Algorithms for Weighted Boolean Optimization

  • Vasco Manquinho
  • Joao Marques-Silva
  • Jordi Planes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5584)

Abstract

The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT, despite the existence of straightforward mappings from PBO to MaxSAT, and vice-versa. This papers proposes Weighted Boolean Optimization (WBO), a new unified framework that aggregates and extends PBO and MaxSAT. In addition, the paper proposes a new unsatisfiability-based algorithm for WBO, based on recent unsatisfiability-based algorithms for MaxSAT. Besides standard MaxSAT, the new algorithm can also be used to solve weighted MaxSAT and PBO, handling pseudo-Boolean constraints either natively or by translation to clausal form. Experimental results illustrate that unsatisfiability-based algorithms for MaxSAT can be orders of magnitude more efficient than existing dedicated algorithms. Finally, the paper illustrates how other algorithms for either PBO or MaxSAT can be extended to WBO.

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References

  1. 1.
    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)Google Scholar
  2. 2.
    Amgoud, L., Cayrol, C., Berre, D.L.: Comparing arguments using preference ordering for argument-based reasoning. In: International Conference on Tools with Artificial Intelligence, pp. 400–403 (1996)Google Scholar
  3. 3.
    Argelich, J., Li, C.M., Manà, F.: An improved exact solver for partial max-sat. In: International Conference on Nonconvex Programming: Local and Global Approaches, pp. 230–231 (2007)Google Scholar
  4. 4.
    Argelich, J., Li, C.M., Manyà, F., Planes, J.: Third Max-SAT evaluation (2008), http://www.maxsat.udl.cat/08/
  5. 5.
    Bailleux, O., Boufkhad, Y., Roussel, O.: A translation of pseudo Boolean constraints to SAT. Journal on Satisfiability, Boolean Modeling and Computation 2, 191–200 (2006)MATHGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Berre, D.L.: SAT4J library, http://www.sat4j.org
  8. 8.
    Biere, A.: PicoSAT essentials. Journal on Satisfiability, Boolean Modeling and Computation 2, 75–97 (2008)MATHGoogle Scholar
  9. 9.
    Bonet, M.L., Levy, J., Manyà, F.: Resolution for Max-SAT. Artificial Intelligence 171(8-9), 606–618 (2007)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Borchers, B., Furman, J.: A two-phase exact algorithm for MAX-SAT and weighted MAX-SAT problems. Journal of Combinatorial Optimization 2, 299–306 (1999)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Chai, D., Kuehlmann, A.: A fast pseudo-Boolean constraint solver. In: Design Automation Conference, pp. 830–835 (2003)Google Scholar
  12. 12.
    Coudert, O.: On Solving Covering Problems. In: Design Automation Conference, pp. 197–202 (1996)Google Scholar
  13. 13.
    Darras, S., Dequen, G., Devendeville, L., Li, C.M.: On inconsistent clause-subsets for Max-SAT solving. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 225–240. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Edmonds, J.: Paths, trees and flowers. Canadian Journal of Mathematics 17, 449–467 (1965)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Een, N., Sörensson, N.: Translating pseudo-Boolean constraints into SAT. Journal on Satisfiability, Boolean Modeling and Computation 2, 1–26 (2006)MATHGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    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)CrossRefGoogle Scholar
  18. 18.
    Heras, F., Larrosa, J., Oliveras, A.: MiniMaxSAT: An efficient weighted Max-SAT solver. Journal of Artificial Intelligence Research 31, 1–32 (2008)MathSciNetMATHGoogle Scholar
  19. 19.
    Larrosa, J., Heras, F., de Givry, S.: A logical approach to efficient Max-SAT solving. Artificial Intelligence 172(2-3), 204–233 (2008)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Li, C.M., Manyà, F., Planes, J.: New inference rules for Max-SAT. Journal of Artificial Intelligence Research 30, 321–359 (2007)MathSciNetMATHGoogle Scholar
  21. 21.
    Liao, S., Devadas, S.: Solving Covering Problems Using LPR-Based Lower Bounds. In: Design Automation Conference, pp. 117–120 (1997)Google Scholar
  22. 22.
    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)Google Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    Manquinho, V., Marques-Silva, J.: Effective lower bounding techniques for pseudo-boolean optimization. In: Design, Automation and Test in Europe Conference, pp. 660–665 (2005)Google Scholar
  25. 25.
    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)CrossRefGoogle Scholar
  26. 26.
    Marques-Silva, J., Planes, J.: On using unsatisfiability for solving maximum satisfiability. Computing Research Repository, abs/0712.0097 (December 2007)Google Scholar
  27. 27.
    Marques-Silva, J., Planes, J.: Algorithms for maximum satisfiability using unsatisfiable cores. In: Design, Automation and Testing in Europe Conference, pp. 408–413 (2008)Google Scholar
  28. 28.
    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)CrossRefGoogle Scholar
  29. 29.
    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 (JSAT) 4, 191–217 (2008)MATHGoogle Scholar
  30. 30.
    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)CrossRefGoogle Scholar
  31. 31.
    Safarpour, S., Mangassarian, H., Veneris, A., Liffiton, M.H., Sakallah, K.A.: Improved design debugging using maximum satisfiability. In: Formal Methods in Computer-Aided Design (2007)Google Scholar
  32. 32.
    Sheini, H., Sakallah, K.A.: Pueblo: A hybrid pseudo-Boolean SAT solver. Journal on Satisfiability, Boolean Modeling and Computation 2, 165–189 (2006)MATHGoogle Scholar
  33. 33.
    Warners, J.: A linear-time transformation of linear inequalities into conjunctive normal form. Information Processing Letters 68(2), 63–69 (1998)MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Xu, H., Rutenbar, R.A., Sakallah, K.A.: sub-SAT: a formulation for relaxed boolean satisfiability with applications in routing. IEEE Transactions on CAD of Integrated Circuits and Systems 22(6), 814–820 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Vasco Manquinho
    • 1
  • Joao Marques-Silva
    • 2
  • Jordi Planes
    • 3
  1. 1.IST/UTL - INESC-IDPortugal
  2. 2.University College DublinIreland
  3. 3.Universitat de LleidaSpain

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