On recombinative sampling

  • Ian R. East
Problem Structure and Fitness Landscapes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1305)


If a population is constrained to exhibit no variation in the allelic frequency distribution of any gene then information may only be recorded by recombining genes into new configurations (schemata). It is shown that such a constraint need lead to no loss of information capacity. A simple algorithm, employing direct replacement and a single uniform genetic operator, is then analysed with regard to schema sampling. The probabilities of schema creation and destruction are proven identical, regardless of operator. The probabilities are then deduced, with which new schemata are sampled by, first, recombination, and, second, mutation, in relation to order and allelic variation. The analysis overcomes limitations inherent in earlier work [4, 9,


Genetic Algorithm Schema Order Genome Length Allelic Frequency Distribution Direct Replacement 
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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  1. 1.
    Booker, L. B.: 1992, “Recombination Distributions for Genetic Algorithms”, in “Proceedings of The Second Workshop on the Foundations of Genetic Algorithms”, Whitley, L. D. (Ed.), Morgan Kaufmann, pp. 29–44.Google Scholar
  2. 2.
    Bridges, C. L. and D. E. Goldberg: 1987, “An Analysis of Reproduction and Crossover in a Binary-Coded Genetic Algorithm”, in “Proceedin s of Second International Conference on Genetic Algorithms”, Grefenstette, J.. (Ed.), Lawrence Erlbaum Associates.Google Scholar
  3. 3.
    Culberson, J. C.: 1993, “Crossover versus Mutation: Fueling the Debate: TGA versus GIGA”, in “Proceedings of the Fifth International Conference on Genetic Algorithms”, Forrest, S. (Ed.), Morgan Kaufmann, p. 632.Google Scholar
  4. 4.
    Dejong, K. A.: 1975, “An Analysis of the Behaviour of a Class of Genetic Adaptive Systems”, Doctoral thesis, University of Michigan, Department of Computer and Communications Sciences, University of Michigan, Ann Arbor, Michigan, USA.Google Scholar
  5. 5.
    East, I. R., & J. Rowe: 1994, “Direct Replacement: A Genetic Algorithm without Mutation Avoids Deception”, in “Progress in Evolutionary Computation: AI '93 and AI '94 Workshops on Evolutionary Computation” Lecture Notes in Artificial Intelligence Vol. 956, Xin Yao (Ed.), Springer-Verlag, pp. 41–48.Google Scholar
  6. 6.
    Geiringer, H.: 1944, “On the probability theory of linkage in Mendelian heredity”, Annals of Mathematical Statistics, 15, pp. 25–57.Google Scholar
  7. 7.
    Holland, J. H.: 1975, “Adaptation in Natural and Artificial Systems”, University of Michigan Press.Google Scholar
  8. 8.
    Shannon, C. E. and W. Weaver: 1949, “The Mathematical Theory of Communication”, (1963) Edition, University of Illinois Press.Google Scholar
  9. 9.
    Spears, W. M. and K. A. D. Jong: 1990, “An Analysis of Multi-Point Crossover”, in “Proceedings of the First Workshop on the Foundations of Genetic Algorithms”, Rawlins, G. J. E. (Ed.), Morgan Kaumann, pp. 301–315.Google Scholar
  10. 10.
    Spears, W. M.: 1992, “Crossover or Mutation?”, in “Proceedings of The Second Workshop on the Foundations of Genetic Algorithms”, Whitley, L. D. (Ed.), Morgan Kaufmann, pp. 221–237.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Ian R. East
    • 1
  1. 1.Islip, OxfordshireEngland

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