Paper:
Language: English:

Maintaining Individual Diversity by Fuzzy c -Means Selection

Yoshiaki Sakakura^, Noriyuki Taniguchi^, Yukinobu Hoshino^,
and Katsuari Kamei^*

^College of Information Science and Engineering, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
^Graduate School of Science and Engineering, Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga 525-8577, Japan
^Department of Electronic and Photonic Systems Engineering, Kochi University of Technology, 185 Miyanokuchi, Tosayamada-cho, Kami, Kochi 782-8502, Japan

Received: March 15, 2007

Accepted: May 23, 2007

Keywords: optimization, genetic algorithm, individual diversity, selection, fuzzy c -means

Journal ref: Journal of Advanced Computational Intelligence and Intelligent Informatics, Vol.11, No.8 pp. 884-890, 2007

Abstract

In a GA search, maintaining diversity of individuals is an effective approach for preventing premature convergence and finding multiple optima. Our research aims to maintain the diversity. In this paper, a new selection for maintaining the diversity is proposed, and the selection is applied to simple GA (sGA). In the selection, the individuals are classified by Fuzzy c -means (FCM). Accordingly, several clusters are identified and each of the individuals gets a membership value for each of the clusters. The proposed selection selects individuals based on both the fitness values and the membership values. We discuss the behavior of maintaining individual diversity and search capabilities of the GA with the proposed selection via comparative experiments with a crisp cluster-based selection. Based on the results of the experiments, we were able to determine that the GA with the proposed selection makes the individuals wider distributed in a solution space compared to the crisp clustering based selection. The GA were also able to find more applicable optima compared to sGA and GA with a crisp clustering selection.

Reference

[1] D. E. Goldberg, “Genetic Algorithms in Search, Optimization and Machine Learning,” Addison-Wesley, 1989.

[2] E. Zitzler and L. Thiele, “Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach,” IEEE Transaction on Evolutionary Computation, Vol.3, No.4, pp. 257-271, 1999.

[3] H. E. Aguirre, K. Tanaka, T. Sugimura, and S. Oshita, “Improved distributed genetic algorithm with cooperative-competitive genetic operators,” Proc. IEEE Int. Conf. on Systems, Man, and Cybernetics, Vol.5, pp. 3816-3822, 2000.

[4] H. Ben Amor and A. Rettinger, “Intelligent exploration for genetic algorithms: Using self-organizing maps in evolutionary computation,” Proc. 2005 Conf. on Genetic and Evolutionary Computation, pp. 1531-1538, 2005.

[5] M. Miki, T. Hiroyasu, M. Kaneko, and K. Hatanaka, “A parallel genetic algorithm with distributed environment scheme,” Proc. IEEE Int. Conf. on Systems, Man, and Cybernetics, Vol.1, pp. 695-700, 1999.

[6] V. Rupela and G. Dozier, “Parallel and distributed evolutionary computations for multimodal functions,” Proc. 5th Biannual World Automation Congress, Vol.13, pp. 307-312, 2002.

[7] F. de Toro, J. Ortega, J. Fernández, and A. Díaz, “PSFGA: A parallel genetic algorithm for multiobjective optimization,” Proc. 10th Euromicro Workshop on Parallel, Distributed and Network-based Processing, pp. 384-391, 2002.

[8] S. Ando, J. Sakuma, and S. Kobayashi, “Adaptive isolation model using data clustering for multimodal function optimization,” Proc. 2005 Conf. on Genetic and Evolutionary Computation, pp. 1417-1424, 2005.

[9] H. Shimodaira, “A diversity-control-oriented genetic algorithm (DCGA): Performance in function optimization,” Proc. 2001 Congress on Evolutionary Computation, Vol.1, pp. 44-51, 2001.

[10] J. A. Martin H., “Search space modulation in genetic algorithms: Evolving the search space by sinusoidal transformations,” Proc. 2005 Conf. on Genetic and Evolutionary Computation, pp. 1559-1560, 2005.

[11] N. Sangkawelert and N. Chaiyaratana, “Diversity control in a multiobjective genetic algorithm,” Proc. 2003 Conf. on Genetic and Evolutionary Computation, Vol.4, pp. 2704-2711, 2003.

[12] H.-Z. Yang, F.-C. Li, and C.-M. Wang, “A density clustering based niching genetic algorithm for multimodal optimization,” Proc. 4th Int. Conf. on Machine Learning and Cybernetics, pp. 1599-1604, 2005.

[13] J. Gan and K. Warwick, “Dynamic niches clustering: A fuzzy variable radius niching technique for multimodal optimisation in GAs,” Proc. 2001 Congress on Evolutionary Computation, Vol.1, pp. 215-222, 2001.

[14] T.-Y. Huang and Y.-Y. Chen, “Diversity-based selection pooling scheme in evolutionary strategies,” Proc. 2001 ACM symposium on Applied computing, pp. 351-355, 2001.

[15] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenum Press, 1981.

[16] J. MacQueen, “Some methods for classification and analysis of multivariate observations,” Proc. 5th Berkeley Symposium on Math, Statistics and Probability, 1, pp. 281-297, 1967.