Fluctuating Crosstalk as a Source of Deterministic Noise and Its Effects on GA Scalability

  • Kumara Sastry
  • Paul Winward
  • David E. Goldberg
  • Cláudio Lima
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3907)

Abstract

This paper explores how fluctuating crosstalk in a deterministic fitness function introduces noise into genetic algorithms. We model fluctuating crosstalk or nonlinear interactions among building blocks via higher-order Walsh coefficients. The fluctuating crosstalk behaves like exogenous noise and can be handled by increasing the population size and run duration. This behavior holds until the strength of the crosstalk far exceeds the underlying fitness variance by a certain factor empirically observed. Our results also have implications for the relative performance of building-block-wise mutation over crossover.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Sastry, K., Goldberg, D.E.: Let’s get Ready to Rumble: Crossover Versus Mutation Head to Head. In: Proceedings of the 2004 Genetic and Evolutionary Computation Conference, vol. 2, pp. 126–137 (2004); Also IlliGAL Report No. 2004005Google Scholar
  2. 2.
    Goldberg, D.E.: Design of Innovation: Lessons from and for Competent Genetic Algorithms. Kluwer Acadamic Publishers, Boston (2002)MATHGoogle Scholar
  3. 3.
    Kumar, V.: Tackling Epistasis: A Survey of Measures and Techniques. In: Goldberg, D.E. (ed.) Assignment from an advanced GEC course taught at UIUC (2002)Google Scholar
  4. 4.
    Davidor, Y.: Epistasis Variance: A Viewpoint on GA-hardness. Foga 91, 23–35 (1991)Google Scholar
  5. 5.
    Naudts, B., Kallel, L.: Some Facts about so-called GA-hardness Measures. Tech. Rep. No. 379, Ecole Polytechnique, CMAP, France (1998)Google Scholar
  6. 6.
    Heckendorn, R.B., Whitley, D.: Predicting Epistasis from Mathematical Models. Evolutionary Computation 7(1), 69–101 (1999)CrossRefGoogle Scholar
  7. 7.
    Mühlenbein, H., Mahnig, T., Rodriguez, A.O.: Schemata, Distributions and Graphical Models in Evolutionary Optimization. Journal of Heuristics 5, 215–247 (1999)MATHCrossRefGoogle Scholar
  8. 8.
    Pelikan, M., Goldberg, D.E., Lobo, F.G.: A Survey of Optimization by Building and Using Probabilistic Models. Comput. Optim. Appl. 21(1), 5–20 (2002)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1998)MATHGoogle Scholar
  10. 10.
    Beasley, D., Bull, D.R., Martin, R.R.: Reducing Epistasis in Combinatorial Problems by Expansive Coding. In: ICGA, pp. 400–407 (1993)Google Scholar
  11. 11.
    Barbulescu, L., Watson, J.P., Whitley, L.D.: Dynamic Representations and Escaping Local Optima: Improving Genetic Algorithms and Local Search. In: AAAI/IAAI, pp. 879–884 (2000)Google Scholar
  12. 12.
    Goldberg, D.E.: Genetic Algorithms and Walsh Functions: Part I, a Gentle Introduction. Complex Systems 3(2), 129–152 (1989) (Also TCGA Report 88006)MATHMathSciNetGoogle Scholar
  13. 13.
    Bethke, A.D.: Genetic Algorithms as Function Optimizers. PhD thesis, The University of Michigan (1981)Google Scholar
  14. 14.
    Sastry, K.: Evaluation-Relaxation Schemes for Genetic and Evolutionary Algorithms. Master’s thesis, University of Illinois at Urbana-Champaign, General Engineering Department, Urbana, IL (2001) (Also IlliGAL Report No. 2002004)Google Scholar
  15. 15.
    Goldberg, D.E., Deb, K., Clark, J.H.: Genetic Algorithms, Noise, and the Sizing of Populations. Complex Systems 6, 333–362 (1992) (Also IlliGAL Report No. 91010)MATHGoogle Scholar
  16. 16.
    Pelikan, M., Goldberg, D.E., Cantú-Paz, E.: Linkage Learning, Estimation Distribution, and Bayesian Networks. Evolutionary Computation 8(3), 314–341 (2000) (Also IlliGAL Report No. 98013)CrossRefGoogle Scholar
  17. 17.
    Harik, G., Cantú-Paz, E., Goldberg, D.E., Miller, B.L.: The Gambler’s Ruin Problem, Genetic Algorithms, and the Sizing of Populations. Evolutionary Computation 7(3), 231–253 (1999) (Also IlliGAL Report No. 96004)CrossRefGoogle Scholar
  18. 18.
    Bulmer, M.G.: The Mathematical Theory of Quantitative Genetics. Oxford University Press, Oxford (1985)Google Scholar
  19. 19.
    Falconer, D.S.: Introduction to Quantitative Genetics, 3rd edn. John Wiley and Sons, New York (1989)Google Scholar
  20. 20.
    Mühlenbein, H., Schlierkamp-Voosen, D.: Predictive Models for the Breeder Genetic Algorithm: I. Continous Parameter Optimization. Evolutionary Computation 1(1), 25–49 (1993)CrossRefGoogle Scholar
  21. 21.
    Mühlenbein, H., Schlierkamp-Voosen, D.: The Science of Breeding and its Application to the Breeder Genetic Algorithm (BGA). Evolutionary Computation 1(4), 335–360 (1994)CrossRefGoogle Scholar
  22. 22.
    Thierens, D., Goldberg, D.E.: Convergence Models of Genetic Algorithm Selection Schemes. Parallel Problem Solving from Nature 3, 116–121 (1994)Google Scholar
  23. 23.
    Thierens, D., Goldberg, D.E.: Elitist Recombination: An Integrated Selection Recombination GA. In: Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 508–512 (1994)Google Scholar
  24. 24.
    Bäck, T.: Generalized Convergence Models for Tournament—and (μ, λ)— Selection. In: Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 2–8 (1995)Google Scholar
  25. 25.
    Miller, B.L., Goldberg, D.E.: Genetic Algorithms, Selection Schemes, and the Varying Effects of Noise. Evolutionary Computation 4(2), 113–131 (1996) (Also IlliGAL Report No. 95009)CrossRefGoogle Scholar
  26. 26.
    Voigt, H.M., Mühlenbein, H., Schlierkamp-Voosen, D.: The Response to Selection Equation for Skew Fitness Distributions. In: Proceedings of the International Conference on Evolutionary Computation, pp. 820–825 (1996)Google Scholar
  27. 27.
    Blickle, T., Thiele, L.: A Mathematical Analysis of Tournament Selection. In: Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 9–16 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kumara Sastry
    • 1
  • Paul Winward
    • 1
  • David E. Goldberg
    • 1
  • Cláudio Lima
    • 2
  1. 1.Illinois Genetic Algorithms Laboratory, Department of General EngineeringUniversity of Illinois at Urbana-Champaign 
  2. 2.DEEI-FCTUniversity of Algarve 

Personalised recommendations