Skip to main content
SpringerLink
Log in
Book cover

International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems

IEA/AIE 2003: Developments in Applied Artificial Intelligence pp 592–603Cite as

Efficient Initial Solution to Extremal Optimization Algorithm for Weighted MAXSAT Problem

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2718))

Abstract

Stochastic local search algorithms are proved to be one of the most effective approach for computing approximate solutions of hard combinatorial problems. Most of them are based on a typical randomness related to uniform distributions for generating initial solutions. Particularly, Extremal Optimization is a recent meta-heuristic proposed for finding high quality solutions to hard optimization problems. In this paper, we introduce an algorithm based on another distribution, known as the Bose-Einstein distribution in quantum physics, which provides a new stochastic initialization scheme to an Extremal Optimization procedure. The resulting algorithm is proposed for the approximated solution to an instance of the weighted maximum satisfiability problem (MAXSAT). We examine its effectiveness by computational experiments on a large set of test instances and compare it with other existing meta-heuristic methods. Our results are remarkable and show that this approach is appropriate for this class of problems.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bak, P., Tang, C., Wiesenfeld, K.: Self-organized Criticality: An Explanation of 1/f-noise. Physical Review Letters, V86 N23. (1987) 5211–5214

    MathSciNet  Google Scholar 

  2. Bak, P., Sneppen, K.: Punctuated Equilibrium and Criticality in a Simple Model of Evolution. Physical Review letters, 59. (1993) 381–384

    Article  Google Scholar 

  3. Battiti, R., Protasi, M.: Reactive Search, a History-Sensitive Heuristic for MAXSAT. ACM Journal of Experimental Algorithmics, Vol. 2, Paper 2 (1997)

    Google Scholar 

  4. Boettcher, S., Percus, A.G.: Nature’s Way of Optimizing. Elsevier Science, Artificial Intelligence, 119. (2000) 275–286

    MATH  Google Scholar 

  5. Boettcher, S., Percus, A.G.: Optimization with Extremal Dynamics. Physical Review Letters, V86 N23. (2001a) 5211–5214

    Article  Google Scholar 

  6. Boettcher, S., Percus, A.G.: Extremal Optimization for Graph Partitioning. Physical Review E, V64 026114. (2001b) 1–13

    Article  Google Scholar 

  7. Cook, S. A.: The Complexity of Theorem Proving Procedures. Proceedings of the 3rd Annual ACM Symposium of the Theory of Computation. (1971) 263–268

    Google Scholar 

  8. Dorigo, M., Maniezzo, V., Colorni, A.: The Ant System: Optimization by a Colony of Cooperating Agents. IEEE Transactions on Systems, Man, and Cybernetics-Part B, Vol. 26, N1. (1996) 1–13

    Article  Google Scholar 

  9. Gent, I.P., Walsh, T.: Towards an Understanding of Hill-Climbing Procedures for SAT. Proceedings of the 11th National Conference on Artificial Intelligence. (1993) 28–33

    Google Scholar 

  10. Glover, F.: Tabu Search: Part I. ORSA Journal on Computing 1(3). (1989a) 190–206

    MATH  Google Scholar 

  11. Glover, F.: Tabu Search: Part II. ORSA Journal on Computing 2(1). (1989a) +32

    MathSciNet  Google Scholar 

  12. Hansen, P., Jaumard, B.: Algorithms for the Maximum Satisfiability Problems. Computing, 44. (1990) 279–303

    Article  MATH  MathSciNet  Google Scholar 

  13. Johnson, D.: Approximation Algorithms for Combinatorial Problems. Journal of Computer and System Sciences, 9. (1974) 256–278

    Article  MATH  MathSciNet  Google Scholar 

  14. Kirkpatrick, S., Gelatt, C.D., Vecchi, P.M.: Optimization by Simulated Annealing. Science, 220. (1983) 671–680

    Article  MathSciNet  Google Scholar 

  15. Mazure, B., Sais, L., Gregoire, E.: Tabu Search for SAT. Proceedings of the 14th National Conference on Artificial Intelligence and 9th Innovative Applications of Artificial Intelligence Conference. (1997) 281–285

    Google Scholar 

  16. McAllester, D., Selman, B., Kautz, H.A.: Evidence for Invariants in Local Search. Proceedings of AAAI’92. MIT Press (1997) 321–326

    Google Scholar 

  17. Menai, M.B., Batouche, M.: Extremal Optimization for MAXSAT. Proceedings of the International Conference on Artificial Intelligence (IC-AI’02), Las Vegas, USA. 954–958

    Google Scholar 

  18. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21. (1953) 1087–1092

    Article  Google Scholar 

  19. Resende, M.G.C., Pitsoulis, L.S., Pardalos, P.M.: Approximate Solution of Weighted MAX-SAT Problems using GRASP. In Satisfiability Problem: Theory and Applications, Vol. 35 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science (American Mathematical Society, 1997). (1997) 393–405

    MathSciNet  Google Scholar 

  20. Ross, M. S.: Introduction to Probability Models. Academic Press, New York. (2000) 137–141

    MATH  Google Scholar 

  21. Selman, B., Kautz, H.A.: An Empirical Study of Greedy Local Search for Satisfiability Testing. Proceedings of the 11th National Conference on Artificial Intelligence. (1993a) 46–51

    Google Scholar 

  22. Selman, B., Kautz, H.A.: Domain Independent Extensions to GSAT: Solving Large Structured Satisfiability Problems. Proceedings of the 13th International Joint Conference on Artificial Intelligence. (1993b) 290–295

    Google Scholar 

  23. Selman, B., Kautz, H.A., Cohen B.: Noise Strategies for Improving Local Search. Proceedings of the 12th National Conference on Artificial Intelligence. (1994) 337–343

    Google Scholar 

  24. Spears, W. M.: Simulated Annealing for Hard Satisfiability Problems. In D.S. Johnson and M.A. Trick (eds.), Cliques, Coloring and Satisfiability: Second DIMACS Implementation Challenge, Vol. 26 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science (American Mathematical Society, 1996). (1996) 553–558

    Google Scholar 

  25. Szedmak, S.: How to Find More Efficient Initial Solution for Searching ? RUTCOR Research Report, 49-2001, Rutgers Center for Operations Research, Rutgers University. (2001)

    Google Scholar 

  26. Yagiura, M., Ibaraki, T.: Efficient 2 and 3-Flip Neighborhood Search Algorithms for the MAX SAT: Experimental Evaluation. Journal of Heuristics, 7. (2001) 423–442

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, Tebessa University, 12000, Tebessa, Algeria

    Mohamed El-bachir Menai

  2. LIRE Laboratory, Computer Science Department, Mentouri University, Constantine, Algeria

    Mohamed Batouche

Authors
  1. Mohamed El-bachir Menai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Batouche
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science, Loughborough University, Loughborough, LE11 3TU, England

    Paul W. H. Chung  & Chris Hinde  & 

  2. Dept. of Computer Science, Southwest Texas State University, 601 University Drive, San Marcos, TX, 78666, USA

    Moonis Ali

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Menai, M.Eb., Batouche, M. (2003). Efficient Initial Solution to Extremal Optimization Algorithm for Weighted MAXSAT Problem. In: Chung, P.W.H., Hinde, C., Ali, M. (eds) Developments in Applied Artificial Intelligence. IEA/AIE 2003. Lecture Notes in Computer Science(), vol 2718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45034-3_60

Download citation

  • DOI: https://doi.org/10.1007/3-540-45034-3_60

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40455-2

  • Online ISBN: 978-3-540-45034-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation