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On the Mean Convergence Time of Multi-parent Genetic Algorithms Without Selection

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Advances in Artificial Life (ECAL 2005)

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Abstract

This paper investigates genetic drift in multi-parent genetic algorithms (MPGAs). An exact model based on Markov chains is proposed to formulate the variation of gene frequency. This model identifies the correlation between the adopted number of parents and the mean convergence time. Moreover, it reveals the pairwise equivalence phenomenon in the number of parents and indicates the acceleration of genetic drift in MPGAs. The good fit between theoretical and experimental results further verifies the capability of this model.

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References

  1. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications, Ninth Dover printing, Mineola (1972)

    MATH  Google Scholar 

  2. Asoh, H., Mühlenbein, H.: On the mean convergence time of evolutionary algorithms without selection and mutation. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 88–97. Springer, Heidelberg (1994)

    Google Scholar 

  3. Brémaud, P.: Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  4. Davis, T.E., Principe, J.C.: A markov chain framework for the simple genetic algorithm. Evolutionary Computation 1(3), 269–288 (1993)

    Article  Google Scholar 

  5. Eiben, A.E.: Multiparent recombination in evolutionary computing. In: Advances in Evolutionary Computing, pp. 175–192. Springer, Heidelberg (2002)

    Google Scholar 

  6. Eiben, A.E., Rau’e, P.-E., Ruttkay, Z.: Genetic algorithms with multi-parent recombination. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 78–87. Springer, Heidelberg (1994)

    Google Scholar 

  7. Eiben, A.E., van Kemenade, C.H.M.: Diagonal crossover in genetic algorithms for numerical optimization. Journal of Control and Cybernetics 26(3), 447–465 (1997)

    MATH  MathSciNet  Google Scholar 

  8. Goldberg, D.E., Segrest, P.: Finite markov chain analysis of genetic algorithms. In: Proceedings of the 2nd International Conference on Genetic Algorithms and their Applications, pp. 1–8. Lawrence Erlbaum, Mahwah (1987)

    Google Scholar 

  9. Hartl, D.L., Clark, A.G.: Principles of Poppulation Genetics, 1st edn. Sinauer Associates (1989)

    Google Scholar 

  10. Horn, J.: Finite markov chain analysis of genetic algorithms with niching. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 110–117. Morgan Kaufmann Publishers, San Francisco (1993)

    Google Scholar 

  11. Nix, A.E., Vose, M.D.: Modeling genetic algorithms with markov chains. Annals of Mathematics and Artificial Intelligence 5, 78–88 (1992)

    Article  MathSciNet  Google Scholar 

  12. Papoulis, A., Pillai, S.U.: Probability, Random Variables, and Stochastic Processes, 4th edn. McGraw-Hill, New York (2002) ISBN 0-07-048477-5

    Google Scholar 

  13. Rudolph, G.: Convergence analysis of canonical genetic algorithms. IEEE Transactions on Neural Networks 5(1), 96–101 (1994)

    Article  Google Scholar 

  14. Schippers, C.A.: Multi-parent scanning crossover and genetic drift. In: Theoretical Aspects of Evolutionary Computing, pp. 307–330. Springer, Heidelberg (2001)

    Google Scholar 

  15. Tsutsui, S., Ghosh, A.: A study on the effect of multi-parent recombination in real coded genetic algorithms. In: Proceedings of International Conference on Evolutionary Computation, pp. 828–833 (1998)

    Google Scholar 

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© 2005 Springer-Verlag Berlin Heidelberg

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Ting, CK. (2005). On the Mean Convergence Time of Multi-parent Genetic Algorithms Without Selection. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds) Advances in Artificial Life. ECAL 2005. Lecture Notes in Computer Science(), vol 3630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11553090_41

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  • DOI: https://doi.org/10.1007/11553090_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28848-0

  • Online ISBN: 978-3-540-31816-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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