Skip to main content

Random Walk with Continuously Smoothed Variable Weights

  • Conference paper
Book cover Theory and Applications of Satisfiability Testing (SAT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3569))

Abstract

Many current local search algorithms for SAT fall into one of two classes. Random walk algorithms such as Walksat/SKC, Novelty+ and HWSAT are very successful but can be trapped for long periods in deep local minima. Clause weighting algorithms such as DLM, GLS, ESG and SAPS are good at escaping local minima but require expensive smoothing phases in which all weights are updated. We show that Walksat performance can be greatly enhanced by weighting variables instead of clauses, giving the best known results on some benchmarks. The new algorithm uses an efficient weight smoothing technique with no smoothing phase.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asahiro, Y., Iwama, K., Miyano, E.: Random Generation of Test Instances with Controlled Attributes. In: Johnson, D.S., Trick, M.A. (eds.) Cliques, Coloring and Satisfiability: Second Implementation Challenge. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 26, pp. 127–154. American Mathematical Society, Providence (1996)

    Google Scholar 

  2. Cha, B., Iwama, K.: Performance Test of Local Search Algorithms Using New Types of Random CNF Formulas. In: Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, pp. 304–310. Morgan Kaufmann, San Francisco (1995)

    Google Scholar 

  3. Culberson, J., Gent, I.P., Hoos, H.H.: On the Probabilistic Approximate Completeness of WalkSAT for 2-SAT. Technical Report APES-15a-2000, APES Research Group (2000)

    Google Scholar 

  4. Frank, J.: Weighting for GODOT: Learning Heuristics for GSAT. In: Proceedings of the Thirteenth National Conference on Artificial Intelligence, pp. 338–343. MIT Press, Cambridge (1996)

    Google Scholar 

  5. Frank, J.: Learning Short-Term Weights for GSAT. In: Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence, pp. 384–389. Morgan Kaufmann, San Francisco (1997)

    Google Scholar 

  6. Fukunaga, A.S.: Variable-Selection Heuristics in Local Search for SAT. In: Proceedings of the Fourteenth National Conference on Artificial Intelligence and Ninth Innovative Applications of Artificial Intelligence Conference, pp. 275–280 (1997)

    Google Scholar 

  7. Gent, I.P., Walsh, T.: Towards an Understanding of Hill-Climbing Procedures for SAT. In: Proceedings of the Eleventh National Conference on Artificial Intelligence, pp. 28–33. AAAI Press, Menlo Park (1993)

    Google Scholar 

  8. Gent, I.P., Walsh, T.: Unsatisfied Variables in Local Search. In: Hallam, J. (ed.) Hybrid Problems, Hybrid Solutions, pp. 73–85. IOS Press, Amsterdam (1995)

    Google Scholar 

  9. Ginsberg, M.L., Parkes, A.J.: Satisfiability Algorithms and Finite Quantification. In: Seventh International Conference on Principles of Knowledge Representation and Reasoning, pp. 690–701. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  10. Gu, J.: Efficient Local Search for Very Large-Scale Satisfiability Problems. Sigart Bulletin 3(1), 8–12 (1992)

    Article  Google Scholar 

  11. Hirsch, E.A., Kojevnikov, A.: Solving Boolean Satisfiability Using Local Search Guided by Unit Clause Elimination. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 605–609. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Hoos, H.H.: On the Run-Time Behaviour of Stochastic Local Search Algorithms. In: Sixteenth National Conference on Artificial Intelligence, pp. 661–666. AAAI Press, Menlo Park (1999)

    Google Scholar 

  13. Huang, W., Zhang, D., Wang, H.: An Algorithm Based on Tabu Search for Satisfiability Problem. Journal of Computer Science and Technology 17(3), Editorial Universitaria de Buenos Aires, 340–346 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Hutter, F., Tompkins, D.A.D., Hoos, H.H.: Scaling and Probabilistic Smoothing: Efficient Dynamic Local Search for SAT. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 233–248. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  15. Mazure, B., Saïs, L., Grégoire, É.: Tabu Search for SAT. In: Proceedings of the Fourteenth National Conference on Artificial Intelligence, pp. 281–285 (1997)

    Google Scholar 

  16. Mazure, B., Saïs, L., Grégoire, É.: Boosting Complete Techniques Thanks to Local Search. Annals of Mathematics and Artificial Intelligence 22, 309–322 (1998)

    Article  Google Scholar 

  17. McAllester, D.A., Selman, B., Kautz, H.A.: Evidence for Invariants in Local Search. In: Fourteenth National Conference on Artificial Intelligence and Ninth Innovative Applications of Artificial Intelligence Conference, pp. 321–326. AAAI Press / MIT Press (1997)

    Google Scholar 

  18. Mills, P., Tsang, E.P.K.: Guided Local Search for Solving SAT and Weighted MAX-SAT Problems. Journal of Automated Reasoning, Special Issue on Satisfiability Problems 24, 205–223 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  19. Morris, P.: The Breakout Method for Escaping from Local Minima. In: Proceedings of the Eleventh National Conference on Artificial Intelligence, pp. 40–45. AAAI Press / MIT Press (1993)

    Google Scholar 

  20. Prestwich, S.D.: Incomplete Dynamic Backtracking for Linear Pseudo-Boolean Problems. Annals of Operations Research 130, 57–73 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  21. Prestwich, S.D.: SAT Problems With Chains of Dependent Variables. Discrete Applied Mathematics 3037, 1–22 (2002)

    Google Scholar 

  22. Schuurmans, D., Southey, F., Holte, R.C.: The Exponentiated Subgradient Algorithm for Heuristic Boolean Programming. In: Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence, pp. 334–341. Morgan Kaufmann, San Francisco (2001)

    Google Scholar 

  23. Schuurmans, D., Southey, F.: Local Search Characteristics of Incomplete SAT Procedures. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 297–302. AAAI Press, Menlo Park (2000)

    Google Scholar 

  24. Selman, B., Kautz, H.A.: Domain-Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems. In: Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pp. 290–295 (1993)

    Google Scholar 

  25. Selman, B., Kautz, H.A., Cohen, B.: Noise Strategies for Improving Local Search. In: Proceedings of the Twelfth National Conference on Artificial Intelligence, pp. 337–343. AAAI Press, Menlo Park (1994)

    Google Scholar 

  26. Selman, B., Levesque, H., Mitchell, D.: A New Method for Solving Hard Satisfiability Problems. In: Proceedings of the Tenth National Conference on Artificial Intelligence, pp. 440–446. MIT Press, Cambridge (1992)

    Google Scholar 

  27. Smyth, K., Hoos, H.H., Stützle, T.: Iterated Robust Tabu Search for MAX-SAT. In: Xiang, Y., Chaib-draa, B. (eds.) Canadian AI 2003. LNCS (LNAI), vol. 2671, pp. 129–144. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  28. Thornton, J.R., Pullan, W., Terry, J.: Towards Fewer Parameters for Clause Weighting SAT Algorithms. In: McKay, B., Slaney, J.K. (eds.) Canadian AI 2002. LNCS (LNAI), vol. 2557, pp. 569–578. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  29. Thornton, J.R., Pham, D.N., Bain, S., Ferreira Jr., V.: Additive versus Multiplicative Clause Weighting for SAT. In: Proceedings of the Nineteenth National Conference on Artificial Intelligence, San Jose, California, pp. 191–196 (2004)

    Google Scholar 

  30. Tompkins, D.A.D., Hoos, H.H.: UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT and MAX-SAT. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 37–46. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  31. Tompkins, D.A.D., Hoos, H.H.: Scaling and Probabilistic Smoothing: Dynamic Local Search for Unweighted MAX-SAT. In: Xiang, Y., Chaib-draa, B. (eds.) Canadian AI 2003. LNCS (LNAI), vol. 2671, pp. 145–159. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  32. Tompkins, D.A.D., Hoos, H.H.: Warped Landscapes and Random Acts of SAT Solving. In: Proceedings of the Eighth International Symposium on Artificial Intelligence and Mathematics (2004) (to appear)

    Google Scholar 

  33. Wei, W., Selman, B.: Accelerating Random Walks. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 216–232. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  34. Wu, Z., Wah, B.W.: An Efficient Global-Search Strategy in Discrete Lagrangian Methods for Solving Hard Satisfiability Problems. In: Proceedings of the Seventeenth National Conference on Artificial Intelligence, pp. 310–315. AAAI Press, Menlo Park (2000)

    Google Scholar 

  35. Zhang, W., Rangan, A., Looks, M.: Backbone Guided Local Search for Maximum Satisfiability. In: Eighteenth International Joint Conference on Artificial Intelligence, pp. 1179–1186 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Prestwich, S. (2005). Random Walk with Continuously Smoothed Variable Weights. In: Bacchus, F., Walsh, T. (eds) Theory and Applications of Satisfiability Testing. SAT 2005. Lecture Notes in Computer Science, vol 3569. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499107_15

Download citation

  • DOI: https://doi.org/10.1007/11499107_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26276-3

  • Online ISBN: 978-3-540-31679-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics