Advertisement

Crossover Operator Effect in Function Optimization with Constraints

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

Abstract

Most real-world optimization problems consist of linear cost functions subject to a set of constraints. In genetic algorithms the techniques for coping with such constraints are manifold: penalty functions, keeping the population in the feasible region, etc. Mutation and crossover operators must take into account the specific features of this kind of problems, as they are the responsible of the generation of new individuals. In this work, we make an analysis of the influence of the selection of the crossover operator in the problem of function optimization with constraints. We focus our work on the crossover operator because this operator is the most characteristic of genetic algorithms. We have used a test set that includes functions with linear and non-linear constraints. The results confirm the importance of crossover operator, as great differences are observed in the performance of the studied operators. The crossover based on confidence intervals shows the most robust behavior.

Keywords

Genetic Algorithm Penalty Function Feasible Region Shape Optimization Linear Constraint 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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
  2. 2.
    Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation 4 (1996) 1–32CrossRefGoogle Scholar
  3. 3.
    Koziel, S., Michalewicz, Z.: Evolutionary algorithms, homomorphous mappings,and constrained parameter optimization. Evolutionary Computation 7 (1999) 19–44CrossRefGoogle Scholar
  4. 4.
    Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, New York (1992)zbMATHGoogle Scholar
  5. 5.
    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
  6. 6.
    Herrera, F., Herrera-Viedma, E., Lozano, E., Verdegay, J.L.: Fuzzy tools to improve genetic algorithms. In: Second European Congress on Intelligent Techniques and Soft Computing. (1994) 1532–1539Google Scholar
  7. 7.
    Mühlebein, H., Schlierkamp-Voosen, D.: Predictive models for breeder genetic algorithm i. continuos parameter optimization. Evolutionary Computation (1993) 25–49Google Scholar
  8. 8.
    Mizumoto, M.: Pictorial representations of fuzzy connectives. part i: Cases of tnorms, t-conorms and averaging operators. Fuzzy Sets Systems 31 (1989) 217–242CrossRefMathSciNetGoogle Scholar
  9. 9.
    Herrera, F., Lozano, M., Verdegay, J.L.: Fuzzy connectives based crossover operators to model genetic algorithms population diversity. Fuzzy Sets Systems 92 (1997) 21–30CrossRefGoogle Scholar
  10. 10.
    Herrera, F., Lozano, M.: Gradual distributed real-coded genetic algorithms. IEEE Transactions on Evolutionary Computation 4 (2000) 43–63CrossRefGoogle Scholar
  11. 11.
    Voigt, H.M., Mühlenbein, H., Cvetkovic, D.: Fuzzy recombination for the breeder genetic algorithms. In Eshelman, L., ed.: The 6th International Conference Genetic Algorithms, San Mateo, CA, Morgan Kaufmann (1995) 104–111Google Scholar
  12. 12.
    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
  13. 13.
    Dolan, E.D., More, J.J.: Benchmarking optimization software with cops. Technical Report ANL/MCS-TM-246, Argonne National Laboratory (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

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

Personalised recommendations