Advertisement

Scaling and Probabilistic Smoothing: Dynamic Local Search for Unweighted MAX-SAT

  • Dave A. D. Tompkins
  • Holger H. Hoos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2671)

Abstract

In this paper, we study the behaviour of the Scaling and Probabilistic Smoothing (SAPS) dynamic local search algorithm on the unweighted MAX-SAT problem. MAX-SAT is a conceptually simple combinatorial problem of substantial theoretical and practical interest; many application-relevant problems, including scheduling problems or most probable explanation finding in Bayes nets, can be encoded and solved as MAX-SAT. This paper is a natural extension of our previous work, where we introduced SAPS, and demonstrated that it is amongst the state-of-the-art local search algorithms for solvable SAT problem instances. We present results showing that SAPS is also very e.ective at finding optimal solutions for unsatisfiable MAX-SAT instances, and in many cases performs better than state-of-the-art MAX-SAT algorithms, such as the Guided Local Search algorithm by Mills and Tsang [8]. With the exception of some configuration parameters, we found that SAPS did not require any changes to effeciently solve unweighted MAX-SAT instances. For solving weighted MAX-SAT instances, a modified SAPS algorithm will be necessary, and we provide some thoughts on this topic of future research.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    B. Borchers and J. Furman. A two-phase exact algorithm for MAX-SAT and weighted MAX-SAT problems. In Journal of Combinatorial Optimization, Vol. 2, pp. 299–306, 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    P. Cheeseman, B. Kanefsky and W. M. Taylor. Where the Really Hard Problems Are. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, IJCAI-91,.331–337, 1997.Google Scholar
  3. [3]
    J. Frank. Learning Short-term Clause Weights for GSAT. In Proc. IJCAI-97, pp. 384–389, Morgan Kaufmann Publishers, 1997.Google Scholar
  4. [4]
    P. Hansen and B. Jaumard. Algorithms for the maximum Satisfiability problem. In Computing, 44: 279–303, 1990.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    H. H. Hoos. On the Run-time Behaviour of Stochastic Local Search Algorithms for SAT. In Proc. AAAI-99, pp 661–666. AAAI Press, 1999.Google Scholar
  6. [6]
    H. H. Hoos and T. Stutzle. Local Search Algorithms for SAT: An Empirical Evaluation. In J. of Automated Reasoning, Vol. 24, No. 4, pp. 421–481, 2000.CrossRefzbMATHGoogle Scholar
  7. [7]
    F. Hutter, D. A. D. Tompkins, and H. H. Hoos. Scaling and Probabilistic Smoothing: Effecient Dynamic Local Search for SAT. In LNCS 2470:Proc. CP-02, pp 233–248, Springer Verlag, 2002.Google Scholar
  8. [8]
    P. Mills and E.P.K. Tsang. Guided Local Search for solving SAT and weighted MAX-SAT problems. In Journal of Automated Reasoning, Special Issue on Satisfiability Problems, 24:205–223, Kluwer, 2000MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    P. Morris. The breakout method for escaping from local minima. In Proc. AAAI-93, pp 40–45. AAAI Press, 1993.Google Scholar
  10. [10]
    J. D. Park. Using Weighted MAX-SAT Engines to Solve MPE. In Proc. AAAI-02, pp 682–687. AAAI Press, 2002.Google Scholar
  11. [11]
    D. Schuurmans and F. Southey. Local search characteristics of incomplete SAT procedures. In Proc. AAAI-2000, pp 297–302, AAAI Press, 2000. Scaling and Probabilistic Smoothing: Dynamic Local SearchGoogle Scholar
  12. [12]
    D. Schuurmans, F. Southey, and R.C. Holte. The exponentiated subgradient algorithm for heuristic boolean programming. In Proc. IJCAI-01, pp 334–341, Morgan Kaufmann Publishers, 2001.Google Scholar
  13. [13]
    B. Selman and H. A. Kautz. Domain-Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems. In Proc. IJCAI-93, pp 290–295, Morgan Kaufmann Publishers, 1993.Google Scholar
  14. [14]
    B. Selman, H.A. Kautz, and B. Cohen. Noise Strategies for Improving Local Search. In Proc. AAAI-94, pp 337–343, AAAI Press, 1994.Google Scholar
  15. [15]
    B. Selman, H. Levesque, and D. Mitchell. A New Method for Solving Hard Satisfiability Problems. In Proc. AAAI-92, pp 440–446, AAAI Press, 1992.Google Scholar
  16. [16]
    B. Selman, D.G. Mitchell, and H. J. Levesque. Generating Hard Satisfiability Problems. In Artificial Intelligence, Vol. 81. pp. 17–29, 1996.MathSciNetCrossRefGoogle Scholar
  17. [17]
    K. Smyth, H. H. Hoos, and T. Stutzle. Iterated Robust Tabu Search for MAXSAT. In Proc. of the 16th Canadian Conference on Artificial Intelligence (AI 2003), to appear, 2003.Google Scholar
  18. [18]
    Z. Wu and B. W. Wah. An Effecient Global-Search Strategy in Discrete Lagrangian Methods for Solving Hard Satisfiability Problems. In Proc. AAAI-00, pp. 310–315, AAAI Press, 2000.Google Scholar
  19. [19]
    M. Yagiura and T. Ibaraki. Analyses on the 2 and 3-Flip Neighborhoods for the MAX SAT. In Journal of Combinatorial Optimization, Vol. 3, No. 1, pp 95–114, July 1999.MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    M. Yagiura and T. Ibaraki. Effecient 2 and 3-Flip Neighborhood Search Algorithms for the MAX SAT: Experimental Evaluation. In Journal of Heuristics, Vol. 7, No. 5, pp. 423–442, 2001.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Dave A. D. Tompkins
    • 1
  • Holger H. Hoos
    • 2
  1. 1.Department of Electrical EngineeringUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

Personalised recommendations