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A bit-wise epistasis measure for binary search spaces

  • Cyril Fonlupt
  • Denis Robilliard
  • Philippe Preux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1498)

Abstract

The epistatic variance has been introduced by Davidor as a tool for the evaluation of interdependences between genes, thus possibly giving clues about the difficulty of optimizing functions with genetic algorithms (GAs). Despite its theoretical grounding in Walsh function analysis, several studies have shown its weakness as a predictor of GAs results. In this paper, we focus on binary search spaces and propose to measure epistatic effect on the level of individual genes, an approach that we call bit-wise epistasis. We give examples of this measure on several well-known test problems, then we take into account this supplementary information to improve the performances of evolutionary algorithms. We conclude by pointing towards possible extensions of this concept to real size problems.

Keywords

Genetic Algorithm Epistatic Effect Fitness Landscape Gray Code Fitness Variance 
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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References

  1. 1.
    Yuva Davidor. Epistasis variance: A viewpoint on GA-hardness. In [20], pages 23–35, 1991.Google Scholar
  2. 2.
    Mauro Manela and J.A. Campbell. Harmonic analysis, epistasis and genetic algorithms. In [21], 1992.Google Scholar
  3. 3.
    C.R. Reeves and C.C. Wright. Epistasis in genetic algorithms: An experimental design perspective. In [22], pages 217–224, 1995.Google Scholar
  4. 4.
    S. Rochet, M. Slimane, and G. Venturini. Epistasis for real encoding in genetic algorithms. In IEEE ANZIIS'96, pages 268–271, 1996.Google Scholar
  5. 5.
    David E. Goldberg. Genetic algorithms and Walsh functions: Part I, a gentle introduction. Complex Systems, 3:129–152, 1989.zbMATHMathSciNetGoogle Scholar
  6. 6.
    David E. Goldberg. Genetic algorithms and Walsh functions: Part II, deception and its analysis. Complex Systems, 3:153–171, 1989.zbMATHMathSciNetGoogle Scholar
  7. 7.
    S. Rochet, G. Venturini, M. Slimane, and E. M. El Kharoubi. A critical and empirical study of epistasis measures for predicting GA performances: a summary. In Evolution Artificielle 97, pages 331–341, Nimes, Frances, October 1997.Google Scholar
  8. 8.
    David E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, 1989.Google Scholar
  9. 9.
    John H. Holland. Adaptation in Natural and Artificial Systems. Michigan Press University, 1975.Google Scholar
  10. 10.
    S.A. Kauffman. Adaptation on rugged fitness landscapes. Lecture in the Sciences of Complexity, pages 527–618, 1989.Google Scholar
  11. 11.
    Kenneth A. De Jong, Mitchell A. Potter, and William M. Spears. Using problem generators to explore the effects of epistasis. In [23], pages 338–345, 1997.Google Scholar
  12. 12.
    D. Whitley, K. Mathias, S. Rana, and J. Dzubera. Building better test functions. In in [22], pages 239–246, 1995.Google Scholar
  13. 13.
    K. A. De Jong. An analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan, MI, USA, 1975.Google Scholar
  14. 14.
    David Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, 1989.Google Scholar
  15. 15.
    G.E. Liepins and M.D. Vose. Representational issues in genetic optimization. Journal of Experimental and Theoretical AI, 2:1–15, 1990.Google Scholar
  16. 16.
    Keith Mathias and Darrell Whitley. Remapping hyperspace during genetic search: Canonical delta folding. In [24], pages 167–186, 1993.Google Scholar
  17. 17.
    Keith E. Mathias and Darrell Whitley. Changing representations during search: A comparative study of delta coding. Evolutionary Computation, 2, 1994.Google Scholar
  18. 18.
    J. David Schaffer and Larry J. Eshelman. On crossover as an evolutionarily viable strategy. In [25], pages 61–67, 1991.Google Scholar
  19. 19.
    Michèle Sebag and Marc Schoenauer. A society of hill-climbers. In [26], 1997.Google Scholar
  20. 20.
    Gregory J.E. Rawlins, editor. Workshop on the Foundations of Genetic Algorithms and Classifiers, Bloomington, IN, USA, July 1991. Morgan Kaufmann.Google Scholar
  21. 21.
    Reinhard Manner and Bernard Manderick, editors. Proceedings of the second Conference on Parallel Problem Solving from Nature, Free University of Brussels, Belgium, September 1992. Elsevier Science.Google Scholar
  22. 22.
    Philips Laboratories Larry J. Eshelman, editor. Proceedings of the 6th International Conference on Genetic Algorithms, University of Pittsburgh, USA, July 1995. Morgan Kaufmann.Google Scholar
  23. 23.
    Proceedings of the 7th International Conference on Genetic Algorithms, East Lansing, Michigan, USA, July 1997. Morgan Kaufmann.Google Scholar
  24. 24.
    Darrell Whitley, editor. Proc. of the Workshop on Foundations of Genetic Algorithms, Vail, CO, USA, 1993. Morgan Kaufmann.Google Scholar
  25. 25.
    Richard K. Belew and Lashon B. Booker, editors. Proceedings of the 4th International. Conference on Genetic Algorithms, La Jolla, California, USA, July 1991. Morgan Kaufmann.Google Scholar
  26. 26.
    International Conference on Evolutionary Computation, Anchorage, USA, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Cyril Fonlupt
    • 1
  • Denis Robilliard
    • 1
  • Philippe Preux
    • 1
  1. 1.Laboratoire d'Informatique du LittoralCalais CedexFrance

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