Abstract
In this paper we introduce MiniMaxSat, a new Max-SAT solver that incorporates the best SAT and Max-SAT techniques. It can handle hard clauses (clauses of mandatory satisfaction as in SAT), soft clauses (clauses whose falsification is penalized by a cost as in Max-SAT) as well as pseudo-boolean objective functions and constraints. Its main features are: learning and backjumping on hard clauses; resolution-based and subtraction-based lower bounding; and lazy propagation with the two-watched literals scheme. Our empirical evaluation on a wide set of optimization benchmarks indicates that its performance is usually close to the best specialized alternative and, in some cases, even better.
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References
Papadimitriou, C.: Computational Complexity. Addison-Wesley, Reading (1994)
Karloff, H.J., Zwick, U.: A 7/8-Approximation Algorithm for MAX 3SAT. In: FOCS (1997)
Shen, H., Zhang, H.: Study of lower bounds for Max-2-SAT. In: AAAI (2004)
Larrosa, J., Heras, F.: Resolution in Max-SAT and its relation to local consistency for weighted CSPs. In: IJCAI (2005)
Larrosa, J., Heras, F., de Givry, S.: A logical approach to efficient max-sat solving (2006), Available at the Computing Research Repository http://arxiv.org/PS_cache/cs/ps/0611/0611025.ps.gz
Xing, Z., Zhang, W.: MaxSolver: An efficient exact algorithm for (weighted) maximum satisfiability. Artificial Intelligence 164, 47–80 (2005)
Manyà, F., Li, C.-M., 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)
Li, C.M., Manyà, F., Planes, J.: Detecting disjoint inconsistent subformulas for computing lower bounds for max-sat. In: AAAI (2006)
Cha, B., et al.: Local search algorithms for partial MAXSAT. In: AAAI/IAAI, pp. 263–268 (1997)
Manyà, F., Alsinet, T., Planès, J.G.: Improved Exact Solvers for Weighted Max-SAT. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 371–377. Springer, Heidelberg (2005)
Argelich, J., Manyà, F.: Learning hard constraints in max-sat. In: CSCLP-2006, pp. 1–12 (2006)
Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into sat. Journal on Satisfiability, Boolean Modeling and Computation 2, 1–26 (2006)
Eén, N., Sörensson, N.: An extensible sat-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)
Heras, F., Larrosa, J.: New inference rules for efficient max-sat solving. In: AAAI (2006)
Moskewicz, M.W., et al.: Chaff: Engineering an efficient sat solver. In: DAC, pp. 530–535 (2001)
Hoos, H.H., Tompkins, D.A.D.: UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT and MAX-SAT. In: H. Hoos, H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 306–320. Springer, Heidelberg (2005)
Larrosa, J.: Node and arc consistency in weighted CSP. In: AAAI, pp. 48–53 (2002)
Lynce, I., Silva, J.P.M.: Probing-based preprocessing techniques for propositional satisfiability. In: ICTAI, p. 105 (2003)
Sheini, H.M., Sakallah, K.A.: Pueblo: A hybrid pseudo-boolean sat solver. Journal on Satisfiability, Boolean Modeling and Computation 2, 165–189 (2006)
Li, C.M., Manyà, F., Planes, J.: New inference rules for max-sat. Submitted (2006)
Larrosa, J., Schiex, T.: In the quest of the best form of local consistency for weighted CSP. In: Proc. of the 18th IJCAI, Acapulco, Mexico (2003)
de Givry, S., et al.: Solving max-SAT as weighted CSP. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 363–376. Springer, Heidelberg (2003)
de Givry, S., et al.: Existential arc consistency: getting closer to full arc consistency in weighted CSPs. In: Proc. of the 19th IJCAI, Edinburgh, U.K. (2005)
Leyton-Brown, K., Pearson, M., Shoham, Y.: Towards a universal test suite for combinatorial auction algorithms. In: ACM E-Commerce, pp. 66–76 (2000)
Cooper, M., et al.: Soft Arc Consistency Applied to Optimal Planning. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 680–684. Springer, Heidelberg (2006)
Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)
Lynce, I., Silva, J.P.M.: Efficient data structures for backtrack search sat solvers. Ann. Math. Artif. Intell. 43, 137–152 (2005)
Zivan, R., Meisels, A.: Conflict directed backjumping for maxcsps. In: IJCAI (2007)
Manquinho, V.M., Silva, J.P.M.: Satisfiability-based algorithms for boolean optimization. Ann. Math. Artif. Intell. 40, 353–372 (2004)
Nieuwenhuis, R., Oliveras, A.: On SAT Modulo Theories and Optimization Problems. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 156–169. Springer, Heidelberg (2006)
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Heras, F., Larrosa, J., Oliveras, A. (2007). MiniMaxSat: A New Weighted Max-SAT Solver. In: Marques-Silva, J., Sakallah, K.A. (eds) Theory and Applications of Satisfiability Testing – SAT 2007. SAT 2007. Lecture Notes in Computer Science, vol 4501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72788-0_8
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DOI: https://doi.org/10.1007/978-3-540-72788-0_8
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