Paper:
A Pareto Optimal Solution Visualization Method Using an Improved Growing Hierarchical Self-Organizing Maps Based on the Batch Learning
Naoto Suzuki, Takashi Okamoto, and Seiichi Koakutsu
Chiba University
1-33 Yayoicho, Inage-ku, Chiba 263-8522, Japan
- [1] A. Abraham, L. Jain, and R. Goldberg (Eds.), “Evolutionary multiobjective optimization,” Springer-Verlag, 2006.
- [2] X. Gandibleux, M. Sevaux, K. Söerensen, and V. T’kindt (Eds.), “Metaheuristics for multiobjective optimisation,” Springer-Verlag, 2004.
- [3] K. Tsuchida, H. Sato, H. E. Aguirre, and K. Tanaka, “Analysis of NSGA-II and NSGA-II with CDAS, and proposal of an enhanced CDAS mechanism,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.13, No.4, pp. 470-480, 2009.
- [4] F. Bourennani, S. Rahnamayan, and G. F. Naterer, “OGDE3: Opposition-based third generalized differential evolution,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.16, No.3, pp. 469-480, 2012.
- [5] M. Miyakawa, K. Takadama, and H. Sato, “Archive of useful solutions for directed mating in evolutionary constrained multiobjective optimization,” J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII), Vol.18, No.2, pp. 221-231, 2014.
- [6] S. Obayashi and D. Sasaki, “Visualization and data mining of Pareto solutions using self-organizing map,” EMO 2003, Lecture Notes in Computer Science, Vol.2632, Springer, pp. 796-809, 2003.
- [7] A. Lotov and K. Miettinen, “Visualizing the Pareto frontier,” Multiobjective Optimization, Lecture Notes in Computer Science, Vol.5252, Springer, pp. 213-243, 2008.
- [8] M. Bagajewicz and E. Cabrera, “Pareto optimal solutions visualization techniques for multiobjective design and upgrade of instrumentation networks,” Ind. Eng. Chem. Res., Vol.42, No.21, pp. 5195-5203, 2003.
- [9] X. Blasco, J. M. Herrero, J. Sanchis, and M. Martinez, “A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization,” Information Sciences, Vol.178, No.20, pp. 3908-3924, 2008.
- [10] S. Chen, D. Amid, O. M. Shir, L. Limonad, D. Boaz, A. Anaby-Tavor, and T. Schreck, “Self-organizing maps for multi-objective Pareto frontiers,” Proc. of IEEE Pacific Visualization Symp. 2013, pp. 153-160, 2013.
- [11] T. Kohonen, “Self-organized formation of topologically correct feature maps,” Biol. Cybern., Vol.43, No.1, pp. 59-69, 1982.
- [12] A. Hironaka, T. Okamoto, S. Koakutsu, and H. Hirata, “Analysis and improvements of the Pareto optimal solution visualization method using the self-organizing maps,” SICE J. of Control, Measurement, and System Integration, Vol.8, No.1, pp. 34-43, 2015.
- [13] T. Okamoto, Y. Hanaoka, E. Aiyoshi, and Y. Kobayashi, “Optimal design of buffer material in the geological disposal of radioactive wastes using the satisficing trade-off method and a self-organizing map,” Electrical Engineering in Japan, Vol.187, No.2, pp. 17-32, 2014.
- [14] N. Suzuki, T. Okamoto, and S. Koakutsu, “Visualization of Pareto optimal solution sets using the growing hierarchical self-organizing maps,” IEEJ Trans. Electronics, Information and Systems, Vol.135, No.7, pp. 908-919, 2015 (in Japanese).
- [15] A. Rauber, D. Merkl, and M. Dittenbach, “The growing hierarchical self-organizing map: Exploratory analysis of high-dimensional data,” IEEE Trans. Neural Networks, Vol.13, No.6, pp. 1331-1341, 2002.
- [16] M. Dittenbach, D. Merkl, and A. Rauber, “Organizing and exploring high-dimensional data with the growing hierarchical self-organizing map,” Proc. of the 1st Int. Conf. on Fuzzy Systems and Knowledge Discovery, Vol.2, pp. 626-630, 2002.
- [17] S. Huband, L. Barone, L. While, and P. Hingston, “A scalable multi-objective test problem toolkit,” EMO 2005, Lecture Notes in Computer Science, Vol.3410, Springer, pp. 280-295, 2005.
- [18] K. Deb, A. Pratp, S. Agarwal, and T. Meyarivan, “A fast and elitist multiobjective genetic algorithm: NSGA-II,” IEEE Trans. Evol. Comput., Vol.6, No.2, pp. 182-197, 2002.
- [19] R. Storn and K. Price, “Differential evolution — a simple and efficient adaptive scheme for global optimization over continuous spaces,” Tech. Rep. of Int. Computer Science Institute, No. TR-95-012, 1995.
- [20] K. Price, R. M. Storn, and J. A. Lampinen, “Differential evolution — A practical approach to global optimization,” Springer, 2005.
- [21] H. Ishibuchi, M, Yamane, N. Akedo, and Y. Nosima, “Many-Objective and Many-Variable Test Problems for Visual Examination of Multiobjective Search,” Proc. of IEEE Congress on Evolutionary Computation 2013, pp. 1491-1498, 2013.
- [22] R. Vlennet, C. Fonteix, and I. Marc, “Multicriteria optimization using a genetic algorithm for determining a Pareto set,” Int. J. of Syst. Sci, Vol.27, No.2, pp. 255-260, 1996.
- [23] K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable Test Problems for Evolutionary Multi-Objective Optimization,” Evolutionary Multiobjective Optimization — Theoretical Advances and Applications, Springer, pp. 105-145, 2005.
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