Abstract
Multi-objective problems with parameter interactions can present difficulties to many optimization algorithms. We have investigated the behaviour of Simplex Crossover (SPX), Unimodal Normally Distributed Crossover (UNDX), Parent-centric Crossover (PCX), and Differential Evolution (DE), as possible alternatives to the Simulated Binary Crossover (SBX) operator within the NSGA-II (Non-dominated Sorting Genetic Algorithm II) on four rotated test problems exhibiting parameter interactions. The rotationally invariant crossover operators demonstrated improved performance in optimizing the problems, over a non-rotationally invariant crossover operator.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Salomon, R.: Re-evaluating genetic algorithm performance under coordinate rotation of benchmark functions: A survey of some theoretical and practical aspects of genetic algorithms. Bio. Systems 39(3), 263–278 (1996)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9(2), 115–148 (1995)
Deb, K., Kumar, A.: Real-coded genetic algorithms with simulated binary crossover: Studies on multi-modal and multi-objective problems. Complex Systems 9(6), 431–454 (1995)
Corne, D., Dorigo, M., Glover, F. (eds.): New Ideas in Optimization. McGraw-Hill, London (1999)
Iorio, A., Li, X.: Incorporating directional information within a differential evolution algorithm for multiobjective optimization. In: Proceedings of the 2006 Genetic and Evolutionary Computation Conference (GECCO 2006), IEEE Press, Los Alamitos (2006)
Iorio, A., Li, X.: Rotated test problems for assessing the performance of multiobjective optimization algorithms. In: Proceedings of the 2006 Genetic and Evolutionary Computation Conference (GECCO 2006), IEEE Press, Los Alamitos (2006)
Price, K.: New Ideas in Optimization, p. 98. McGraw-Hill, New York (1999)
Ballester, P., Carter, J.N.: Real-parameter genetic algorithms for finding multiple optimal solutions in multi-modal optimization. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 707–717. Springer, Heidelberg (2003)
Ono, I., Kita, H., Kobayashi, S.: A Real-coded Genetic Algorithm using the Unimodal Normal Distribution Crossover. Advances in Evolutionary Computing: Theory and Applications, pp. 213–237. Springer, Heidelberg (2003)
Kita, H.: A comparison study of self-adaptation in evolution strategies and real-coded genetic algorithms. Evolutionary Computation 9(2), 223–241 (2001)
Ono, I., Kobayashi, S., Yoshida, K.: Optimal lens design by real-coded genetic algorithms using UNDX. Computer Methods in Applied Mechanics and Engineering 186, 483–497 (2000)
Kita, H., Ono, I., Kobayashi, S.: Multi-parental extension of the unimodal normal distribution crossover for real-coded genetic algorithms. In: Proc. 1999 Congress on Evolutionary Computation (CEC 1999), pp. 1581–1587 (1999)
Deb, K., Joshi, D., Anand, A.: Real-coded evolutionary algorithms with parent-centric recombination. Indian Institute of Technology, Kanpur, Tech. Rep. KanGAL Report No.2001003 (2001)
Deb, K., Joshi, D., Anand, A.: Real-coded evolutionary algorithms with parent-centric recombination. In: Proceedings of the 2002 Congress on Evolutionary Computation CEC 2002, pp. 61–66. IEEE Press, Los Alamitos (2002)
Tsutsui, S., Yamamura, M.: Multi-parent recombination with simplex crossover in real coded genetic algorithms. In: Proceedings of the 1999 Genetic and Evolutionary Computation Conference (GECCO 1999), pp. 657–664 (1999)
Chang, C.S., Xu, D.Y.: Differential evolution of fuzzy automatic train operation for mass rapid transit system. IEEE Proceedings of Electric Power Applications 147(3), 206–212 (2000)
Abbass, H.A., Sarker, R., Newton, C.: PDE: A Pareto-frontier differential evolution approach for multi-objective optimization problems. In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), vol. 2, pp. 971–978 (2001)
Xue, F., Sanderson, A.C., Graves, R.J.: Pareto-based multi-objective differential evolution. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), vol. 2, pp. 862–869. IEEE Press, Los Alamitos (2003)
Madavan, N.K.: Multiobjective optimization using a Pareto differential evolution approach. In: Proceedings of the 2002 Congress on Evolutionary Computation (CEC 2002), vol. 2, pp. 1145–1150. IEEE Press, Los Alamitos (2002)
Price, K., Storn, R.M., Lampinen, J.A.: Differential Evolution - A Practical Approach to Global Optimization, p. 88. Springer, Heidelberg (2005)
Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On test functions for evolutionary multi-objective optimization. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 792–802. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Iorio, A., Li, X. (2006). Rotationally Invariant Crossover Operators in Evolutionary Multi-objective Optimization. In: Wang, TD., et al. Simulated Evolution and Learning. SEAL 2006. Lecture Notes in Computer Science, vol 4247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11903697_40
Download citation
DOI: https://doi.org/10.1007/11903697_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47331-2
Online ISBN: 978-3-540-47332-9
eBook Packages: Computer ScienceComputer Science (R0)