 (2011)
Li, C.M., Manyà, F., Mohamedou, N., Planes, J.: Exploiting Cycle Structures in Max-SAT. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 467–480. Springer, Heidelberg (2009)
Lin, H., Su, K., Li, C.M.: Within-problem learning for efficient lower bound computation in Max-SAT solving. In: AAAI 2008, pp. 351–356 (2008)
Manquinho, V., Marques-Silva, J., Planes, J.: Algorithms for Weighted Boolean Optimization. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 495–508. Springer, Heidelberg (2009)
Marques-Silva, J., Argelich, J., Graça, A., Lynce, I.: Boolean lexicographic optimization: algorithms & applications. Ann. Math. Artif. Intell. 62(3-4), 317–343 (2011)
Marques-Silva, J., Lynce, I., Manquinho, V.: Symmetry Breaking for Maximum Satisfiability. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 1–15. Springer, Heidelberg (2008)
Marques-Silva, J., Manquinho, V.: Towards More Effective Unsatisfiability-Based Maximum Satisfiability Algorithms. In: Kleine Büning, H., Zhao, X. (eds.) SAT 2008. LNCS, vol. 4996, pp. 225–230. Springer, Heidelberg (2008)
Marques-Silva, J., Planes, J.: On using unsatisfiability for solving maximum satisfiability. CoRR abs/0712.1097 (2007)
Sanchez, M., Bouveret, S., Givry, S.D., Heras, F., Jégou, P., Larrosa, J., Ndiaye, S., Rollon, E., Schiex, T., Terrioux, C., Verfaillie, G., Zytnicki, M.: Max-CSP competition 2008: toulbar2 solver description (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ansótegui, C., Bonet, M.L., Gabàs, J., Levy, J. (2012). Improving SAT-Based Weighted MaxSAT Solvers. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-33558-7_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33557-0
Online ISBN: 978-3-642-33558-7
eBook Packages: Computer ScienceComputer Science (R0)