Growth Curves and Takeover Time in Distributed Evolutionary Algorithms

  • Enrique Alba
  • Gabriel Luque
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3102)

Abstract

This paper presents a study of different models for the growth curves and takeover time in a distributed EA (dEA). The calculation of the takeover time and the dynamical growth curves is a common analytical approach to measure the selection pressure of an EA. This work is a first step to mathematically unify and describe the roles of the migration rate and the migration frequency in the selection pressure induced by the dynamics of dEAs. In order to achieve these goals we evaluate the appropriateness of the well-known logistic model and of a hypergraph model for dEAs. After that, we propose a corrected hypergraph model and two new models based in an extension of the logistic one. Our results show that accurate models for growth curves can be defined for dEAs, and explain analytically the migration rate and frequency effects.

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References

  1. 1.
    Alba, E., Tomassini, M.: Parallelism and Evolutionary Algorithms. IEEE Transactions on Evolutionary Computation 6, 443–462 (2002)CrossRefGoogle Scholar
  2. 2.
    Gordon, V.S., Whitley, D.: Serial and Parallel Genetic Algorithms as Function Optimizers. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 177–183. Morgan Kaufmann, San Francisco (1993)Google Scholar
  3. 3.
    Alba, E., Troya, J.M.: Influence of the Migration Policy in Parallel dGAs with Structured and Panmictic Populations. Applied Intelligence 12, 163–181 (2000)CrossRefGoogle Scholar
  4. 4.
    Sarma, J., De Jong, K.: An Analysis of the Effects of Neighborhood Size and Shape on Local Selection Algorithms. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 236–244. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  5. 5.
    Sarma, J., De Jong, K.: An Analysis of Local Selection Algorithms in a Spatially Structured Evolutionary Algorithm. In: Bäck, T. (ed.) Proceedings of the 7th International Conference on Genetic Algorithms, pp. 181–186. Morgan Kaufmann, San Francisco (1997)Google Scholar
  6. 6.
    Gorges-Schleuter, M.: An Analysis of Local Selection in Evolution Strategies. In: Banzhaf, W., Daida, J., Eiben, A.E., Garzon, M.H., Honavar, V., Jakiela, M., Smith, R.E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, Orlando, Florida, USA, vol. 1, pp. 847–854. Morgan Kaufmann, San Francisco (1999)Google Scholar
  7. 7.
    Rudolph, G.: Takeover Times in Spatially Structured Populations: Array and Ring. In: Lai, K.K., Katai, O., Gen, M., Lin, B. (eds.) 2nd Asia-Pacific Conference on Genetic Algorithms and Applications, pp. 144–151. Global-Link Publishing (2000)Google Scholar
  8. 8.
    Giacobini, M., Tettamanzi, A., Tomassini, M.: Modelling Selection Intensity for Linear Cellular Evolutionary Algorithms. In: Liardet, P., et al. (eds.) Artificial Evolution, Sixth International Conference, Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Giacobini, M., Alba, E., Tomassini, M.: Selection Intensity in Asynchronous Cellular Evolutionary Algorithms. In: Cantú-Paz, E. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference, Chicago, USA, pp. 955–966 (2003)Google Scholar
  10. 10.
    Sprave, J.: A Unified Model of Non-Panmictic Population Structures in Evolutionary Algorithms. In: Angeline, P.J., Michalewicz, Z., Schoenauer, M., Yao, X., Zalzala, A. (eds.) Proceedings of the Congress of Evolutionary Computation, Mayflower Hotel, Washington D.C., USA, vol. 2, pp. 1384–1391. IEEE Press, Los Alamitos (1999)Google Scholar
  11. 11.
    Goldberg, D.E., Deb, K.: A Comparative Analysis of Selection Schemes Used in Genetic Algorithms. In: Rawlins, G.J. (ed.) Foundations of Genetic Algorithms, pp. 69–93. Morgan Kaufmann, San Mateo (1991)Google Scholar
  12. 12.
    Chakraborty, U.K., Deb, K., Chakraborty, M.: Analysis of Selection Algorithms: A Markov Chain Approach. Evolutionary Computation 4, 133–167 (1997)CrossRefGoogle Scholar
  13. 13.
    Cantú-Paz, E.: 7. Migration, Selection Pressure, and Superlinear Speedups. In: Efficient and Accurate Parallel Genetic Algorithms, pp. 97–120. Kluwer, Dordrecht (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Enrique Alba
    • 1
  • Gabriel Luque
    • 1
  1. 1.Departamento de Lenguajes y Ciencias de la ComputaciónE.T.S.I. Informática, Campus TeatinosMálagaEspaña

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