Multi-parent recombination in genetic algorithms with search space boundary extension by mirroring

  • Shigeyoshi Tsutsui
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1498)


In previous work, we have investigated real coded genetic algorithms with several types of multi-parent recombination operators and found evidence that multi-parent recombination with center of mass crossover (CMX) seems a good choice for real coded GAs. But CMX does not work well on functions which have their optimum on the corner of the search space. In this paper, we propose a method named boundary extension by mirroring (BEM) to cope with this problem. Applying BEM to CMX, the performance of CMX on the test functions which have their optimum on the corner of the search space was much improved. Further, by applying BEM, we observed clear improvement in performance of two-parent recombination on the functions which have their optimum on the corner of the search space. Thus, we suggest that BEM is a good general technique to improve the efficiency of crossover operators in real-coded GAs for a wide range of functions.


Genetic Algorithm Search Space Crossover Operator Extension Rate None None 
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  1. 1.
    Bäck, T.,Hoffmeister, F. and Schewfel, H.-P.: A survey of evolution strategies, Proc. of the 4th ICGA, pp. 2–9 (1991).Google Scholar
  2. 2.
    Beyer, H.-G.: Toward a theory of evolution strategies: On the benefits of sex-the (Μ/Μ,λ) theory, Evolutionary Computation, 3(1), pp. 81–111 (1995).MathSciNetGoogle Scholar
  3. 3.
    Davis, L.: The handbook of genetic algorithms, Von Nostrand Reinhold, New York (1991).Google Scholar
  4. 4.
    De Jong, K. A.: Analysis of the behavior of a class of genetic adaptive systems. Ph. D. dissertation, Dept. Computer and Communication Sciences, University of Michigan, Ann Arbor (1975).Google Scholar
  5. 5.
    De Jong, K. A., Potter M. A. and Spears, W. M.: Using problem generators to explore the effects of epistasis, Proc. the 7th ICGA, pp. 338–345 (1997).Google Scholar
  6. 6.
    Eiben, A. E., Raue, P-E. and Ruttkay, Zs.: Genetic algorithms with multi-parent recombination, Proc. of the PPSN III, pp. 78–87(1994).Google Scholar
  7. 7.
    Eiben, A. E., van Kemenade, C. H. M. and Kok, J. N.: Orgy in the computer: Multi-parent reproduction in genetic algorithms, Proc. of the 3rd European Conference on Artificial Life, LNAI 929, Springer-Verlag, pp. 934–945(1995).Google Scholar
  8. 8.
    Eiben, A. E. and Schippers, C. A.: Multi-parent's niche: n-ary crossover on NK-landscapes, Proc. of the PPSN IV, pp. 319–328 (1996).Google Scholar
  9. 9.
    Eiben, A. E, Bäck, T.: Empirical investigation of multiparent recombination operators in evolution strategies, Evolutionary Computation, 5(3), pp. 347–365 (1997).Google Scholar
  10. 10.
    Eshelman, L. J.: The CHC adaptive search algorithm: how to have safe search when engaging in nontraditional genetic recombination, Foundations of Genetic Algorithms, Morgan Kaufmann, pp.265–283 (1991).Google Scholar
  11. 11.
    Eshelman, L. J. and Schaffer, J. D.: Real-coded genetic algorithms and interval-schemata, Foundations of Genetic Algorithms 2, Morgan Kaufman, pp. 187–202 (1993).Google Scholar
  12. 12.
    Eshelman, L. J., Mathias, K. E. and Schaffer, J. D.: Crossover operator biases: Exploiting the population distribution, Proc. of the 7th ICGA, pp. 354–361 (1997).Google Scholar
  13. 13.
    Fogel, D. B., and Atmar, J. W.: Comparing genetic operators with Gaussian mutations in simulated evolutionary processes using linear systems, Biological Cybernetics, 66, pp. 111–114 (1990).CrossRefGoogle Scholar
  14. 14.
    Janikow, C. Z. and Michalewicz, Z.: An experimental comparison of binary and floating point representations in genetic algorithms, Proc. of the Fourth ICGA, pp. 31–36 (1991).Google Scholar
  15. 15.
    Kauffman, S. A.: Adaptation on rugged fitness landscapes, Lecture in the Science of Complexity, edited by Stein, D. Santa Fe Institute Studies in the Science of Complexity, Lect. Vol. I, Addison Wesley, pp.527–618 (1989).Google Scholar
  16. 16.
    Michalewicz, Z.: Genetic algorithms + data structures = evolution program, Springer-Verlag (1994).Google Scholar
  17. 17.
    Mühlenbein, H., Schomisch, M. and Born, J.: The parallel genetic algorithm as function optimizer, Proc. of the 4th ICGA, pp. 271–278 (1991).Google Scholar
  18. 18.
    Ono, I and Kobayashi, S: A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover, Proc. of the 7th ICGA, pp. 246–253 (1997).Google Scholar
  19. 19.
    Schewefel, H.-P.: Evolution and optimum seeking, Sixth-Generation Computer Technology Series, Wiley (1995).Google Scholar
  20. 20.
    Smith, J and Fogarty, T. C.: Recombination strategy adaptation via evolution of gene linkage, Proc. of the 1996 IEEE ICEC, pp. 826–831, 1996.Google Scholar
  21. 21.
    Tsutsui, S and Ghosh, A.: A study on the effect of multi-parent recombination in real coded genetic algorithms, Proc. of the 1998 IEEE ICEC, pp. 828–833 (1998).Google Scholar
  22. 22.
    Wright, A. H.: Genetic algorithms for real parameter optimization, Foundations of Genetic Algorithms, Morgan Kaufman, pp. 205–218 (1991).Google Scholar
  23. 23.
    Voigt, H.-M. and Mühlenbein, H.: Gene pool recombination and utilization of covariances for the breeder genetic algorithms, Proc. of the 1995 IEEE ICEC, pp. 172–177 (1995).Google Scholar

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© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Shigeyoshi Tsutsui
    • 1
  1. 1.Department of Management and Information ScienceHannan UniversityOsakaJapan

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