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.
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Ackley, D.H.: An empirical study of bit vector function optimization. In: Genetic Algorithms and Simulated Annealing, pp. 170–215. Kaufmann, San Mateo (1987)
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)
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
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)
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)
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)
Beyer, H.-G., Deb, K.: On self-adapting features in real-parameter evolutionary algorithms. IEEE Trans. Evol. Comput. 5(3), 250–270 (2001)
Bäck, J.H.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, Oxford (1996)
Bäck, T., Fogel, D., Michalewicz, Z.: Handbook of Evolutionary Computation. Institute of Physics Publishing Ltd/Oxford University Press, Bristol/New York (1997)
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)
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)
Deb, K., Beyer, H.: Self-adaptive genetic algorithms with simulated binary crossover. Evol. Comput. 9(2), 195–219 (2001)
Eiben, A.E., Bäck, T.: An empirical investigation of multi-parent recombination operators in evolution strategies. Evol. Comput. 5(3), 347–365 (1997)
Eiben, A., van der Hauw, J., van Hemert, J.: Graph coloring with adaptive evolutionary algorithms. J. Heuristics 4(1), 25–46 (1998)
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)
Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for minimization. Comput. J. 6, 163–168 (1963)
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)
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)
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)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison–Wesley, New York (1989)
Goldberg, D.E.: Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Syst. 5, 139–167 (1991)
Hajela, P.: Soft computing in multidisciplinary aerospace design-new direction for research. Prog. Aerosp. Sci. 38(1), 1–21 (2002)
Herrera, F., Lozano, M.: Gradual distributed real-coded genetic algorithms. IEEE Trans. Evol. Comput. 4(1), 43–63 (2000)
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)
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)
Hervás-Martínez, C., Ortiz-Boyer, D.: Analizing the statistical features of CIXL2 crossover offspring. Soft Comput. 9(4), 270–279 (2005)
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)
Hettmansperger, T.P., McKean, J.W.: Robust Nonparametric Statistical Methods. Arnold John/Wiley, London (1998)
Holland, J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)
Hollander, M., Wolfe, D.: Nonparametric Statistical Methods. Wiley, New York (1973)
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)
Koza, J.R.: Genetic Programming. MIT Press, Cambridge (1992)
Levene, H.: Essays in Honor of Harold Hotelling. In: Contributions to Probability and Statistics, pp. 278–292. Stanford University Press, Stanford (1960)
Liepins, G.E., Vose, M.D.: Characterizing crossover in genetic algorithms. Ann. Math. Artif. Intell. 5, 27–34 (1992)
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)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, New York (1992)
Miller, R.G.: Beyond ANOVA, Basics of Applied Statistics, 2nd edn. Chapman & Hall, London (1996)
Mühlebein, H., Schlierkamp-Voosen, D.: Predictive models for breeder genetic algorithm i. continuous parameter optimization. Evol. Comput. 1, 25–49 (1993)
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)
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)
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)
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)
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)
Radcliffe, N.J.: Equivalence class analysis of genetic algorithms. Complex Syst. 2(5), 183–205 (1991)
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)
Rastrigin, L.A.: Extremal control systems. In: Theoretical Foundations of Engineering Cybernetics Series, vol. 3. Nauka, Moscow (1974)
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)
Rudolph, G.: Convergence analysis of canonical genetic algorithms. IEEE Trans. Neural Netw. 5(1), 96–101 (1994)
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)
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)
Schwefel, H.P.: Evolution and Optimum Seeking. Wiley, New York (1995)
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)
Tamhane, A.C., Dunlop, D.D.: Statistics and Data Analysis. Prentice Hall, New York (2000)
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)
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)
Weierstrass, F.: Über continuirlichefunctionen eines reellen arguments die für keinen werth des letzteren einen bestimmter differentialquotienten besitzen. Math. Werke II, 71–72 (1872)
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)
Zhang, B.T., Kim, J.J.: Comparison of selection methods for evolutionary optimization. Evol. Optim. 2(1), 55–70 (2000)
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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
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DOI: https://doi.org/10.1007/s10732-007-9018-2