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Takeover Times of Noisy Non-Generational Selection Rules that Undo Extinction

  • Günter Rudolph

Abstract

The takeover time of some selection method is the expected number of iterations of this selection method until the entire population consists of copies of the best individual under the assumption that the initial population consists of a single copy of the best individual. We consider a class of non-generational selection rules that run the risk of loosing all copies of the best individual with positive probability. Since the notion of a takeover time is meaningless in this case these selection rules are modified in that they undo the last selection operation if the best individual gets extinct from the population. We derive exact results or upper bounds for the takeover time for three commonly used selection rules via a random walk or Markov chain model. The takeover time for each of these three selection rules is O(n log n) with population size n.

Keywords

Selection Method Selection Rule Good Individual Markov Chain Model Selection Operation 
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References

  1. [1]
    D. E. Goldberg and K. Deb, “A comparative analysis of selection schemes used in genetic algorithms” in Foundations of Genetic Algorithms (G. J. E. Rawlins, ed.), pp. 69-93, San Mateo (CA): Morgan Kaufmann, 1991.Google Scholar
  2. [2]
    J. Smith and F. Vavak, “Replacement strategies in steady state genetic algorithms: Static environments” in Foundations of Genetic Algorithms 5 (W. Banzhaf and C. Reeves eds.), pp. 219–233, San Francisco (CA): Morgan Kaufmann, 1999.Google Scholar
  3. [3]
    G. Rudolph, “Takeover times and probabilities of non-generational selection rules” in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2000) (D. Whitley et al., eds.), pp. 903–910, San Fransisco (CA): Morgan Kaufmann, 2000.Google Scholar
  4. [4]
    M. Iosifescu, Finite Markov Processes and Their Applications. Chichester: Wiley, 1980.MATHGoogle Scholar
  5. [5]
    G. Rudolph, “The fundamental matrix of the general random walk with absorbing boundaries” Technical Report CI-75 of the Collaborative Research Center “Computational Intelligence”, University of Dortmund, October 1999.Google Scholar

Copyright information

© Springer-Verlag Wien 2001

Authors and Affiliations

  • Günter Rudolph
    • 1
  1. 1.Department of Computer ScienceUniversity of DortmundGermany

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