Local search algorithms are one of the effective methods for solving hard combinatorial problems. However, a serious problem of this approach is that the search often traps at local optima. At AAAI 2004, Fang and Ruml proposed a novel approach which makes local optima disappeared. The basic idea is that, at each local optimal point during the search, the value of the objective function (a local gradient function) at that point is changed by adding some information into the database. Once no more local optima exist, the local search can always find a global optimal. In this paper, along the same approach of Fang and Ruml, we propose a different objective function based on an ordering of propositional variables. Based on this ordering, ordered resolution is performed at each local optimal point and the resolvent is added into the database. This resolvent always increases the value of the objective function so that the local optimal point disappears after a finite number of steps. Preliminary experimental results show that our method and Fang and Ruml’s method have better performances in different areas.


Objective Function Local Search Local Search Algorithm Preliminary Experimental Result Current Assignment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [BG2002]
    Bachmair, L., Ganzinger, H.: Resolution theorem proving. In: Robinson, A., Voronkov, A. (eds.) The Hanfbook of Automated Reasoning, vol. I, ch.2, pp. 19–99. Elsevier Science Pub., Amsterdam (2001)CrossRefGoogle Scholar
  2. [B2003]
    Beame, P., Kautz, H., Sabharwal, A.: Understanding the power of clause learning. In: Proceedings of IJCAI 2003, pp. 1194–1201 (2003)Google Scholar
  3. [CI1996]
    Cha, B., Iwama, K.: Adding new clauses for faster local search. In: Proceedings of AAAI 1996, pp. 332–337 (1996)Google Scholar
  4. [DP1960]
    Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM 7, 201–215 (1960)zbMATHCrossRefMathSciNetGoogle Scholar
  5. [DLL1962]
    Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Journal of the ACM 5(7), 394–397 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  6. [FR2004]
    Fang, H., Ruml, W.: Complete Local Search for Propositional Satisfiability. In: Proc. of 19th National Conference on Artificial Intelligence, pp. 161–166 (2004)Google Scholar
  7. [GN2002]
    Boldberg, E., Novikov, Y.: BerkMin: a Fast and Robust SAT-Solver. In: Proc. of DATE 2002, pp. 142–149 (2002)Google Scholar
  8. [HS2000]
    Hoos, H.H., Stützle, T.: SATLIB: An Online Resource for Research on SAT. In: Gent, I.P., Maaren, H.V., Walsh, T. (eds.) SAT 2000, pp. 283–292. IOS Press, Amsterdam (2000) SATLIB is available online at, Google Scholar
  9. [HS2005]
    Hoos, H.H., Stützle, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann Publishers, San Francisco (2005)zbMATHGoogle Scholar
  10. [KS2003]
    Kautz, H., Selman, B.: Ten challenges redux: Recent progress in propositional reasoning and search. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 1–18. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. [MS1999]
    Marques-Silva, J.P., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Trans. Comput. 48(5), 506–520 (1999)CrossRefMathSciNetGoogle Scholar
  12. [M1993]
    Morris, P.: The breakout method for escaping from local minima. In: Proceedings of AAAI 1993, pp. 40–45 (1993)Google Scholar
  13. [M2001]
    Moskewicz, M., Madigan, C., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proc. of Design Automation Conference, pp. 530–535 (2001)Google Scholar
  14. [N2002]
    Nadel, A.: Backtrack Search Algorithms for Propositional Logic Satisfiability: Review and Innovations. Thesis of Nadel, A (2002)Google Scholar
  15. [SKM1995]
    Selman, B., Kautz, H., McAllester, D.: Ten challenges in propositional reasoning and search. In: Proc. of IJCAI 1995, pp. 50–54 (1995)Google Scholar
  16. [SW1997]
    Shang, Y., Wah, B.W.: A discrete Lagrangian-based global-search method for solving satisfiability problems. Journal of Global Optimization 10, 1–40 (1997)CrossRefGoogle Scholar
  17. [WW2000]
    Wu, Z., Wah, B.W.: An efficient global-search strategy in discrete Lagrangian methods for solving hard satisfiability problems. In: Proceedings of AAAI 2000, pp. 310–315 (2000)Google Scholar
  18. [Y1997]
    Yokoo, M.: Why adding more constraints makes a problem easier for hill-climbing algorithms: Analyzing landscapes of CSPs. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 356–370. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  19. [Z1997]
    Zhang, H.: SATO: An efficient propositional prover. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS (LNAI), vol. 1104, pp. 308–312. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Haiou Shen
    • 1
  • Hantao Zhang
    • 1
  1. 1.Department of Computer ScienceUniversity of IowaIowa CityU.S.A.

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