Abstract
A new approach for multi-objective robust design optimization was proposed and applied to a real-world design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, and resulted in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can markedly reduce the computational time for predictions of robustness. In addition, the use of self-organizing maps as a data- mining technique allows visualization of complicated design information between optimality and robustness in a comprehensible two- dimensional form. Therefore, the extraction and interpretation of trade-off relations between optimality and robustness of design, and also the location of sweet spots in the design space, can be performed in a comprehensive manner.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gunawan, S., Azarm, S.: Multi-objective robust optimization using a sensitivity region concept. Structural Multidisciplinary Optimization 29, 50–60 (2005)
Li, M., Azarm, S., Aute, V.: A multi-objective genetic algorithm for robust design optimization. In: Proceedings of the 2005 Genetic and Evolutionary Computation Conference, pp. 771–778. ACM Press, New York (2005)
Deb, K., Gupta, H.: Searching for robust pareto-optimal solutions in multi-objective optimization. In: Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization, pp. 150–164. Springer, Heidelberg (2005)
Ong, Y.-S., Nair, P.B., Lum, K.Y.: Max–min surrogate-assisted evolutionary algorithm for robust design. IEEE Transactions on Evolutionary Computation 10, 392–404 (2006)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Ltd., Chichester (2001)
Shimoyama, K., Oyama, A., Fujii, K.: A new efficient and useful robust optimization approach – design for multi-objective six sigma. In: Proceedings of the 2005 IEEE Congress on Evolutionary Computation, vol. 1, pp. 950–957. IEEE Press, Piscataway (2005)
Shimoyama, K., Oyama, A., Fujii, K.: Multi-objective six sigma approach applied to robust airfoil design for Mars airplane. AIAA Paper 2007–1966 (April 2007)
Ray, T.: Constrained robust optimal design using a multiobjective evolutionary algorithm. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation, vol. 1, pp. 419–424. IEEE Press, Piscataway (2002)
Jin, Y., Sendhoff, B.: Trade-off between performance and robustness: An evolutionary multiobjective approach. In: Proceedings of the 2nd International Conference on Evolutionary Multi-Criterion Optimization, pp. 237–251. Springer, Heidelberg (2003)
Engineous Software, Inc., iSIGHT Reference Guide Version 7.1, pp. 220–233. Engineous Software, Inc. (2002)
Myers, R.H., Montgomery, D.C.: Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley & Sons, Ltd., New York (1995)
Chen, W., Allen, J.K., Schrage, D.P., Mistree, F.: Statistical experimentation methods for achieving affordable concurrent systems design. AIAA Journal 33(5), 409–435 (1997)
Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Statistical Science 4(4), 409–435 (1989)
Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box function. Journal of Global Optimization 13, 455–492 (1998)
Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)
McKay, M.D., Beckman, R.J., Conover, W.J.: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21, 239–245 (1979)
Saliby, E.: Descriptive sampling: A better approach to Monte Carlo simulation. Journal of the Operational Research Society 41(12), 1133–1142 (1990)
Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: Proceedings of the 5th International Conference on Genetic Algorithms, pp. 416–423. Morgan Kaufmann Publishers, Inc., San Mateo (1993)
Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proceedings of the 2nd International Conference on Genetic Algorithms, pp. 41–49. Morgan Kaufmann Publishers, San Mateo (1987)
Eshelman, L.J.: The CHC adaptive search algorithm: How to have safe when engaging in nontraditional genetic recombination. In: Foundations of Genetic Algorithms, pp. 265–283. Morgan Kaufmann Publishers, San Mateo (1991)
Tsutsui, S., Fujimoto, Y.: Forking genetic algorithms with blocking and shrinking modes (fGA). In: Proceedings of the 5th International Conference on Genetic Algorithms, pp. 206–213. Morgan Kaufmann Publishers, San Mateo (1993)
Eudaptics Software GmbH (2007), http://www.eudaptics.com/somine/ (cited January 10, 2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shimoyama, K., Lim, J.N., Jeong, S., Obayashi, S., Koishi, M. (2009). Multi-Objective Robust Optimization Assisted by Response Surface Approximation and Visual Data-Mining. In: Goh, CK., Ong, YS., Tan, K.C. (eds) Multi-Objective Memetic Algorithms. Studies in Computational Intelligence, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88051-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-540-88051-6_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-88050-9
Online ISBN: 978-3-540-88051-6
eBook Packages: EngineeringEngineering (R0)