An Analysis of Recombination in Some Simple Landscapes

  • David A. Rosenblueth
  • Christopher R. Stephens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5845)

Abstract

Recombination is an important operator in the evolution of biological organisms and has also played an important role in Evolutionary Computation. In neither field however, is there a clear understanding of why recombination exists and under what circumstances it is useful. In this paper we consider the utility of recombination in the context of a simple Genetic Algorithm (GA). We show how its utility depends on the particular landscape considered. We also show how the facility with which this question may be addressed depends intimately on the particular representation used for the population in the GA, i.e., a representation in terms of genotypes, Building Blocks or Walsh modes. We show how, for non-epistatic landscapes, a description in terms of Building Blocks manifestly shows that recombination is always beneficial, leading to a “royal road” towards the optimum, while the contrary is true for highly epistatic landscapes such as “needle-in-a-haystack”.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aguilar, A., Rowe, J., Stephens, C.R.: Coarse graining in genetic algorithms: Some issues and examples. In: Cantú-Paz, E. (ed.) GECCO 2003. Springer, Heidelberg (2003)Google Scholar
  2. 2.
    Aguirre, H., Tanaka, K.: Genetic algorithms on NK-landscapes: Effects of selection, drift, mutation and recombination. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoIASP 2003, EvoWorkshops 2003, EvoSTIM 2003, EvoROB/EvoRobot 2003, EvoCOP 2003, EvoBIO 2003, and EvoMUSART 2003. LNCS, vol. 2611, pp. 131–142. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Goldberg, D.E.: Genetic algorithms and Walsh functions: Part I. A gentle introduction. Complex Systems 3, 123–152 (1989)Google Scholar
  4. 4.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, Reading (1989)MATHGoogle Scholar
  5. 5.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. MIT Press, Cambridge (1993)Google Scholar
  6. 6.
    Langdon, W.B., Poli, R.: Foundations of Genetic Programming. Springer, Berlin (2002)MATHGoogle Scholar
  7. 7.
    Stephens, C.R.: The renormalization group and the dynamics of genetic systems. Acta Phys. Slov. 52, 515–524 (2002)Google Scholar
  8. 8.
    Stephens, C.R., Waelbroeck, H.: Schemata evolution and building blocks. Evol. Comp. 7, 109–124 (1999)CrossRefGoogle Scholar
  9. 9.
    Vose, M.D., Wright, A.H.: The simple genetic algorithm and the Walsh transform: Part II, the inverse. Evolutionary Computation 6(3), 275–289 (1998)CrossRefGoogle Scholar
  10. 10.
    Weinberger, E.D.: Fourier and Taylor series on fitness landscapes. Biological Cybernetics 65th, 321–330 (1991)CrossRefGoogle Scholar
  11. 11.
    Wright, A.H.: The exact schema theorem (January 2000), http://www.cs.umt.edu/CS/FAC/WRIGHT/papers/schema.pdf

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • David A. Rosenblueth
    • 1
  • Christopher R. Stephens
    • 2
  1. 1.C3 - Centro de Ciencias de la ComplejidadInstituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, UNAMMéxico
  2. 2.C3 - Centro de Ciencias de la ComplejidadInstituto de Ciencias Nucleares, UNAM Circuito ExteriorMéxico

Personalised recommendations