Skip to main content

Advertisement

Log in

Improving crossover operator for real-coded genetic algorithms using virtual parents

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

The crossover operator is the most innovative and relevant operator in real-coded genetic algorithms. In this work we propose a new strategy to improve the performance of this operator by the creation of virtual parents obtained from the population parameters of localisation and dispersion of the best individuals. The idea consists of mating these virtual parents with individuals of the population. In this way, the offspring are created in the most promising regions. This strategy has been incorporated into several crossover operators. After analysing the results we can conclude that this strategy significantly improves the performance of the algorithm in most problems analysed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ackley, D.H.: An empirical study of bit vector function optimization. In: Genetic Algorithms and Simulated Annealing, pp. 170–215. Kaufmann, San Mateo (1987)

    Google Scholar 

  • Affenzeller, M., Wagner, S.: A self-adaptive model for selective pressure handling within the theory of genetic algorithms. In: Computer Aided Systems Theory: EUROCAST 2003. Lecture Notes in Computer Science, vol. 2809, pp. 384–393. Springer, Berlin (2003)

    Google Scholar 

  • Affenzeller, M., Wagner, S.: Sasegasa: A new generic parallel evolutionary algorithm for achieving highest quality results. J. Heuristics 10, 239–263 (2004). Special Issue on New Advances on Parallel Meta-Heuristics for Complex Problems

    Article  Google Scholar 

  • Antonisse, J.: A new interpretation of schema notation that overturns the binary encoding constraint. In: Schaffer, J.D. (ed.) Third International Conference on Genetic Algorithms, pp. 86–91. Kaufmann, San Mateo (1989)

    Google Scholar 

  • Auger, A., Hansen, N.: A restart cma evolution strategy with increasing population size. In: IEEE Congress on Evolutionary Computation (CEC’05), vol. 2, pp. 1769–1776. IEEE Press, Napier University, Edinburgh, UK (2005)

  • Bebis, G., Georgiopoulos, M., Kasparis, T.: Coupling weight elimination with genetic algorithms to reduce network size and preserve generalization. Neurocomputing 17, 167–194 (1997)

    Article  Google Scholar 

  • Bersini, H., Dorigo, M., Langerman, S., Seront, G., Gambardella, L.M.: Results of the first international contest on evolutionary optimisation (1st ICEO). In: Proceedings of IEEE International Conference on Evolutionary Computation, IEEE-EC 96, pp. 611–615. IEEE Press, Nagoya (1996)

    Chapter  Google Scholar 

  • Beyer, H.-G., Deb, K.: On self-adapting features in real-parameter evolutionary algorithms. IEEE Trans. Evol. Comput. 5(3), 250–270 (2001)

    Article  Google Scholar 

  • Bäck, J.H.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, Oxford (1996)

    MATH  Google Scholar 

  • Bäck, T., Fogel, D., Michalewicz, Z.: Handbook of Evolutionary Computation. Institute of Physics Publishing Ltd/Oxford University Press, Bristol/New York (1997)

    MATH  Google Scholar 

  • Czarn, A., MacNish, C., Vijayan, K., Turlach, B., Gupta, R.: Statistical exploratory analysis of genetic algorithms. IEEE Trans. Evol. Comput. 8(4) (2004)

  • De Jong, K.D.: An analysis of the behavior of a class of genetic adaptive systems. Ph.D. thesis, Department of Computer and Communication Sciences, University of Michigan, Ann Arbor (1975)

  • De Jong, K., Spears, W.: A formal analysis of the role of multi-point crossover in genetic algorithms. Ann. Math. Artif. Intell. 5(1), 1–26 (1992)

    Article  MATH  Google Scholar 

  • De Jong, M.B., Kosters, W.: Solving 3-SAT using adaptive sampling. In: Poutré, H., van den Herik, J. (eds.) Proceedings of the Tenth Dutch/Belgian Artificial Intelligence Conference, pp. 221–228 (1998)

  • Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)

    MATH  MathSciNet  Google Scholar 

  • Deb, K., Beyer, H.: Self-adaptive genetic algorithms with simulated binary crossover. Evol. Comput. 9(2), 195–219 (2001)

    Article  Google Scholar 

  • Eiben, A.E., Bäck, T.: An empirical investigation of multi-parent recombination operators in evolution strategies. Evol. Comput. 5(3), 347–365 (1997)

    Google Scholar 

  • Eiben, A., van der Hauw, J., van Hemert, J.: Graph coloring with adaptive evolutionary algorithms. J. Heuristics 4(1), 25–46 (1998)

    Article  MATH  Google Scholar 

  • Eshelman, L.J., Schaffer, J.D.: Real-coded genetic algorithms and interval-schemata. In: Whitley, L.D. (ed.) Foundation of Genetic Algorithms 2, 187C3.3.7:1–C3.3.7:8.–202, Kaufmann, San Mateo (1993)

  • Eshelman, L.J., Caruana, A., Schaffer, J.D.: Biases in the crossover landscape. In: Schaffer, J.D. (ed.) Third International Conference on Genetic Algorithms, pp. 86–91. Kaufmann, San Mateo (1989)

    Google Scholar 

  • Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for minimization. Comput. J. 6, 163–168 (1963)

    MATH  MathSciNet  Google Scholar 

  • Friedman, J.H., An overview of predictive learning and function approximation. In: Cherkassky, V., Friedman, J.H., Wechsler, H. (eds.) From Statistics to Neural Networks, Theory and Pattern Recognition Applications. NATO ASI Series F, vol. 136, pp. 1–61. Springer, Berlin (1994)

    Google Scholar 

  • García-Pedrajas, N., Hervás-Martínez, C., Ortiz-Boyer, D.: Cooperative coevolution of artificial neural network ensembles for pattern classification. IEEE Trans. Evol. Comput. 9(3), 271–302 (2005a)

    Article  Google Scholar 

  • García-Pedrajas, N., Ortiz-Boyer, D., Hervas-Martínez, C.: An alternative approach for neural network evolution with a genetic algorithm: Crossover by combinatorial optimization. Neural Netw. 19, 514–528 (2005b)

    Article  Google Scholar 

  • Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison–Wesley, New York (1989)

    MATH  Google Scholar 

  • Goldberg, D.E.: Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Syst. 5, 139–167 (1991)

    MATH  Google Scholar 

  • Hajela, P.: Soft computing in multidisciplinary aerospace design-new direction for research. Prog. Aerosp. Sci. 38(1), 1–21 (2002)

    Article  Google Scholar 

  • Herrera, F., Lozano, M.: Gradual distributed real-coded genetic algorithms. IEEE Trans. Evol. Comput. 4(1), 43–63 (2000)

    Article  Google Scholar 

  • Herrera, F., Lozano, M., Verdegay, J.L.: Tackling real-coded genetic algorithms: Operators and tools for behavioural analysis. In: Artificial Inteligence Review, pp. 265–319. Kluwer Academic, Netherlands (1998)

    Google Scholar 

  • Herrera, F., Lozano, M., Sánchez, A.M.: A taxonomy for the crossover operator for real-coded genetic algorithms: An experimental study. Int. J. Intell. Syst. 18, 309–338 (2003)

    Article  MATH  Google Scholar 

  • Hervás-Martínez, C., Ortiz-Boyer, D.: Analizing the statistical features of CIXL2 crossover offspring. Soft Comput. 9(4), 270–279 (2005)

    Article  MATH  Google Scholar 

  • Hervás-Martínez, C., García-Pedrajas, N., Ortiz-Boyer, D.: Confidence interval based crossover using a L1 norm localization estimator for real-coded genetic algorithms. In: Benitez, J., Cordón, O., Hoffmann, F., Roy, R. (eds.) Advances in Soft Computing, pp. 297–305. Springer, Berlin (2003)

    Google Scholar 

  • Hettmansperger, T.P., McKean, J.W.: Robust Nonparametric Statistical Methods. Arnold John/Wiley, London (1998)

    MATH  Google Scholar 

  • Holland, J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  • Hollander, M., Wolfe, D.: Nonparametric Statistical Methods. Wiley, New York (1973)

    MATH  Google Scholar 

  • Kendall, M., Stuart, S.: The Advanced Theory of Statistics, vol. 1. Charles GriOEn & Company (1977)

  • Kita, H.: A comparison study of self-adaptation in evolution strategies and real-code genetic algorithms. Evol. Comput. 9(2), 223–241 (2001)

    Article  MathSciNet  Google Scholar 

  • Koza, J.R.: Genetic Programming. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  • Levene, H.: Essays in Honor of Harold Hotelling. In: Contributions to Probability and Statistics, pp. 278–292. Stanford University Press, Stanford (1960)

    Google Scholar 

  • Liepins, G.E., Vose, M.D.: Characterizing crossover in genetic algorithms. Ann. Math. Artif. Intell. 5, 27–34 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  • McNeils, J.D.P.: Approximating and simulating the stochastic growth model: Parameterized expectations, neural networks, and the genetic algorithm. J. Econ. Dyn. Control 25(9), 1273–1303 (2001)

    Article  Google Scholar 

  • Michalewicz, Z.: Genetic Algorithms  +  Data Structures = Evolution Programs. Springer, New York (1992)

    MATH  Google Scholar 

  • Miller, R.G.: Beyond ANOVA, Basics of Applied Statistics, 2nd edn. Chapman & Hall, London (1996)

    Google Scholar 

  • Mühlebein, H., Schlierkamp-Voosen, D.: Predictive models for breeder genetic algorithm i. continuous parameter optimization. Evol. Comput. 1, 25–49 (1993)

    Google Scholar 

  • Neyman, J.: Outline of a theory of statistical estimation based on the classical theory of probability. Philos. Trans. Roy. Soc. Lond. A 236, 333–380 (1937)

    Google Scholar 

  • Ortiz-Boyer, D., Hervás-Martínez, C., García-Pedrajas, N.: Crossover operator effect in function optimization with constraints. In: Merello, J., Adamidis, P., Beyer, H.-G., Fernandez, J.L., Schwefel, H.P. (eds.) The 7th Conference on Parallel Problem Solving from Nature. Lecture Notes in Computer Science, vol. 2439, pp. 184–193. Springer, Granada (2002)

    Google Scholar 

  • Ortiz-Boyer, D., Hervás-Martínez, C., Muñoz-Pérez, J.: Study of genetic algorithms with crossover based on confidence intervals as an alternative to classic least squares estimation methods for non-linear models. In: Resende, M.G.C., de Sousa, J.P. (eds.) Metaheuristics: Computer Decision-Making, pp. 127–151. Kluwer Academic, Dordrecht (2003)

    Google Scholar 

  • Ortiz-Boyer, D., Hervás-Martínez, C., García-Pedrajas, N.: Cixl2: A crossover operator for evolutionary algorithms based on population features. J. Artif. Intell. Res. 24, 1–48 (2005)

    Article  MATH  Google Scholar 

  • Périauz, J., Sefioui, M., Stoufflet, B., Mantel, B., Laporte, E.: Robust genetic algorithm for optimization problems in aerodynamic design. In: Winter, G., Periaux, J., Galan, M., Cuesta, P. (eds.) Genetic Algorithms in Engineering and Computer Science, pp. 370–396. Wiley, New York (1995)

    Google Scholar 

  • Radcliffe, N.J.: Equivalence class analysis of genetic algorithms. Complex Syst. 2(5), 183–205 (1991)

    MathSciNet  Google Scholar 

  • Radcliffe, N.J.: Non-linear genetic representations. In: Männer, R., Manderick, B. (eds.) Second International Conference on Parallel Problem Solving from Nature, pp. 259–268. Elsevier, Amsterdam (1992)

    Google Scholar 

  • Rastrigin, L.A.: Extremal control systems. In: Theoretical Foundations of Engineering Cybernetics Series, vol. 3. Nauka, Moscow (1974)

    Google Scholar 

  • Rosenbrock, H.H.: An automatic method for finding the greatest or least value of a function. Comput. J. 175–184 (1960)

  • Roubos, J., van Straten, G., van Boxtel, A.: An evolutionary strategy for fed-batch bioreactor optimization; concepts and performance. J. Biotechnol. 67(2-3), 173–187 (1999)

    Article  Google Scholar 

  • Rudolph, G.: Convergence analysis of canonical genetic algorithms. IEEE Trans. Neural Netw. 5(1), 96–101 (1994)

    Article  Google Scholar 

  • Schaffer, J., Caruana, R., Eshelman, L., Das, R.: A study of control parameters affecting online performance of genetic algorithms for function optimization. In: Schaffer, J. (ed.) 3rd International Conference on Genetic Algorithms, pp. 51–60. Kaufmann, San Mateo (1989)

    Google Scholar 

  • Schlierkamp-Voosen, D.: Strategy adaptation by competition. In: Second European Congress on Intelligent Techniques and Soft Computing, pp. 1270–1274 (1994)

  • Schwefel, H.P.: Numerical Optimization of Computer Models. Wiley, New York (1981)

    MATH  Google Scholar 

  • Schwefel, H.P.: Evolution and Optimum Seeking. Wiley, New York (1995)

    Google Scholar 

  • Spedicato, E.: Computational experience with quasi-newton algorithms for minimization problems of moderately large size, CISE-N-175, Centro Informazioni Studi Esperienze, Segrate (Milano), Italy (1975)

  • Syswerda, G.: Uniform crossover in genetic algorithms. In: Schasffer, J. (ed.) 3rd International Conference on Genetic Algorithm, pp. 2–9. Kaufmann, San Mateo (1989)

    Google Scholar 

  • Tamhane, A.C., Dunlop, D.D.: Statistics and Data Analysis. Prentice Hall, New York (2000)

    Google Scholar 

  • Voigt, H.M.: Soft genetic operators in evolutionary algorithms. In: Banzhaf, W., Eeckman, F. (eds.) Evolution and Biocomputation. Lecture Notes in Computer Science, vol. 899, pp. 123–141. Springer, Berlin (1995)

    Google Scholar 

  • Voigt, H.M., Mühlenbein, H., Cvetkovic, D.: Fuzzy recombination for the breeder genetic algorithms. In: Eshelman, L. (ed.) The 6th International Conference Genetic Algorithms, pp. 104–111. Kaufmann, San Mateo (1995)

    Google Scholar 

  • Weierstrass, F.: Über continuirlichefunctionen eines reellen arguments die für keinen werth des letzteren einen bestimmter differentialquotienten besitzen. Math. Werke II, 71–72 (1872)

    Google Scholar 

  • Wright, A.: Genetic algorithms for real parameter optimization. In: Rawlin, G.J.E. (ed.) Foundations of Genetic Algorithms 1, pp. 205–218. Kaufmann, San Mateo (1991)

    Google Scholar 

  • Zhang, B.T., Kim, J.J.: Comparison of selection methods for evolutionary optimization. Evol. Optim. 2(1), 55–70 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Domingo Ortiz-Boyer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ortiz-Boyer, D., Hervás-Martínez, C. & García-Pedrajas, N. Improving crossover operator for real-coded genetic algorithms using virtual parents. J Heuristics 13, 265–314 (2007). https://doi.org/10.1007/s10732-007-9018-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-007-9018-2

Keywords

Navigation