Abstract
Recently, several unsatisfiability-based algorithms have been proposed for Maximum Satisfiability (MaxSAT) and other Boolean Optimization problems. These algorithms are based on being able to iteratively identify and relax unsatisfiable sub-formulas with the use of fast Boolean satisfiability solvers. It has been shown that this approach is very effective for several classes of instances, but it can perform poorly on others for which classical Boolean optimization algorithms find it easy to solve. This paper proposes the use of Pseudo-Boolean Optimization (PBO) solvers as a preprocessor for unsatisfiability-based algorithms in order to increase its robustness. Moreover, the use of constraint branching, a well-known technique from Integer Linear Programming, is also proposed into the unsatisfiability-based framework. Experimental results show that the integration of these features in an unsatisfiability-based algorithm results in an improved and more effective solver for Boolean optimization problems.
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
Aloul, F., Ramani, A., Markov, I., Sakallah, K.A.: Generic ILP versus specialized 0-1 ILP: An update. In: International Conference on Computer-Aided Design, pp. 450–457 (2002)
Ansótegui, C., Bonet, M., Levy, J.: Solving (Weighted) Partial MaxSAT through Satisfiability Testing. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 427–440. Springer, Heidelberg (2009)
Argelich, J., Li, C.M., Manyà, F.: An improved exact solver for partial max-sat. In: Proceedings of the International Conference on Nonconvex Programming: Local and Global Approaches (NCP-2007), pp. 230–231 (2007)
Argelich, J., Li, C.M., Manyà, F., Planes, J.: Fourth Max-SAT evaluation (2009), http://www.maxsat.udl.cat/09/
Bacchus, F., Winter, J.: Effective preprocessing with hyper-resolution and equality reduction. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 183–192. Springer, Heidelberg (2004)
Barnhart, C., Johnson, E., Nemhauser, G., Savelsbergh, M., Vance, P.: Branch-and-price: Column generation for solving huge integer programs. Operations Research 46(3), 316–329 (1998)
Barth, P.: A Davis-Putnam Enumeration Algorithm for Linear Pseudo-Boolean Optimization. Technical Report MPI-I-95-2-003, Max Plank Institute for Computer Science (1995)
Berre, D.L.: SAT4J library, http://www.sat4j.org
Biere, A.: PicoSAT essentials. Journal on Satisfiability, Boolean Modeling and Computation 2, 75–97 (2008)
Chai, D., Kuehlmann, A.: A fast pseudo-Boolean constraint solver. In: Design Automation Conference, pp. 830–835 (2003)
Eén, N., Sörensson, N.: Minisat 2.0 sat solver, http://minisat.se/MiniSat.html
Eén, N., Sörensson, N.: Translating pseudo-Boolean constraints into SAT. Journal on Satisfiability, Boolean Modeling and Computation 2 (2006)
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: An efficient weighted Max-SAT solver. Journal of Artificial Intelligence Research 31, 1–32 (2008)
Larrosa, J., Heras, F., de Givry, S.: A logical approach to efficient Max-SAT solving. Artificial Intelligence 172(2-3), 204–233 (2008)
Li, C.M., Manyà, F., Planes, J.: New inference rules for Max-SAT. Journal of Artificial Intelligence Research 30, 321–359 (2007)
Lin, H., Su, K.: Exploiting inference rules to compute lower bounds for MAX-SAT solving. In: International Joint Conference on Artificial Intelligence, pp. 2334–2339 (2007)
Manquinho, V., Marques-Silva, J.: Search pruning techniques in SAT-based branch-and-bound algorithms for the binate covering problem. IEEE Transactions on Computer-Aided Design 21(5), 505–516 (2002)
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., 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.: Algorithms for maximum satisfiability using unsatisfiable cores. In: Design, Automation and Testing in Europe Conference, March 2008, pp. 408–413 (2008)
Martins, R., Lynce, I., Manquinho, V.: Preprocessing in pseudo-boolean optimization: An experimental evaluation. In: Eighth International Workshop on Constraint Modelling and Reformulation (2009)
Pipatsrisawat, K., Palyan, A., Chavira, M., Choi, A., Darwiche, A.: Solving weighted Max-SAT problems in a reduced search space: A performance analysis. Journal on Satisfiability Boolean Modeling and Computation 4, 191–217 (2008)
Ramírez, M., Geffner, H.: Structural relaxations by variable renaming and their compilation for solving MinCostSAT. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 605–619. Springer, Heidelberg (2007)
Ryan, D., Foster, B.: An integer programming approach to scheduling. In: Computer Scheduling of Public Transport, pp. 269–280 (1981)
Sheini, H., Sakallah, K.: Pueblo: A Modern Pseudo-Boolean SAT Solver. In: Design, Automation and Testing in Europe Conference, pp. 684–685 (March 2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Manquinho, V., Martins, R., Lynce, I. (2010). Improving Unsatisfiability-Based Algorithms for Boolean Optimization. In: Strichman, O., Szeider, S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14186-7_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-14186-7_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14185-0
Online ISBN: 978-3-642-14186-7
eBook Packages: Computer ScienceComputer Science (R0)