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Diversification and Determinism in Local Search for Satisfiability

  • Chu Min Li
  • Wen Qi Huang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3569)

Abstract

The choice of the variable to flip in the Walksat family procedures is always random in that it is selected from a randomly chosen unsatisfied clause c. This choice in Novelty or R-Novelty heuristics also contains some determinism in that the variable to flip is always limited to the two best variables in c. In this paper, we first propose a diversification parameter for Novelty (or R-Novelty) heuristic to break the determinism in Novelty and show its performance compared with the random walk parameter in Novelty+. Then we exploit promising decreasing paths in a deterministic fashion in local search using a gradient-based approach. In other words, when promising decreasing paths exist, the variable to flip is no longer selected from a randomly chosen unsatisfied clause but in a deterministic fashion to surely decrease the number of unsatisfied clauses. Experimental results show that the proposed diversification and the determinism allow to significantly improve Novelty (and Walksat).

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References

  1. 1.
    Cook, S.A.: The complexity of theorem-proving procedures. In: Proceedings of 3rd Annual ACM Symp. Theory of Computing, pp. 151–158 (1971)Google Scholar
  2. 2.
    Fukunaga, A.: Efficient implementation of sat local search. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 306–320. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Gent, I., Walsh, T.: Towards an understanding of hill-climbing procedures for SAT. In: Proceedings of AAAI 1993 (1993)Google Scholar
  4. 4.
    Hirsch, E.A., Kojevnikov, A.: Unitwalk: A new sat solver that uses local search guided by unit clause elimination. Annals of Mathematics and Artificial Intelligence 43(1-4), 91–111 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Hoos, H.: On the run-time behavior of stochastic local search algorithms for sat. In: Proceedings of AAAI 1999, pp. 661–666 (1999)Google Scholar
  6. 6.
    Hoos, H.: An adaptive noise mechanism for walksat. In: Proceedings of AAAI 2002, pp. 655–660. AAAI Press/The MIT Press (2002)Google Scholar
  7. 7.
    Huang, W.Q., Chao, J.R.: Solar: a learning from human algorithm for solving sat. Science in China (Series E) 27(2), 179–186 (1997)Google Scholar
  8. 8.
    Li, C.M., Anbulagan, A.: Look-Ahead Versus Look-Back for Satisfiability Problems. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 342–356. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Mazure, B., Saïs, L., Grégoire, É.: Tabu Search for SAT. In: Proceedings of AAAI 1997 (1997)Google Scholar
  10. 10.
    McAllester, D.A., Selman, B., Kautz, H.: Evidence for invariant in local search. In: Proceedings of AAAI 1997, pp. 321–326 (1997)Google Scholar
  11. 11.
    Schuurmans, D., Southey, F.: Local search characteristics of incomplete sat procedures. Artificial Intelligence 132(2), 121–150 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Selman, B., Kautz, H.: Domain-independent extensions to gsat: Solving large structured satisfiability problems. In: Proceedings of IJCAI 1993 (1993)Google Scholar
  13. 13.
    Selman, B., Kautz, H., Cohen, B.: Noise strategies for improving local search. In: Proceedings of AAAI 1994, 12th National Conference on Artificial Intelligence, pp. 337–343. AAAI Press, Seattle (1994)Google Scholar
  14. 14.
    Selman, B., Mitchell, D., Levesque, H.: A new Method for Solving Hard Satisfiability Problems. In: Proceedings of AAAI 1992, pp. 440–446 (1992)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Chu Min Li
    • 1
  • Wen Qi Huang
    • 2
  1. 1.LaRIAUniversité de Picardie Jules VerneAmiens Cedex 1France
  2. 2.Huazhong university of science and technologyWuhanChina

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