Theoretical Analysis of the Confidence Interval Based Crossover for Real-Coded Genetic Algorithms

  • C. Hervás-Martínez
  • D. Ortiz-Boyer
  • N. García-Pedrajas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2439)


In this paper we study some theoretical aspects of a new crossover operator for real-coded genetic algorithms based on the statistical features of the best individuals of the population. This crossover is based on defining a confidence interval for a localization estimator using the L 2 norm. From this confidence interval we obtain three parents: the localization estimator and the lower and upper limits of the confidence interval. In this paper we analyze the mean and variance of the population when this crossover is applied, studying the behavior of the distribution of the fitness of the individuals in a problem of optimization. We also make a comparison of our crossover with the crossovers BLX-α and UNDX-m, showing the robustness of our operator.


Genetic Algorithm Crossover Operator Good Individual Population Density Function Ackley Function 
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.
    Goldberg, D.E.: Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Systems (1991) 139–167Google Scholar
  2. 2.
    Eshelman, L.J., Schaffer, J.D.: Real-coded genetic algorithms and intervalshemata. In Whitley, L.D., ed.: Foundation of Genetic Algorithms 2, San Mateo, Morgan Kaufmann (1993) 187C3.3.7:1-C3.3.7:8.-202Google Scholar
  3. 3.
    Janikow, C.Z., Michalewicz, Z.: An experimental comparison of binary and floating point representations in genetic algorithms. In: Proc. of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann Publishers, San Mateo (1991) 31–36Google Scholar
  4. 4.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, New York (1992)zbMATHGoogle Scholar
  5. 5.
    Ono, I., Kobayashi, S.: A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover. In: 7th International Conference on Genetic Algorithms, Michigan, USA, Michigan State University, Morgan Kaufman (1997) 246–253Google Scholar
  6. 6.
    Ono, I., Kita, H., Kobayashi, S.: A robust real-coded genetic algorithm using unimodal normal distribution crossover augmented by uniform crossover: Effects of self-adaptation of crossover probabilities. In Banzhaf, W., Daida, J., Eiben, A.E., Garzon, M.H., Honavar, V., Jakiela, M., Smith, R.E., eds.: Genetic and Evolutionary Computation Conf. (GECCO’99), San Francisco, CA, Morgan Kaufmann (1999) 496–503Google Scholar
  7. 7.
    Herrera, F., Lozano, M., Verdegay, J.L.: Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis. Artificial Inteligence Review (1998) 265–319 Kluwer Academic Publisherr. Printed in Netherlands.Google Scholar
  8. 8.
    Tsutsui, S., Yamamura, M., Higuchi, T.: Multi-parent recombination with simplex crossover in real coded genetic algorithms. In: PPSN. Volume VI., Springer-Verlag (1999) 657–664Google Scholar
  9. 9.
    Tsutsui, S., Goldberg, D.E.: Search space boundary extension method in real coded genetic algorithms. Information Science 133 (2001) 229–247zbMATHCrossRefGoogle Scholar
  10. 10.
    Qi, X., Palmieri, F.: Theoretical analysis of evolutionary algorithms with an infinite population size on continuous space. part i: Basic properties of selection and mutation. IEEE Trans. Neural Networks 5 (1994) 102–119CrossRefGoogle Scholar
  11. 11.
    Qi, X., Palmieri, F.: Theoretical analysis of evolutionary algorithms with an infinite population size on continuous space. part ii: Analysis of the diversification role of crossover. IEEE Trans. Neural Networks 5 (1994) 120–128CrossRefGoogle Scholar
  12. 12.
    Nomura, T.: An analysis on crossorvers for real number chromosomes in an infinite population size. In: Fifteenth International Joint Conference on Artificial Intelligence (IJCAI’97), NAGOYA, Aichi, Japan (1997) 936–941Google Scholar
  13. 13.
    Kita, H., Ono, I., Kobayashi, S.: Theoretical analysis of the unimodal normal distribution crossover for real-coded genetic algorithms. In: IEEE International Conference on Evolutionary Computation ICEC’98, Anchorage, Alaska, USA (1998) 529–534Google Scholar
  14. 14.
    Eiben, A., Raué, P.E., Ruttkay, A.: Genetic algorithms with multi-parent recombination. In Davidor, Y., Schwefel, H.P., Männer, R., eds.: The 3rd Conference on Parallel Problem Solving from Nature. Number 866 in Lecture Notes in Computer Science. Springer-Verlag (1994) 78–87Google Scholar
  15. 15.
    Eiben, A., Schippers, C.: Multi-parent’s niche: n-ary crossovers on nk-landscapes. In Voigt, H.M., Ebeling, W., Rechenberg, I., Schwefel, H.P., eds.: The 4rd Conference on Parallel Problem Solving from Nature. Number 1141 in Lecture Notes in Computer Science. Springer, Berlin (1994) 319–328Google Scholar
  16. 16.
    Tsutsui, S., Ghosh, A.: A study of the effect of multi-parent recombination in real coded genetic algorithms. In: Proc. of the ICEC. (1998) 828–833Google Scholar
  17. 17.
    Eshelman, L.J.: The CHC adaptive search algorithm: How to safe search when engaging in non-traditional genetic recombination. In: Foundations of Genetic Algorithms. Morgan Kaufman Publisher, San Mateo (1991) 256–283Google Scholar
  18. 18.
    Eiben, A., Bäck, T.: Multi-parent recombination operators in continuous search spaces. Technical Report TR-97-01, Leiden University (1997)Google Scholar
  19. 19.
    Hervás, C., Ortiz, D.: Operadores de cruce basados en estadísticos de localización para algoritmos genéticos con codificación real. In Alba, E., Fernandez, F., Gomez, J.A., Herrera, F., Hidalgo, J.I., Lanchares, J., Merelo, J.J., Sánchez, J.M., eds.: Primer Congreso Español De Algoritmos Evolutivos y Bioinspirados (AEB’02), Mérida, Spain (2002) 1–8Google Scholar
  20. 20.
    Eshelman, L.J., Mathias, K.E., Schaffer, J.D.: Crossover operator biases: Exploiting the population distribution. In: Proceedings of the Seventh International Conference on Genetic Algorithms. (1997) 354–361Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • C. Hervás-Martínez
    • 1
  • D. Ortiz-Boyer
    • 1
  • N. García-Pedrajas
    • 1
  1. 1.Department of Computing and Numerical AnalysisUniversity of CórdobaCórdobaSpain

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