Advertisement

Representations, fitness functions and genetic operators for the satisfiability problem

  • Jens Gottlieb
  • Nico Voss
Genetic Operators
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1363)

Abstract

Two genetic algorithms for the satisfiability problem (SAT) are presented which mainly differ in the solution representation. We investigate these representations - the classical bit string representation and the path representation - with respect to their performance. We develop fitness functions which transform the traditional fitness landscape of SAT into more distinguishable ones. Furthermore, new genetic operators (mutation and crossover) are introduced. These genetic operators incorporate problem specific knowledge and thus, lead to increased performance in comparison to standard operators.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [DP60]
    M. Davis and H. Putnam. A Computing Procedure for Quantification Theory. Journal of the ACM, Volume 7, 201–215, 1960Google Scholar
  2. [DJS89]
    K. A. De Jong and W. M. Spears. Using Genetic Algorithms to Solve NPComplete Problems. In J. D. Schaffer (ed.), Proceedings of the Third International Conference on Genetic Algorithms, 124–132, Morgan Kaufmann Publishers, San Mateo, CA, 1989Google Scholar
  3. [EH96]
    A. E. Eiben and J. K. van der Hauw. Graph Coloring with Adaptive Genetic Algorithms. Technical Report 96-11, Department of Computer Science, Leiden University, 1996Google Scholar
  4. [EH97]
    A. E. Eiben and J. K. van der Hauw. Solving 3-SAT with Adaptive Genetic Algorithms. In Proceedings of the 4th IEEE Conference on Evolutionary Computation, 81–86, IEEE Service Center, Piscataway, NJ, 1997Google Scholar
  5. [FF96]
    C. Fleurent and J. A. Ferland. Object-oriented Implementation of Heuristic Search Methods for Graph Coloring, Maximum Clique and Satisfiability. In D. S. Johnson and M. A. Trick (eds.), Cliques, Coloring and Satisfiability: 2nd DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Volume 26, 619–652, 1996Google Scholar
  6. [Fra94]
    J. Frank. A Study of Genetic Algorithms to Find Approximate Solutions to Hard 3CNF Problems. Golden West International Conference on Artificial Intelligence, 1994Google Scholar
  7. [Fra96]
    J. Frank. Weighting for Godot: Learning Heuristics for GSAT. In Proceedings of the 13th National Conference on Artificial Intelligence and the 8th Innovative Applications of Artificial Intelligence Conference, 338–343, 1996Google Scholar
  8. [Fra97]
    J. Frank. Learning Short-Term Weights for GSAT. Submitted to 15th International Joint Conference on Artificial Intelligence, 1997Google Scholar
  9. [GJ79]
    M. R. Carey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco, CA, 1979Google Scholar
  10. [Gu94]
    J. Cu. Global Optimization for Satisfiability (SAT) Problem. IEEE Transactions on Knowledge and Data Engineering, Volume 6, Number 3, 361–381, 1994Google Scholar
  11. [Hao95]
    J.-K. Hao. A Clausal Genetic Representation and its Evolutionary Procedures for Satisfiability Problems. In D. W. Pearson, N. C. Steele, and R. F. Albrecht (eds.), Proceedings of the International Conference on Artificial Neural Nets and Genetic Algorithms, 289–292, Springer, Wien, 1995Google Scholar
  12. [Mic96]
    Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs. Third Edition, Springer, 1996Google Scholar
  13. [MSL92]
    D. Mitchell, B. Selman, and H. Levesque. Hard and Easy Distributions of SAT Problems. In Proceedings of the 10th National Conference on Artificial Intelligence, 459–465, 1992Google Scholar
  14. [Par95]
    K. Park. A Comparative Study of Genetic Search. In L. J. Eshelman (ed.), Proceedings of the Sixth International Conference on Genetic Algorithms, 512–519, Morgan Kaufmann, San Mateo, CA, 1995Google Scholar
  15. [SKC94]
    B. Selman, H. A. Kautz, and B. Cohen. Noise Strategies for Improving Local Search. In Proceedings of the 12th National Conference on Artificial Intelligence, 337–343, 1994Google Scholar
  16. [SLM92]
    B. Selman, H. Levesque, and D. Mitchell. A New Method for Solving Hard Satisfiability Problems. In Proceedings of the 10th National Conference on Artificial Intelligence, 440–446, 1992Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jens Gottlieb
    • 1
  • Nico Voss
    • 1
  1. 1.Institut für InformatikTechnische Universität ClausthalClausthal-ZellerfeldGermany

Personalised recommendations