Abstract
This paper presents a methodology based on genetic algorithms, which finds feasible and reasonably adequate solutions to problems of robust design in multivariate systems. We use a genetic algorithm to determine the appropriate control factor levels for simultaneously optimizing all of the responses of the system, considering the noise factors which affect it. The algorithm is guided by a desirability function which works with only one fitness function although the system may have many responses. We validated the methodology using data obtained from a real system and also from a process simulator, considering univariate and multivariate systems. In all cases, the methodology delivered feasible solutions, which accomplished the goals of robust design: obtain responses very close to the target values of each of them, and with minimum variability. Regarding the adjustment of the mean of each response to the target value, the algorithm performed very well. However, only in some of the multivariate cases, the algorithm was able to significantly reduce the variability of the responses.
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Allende, H., Canessa, E., Galbiati, J.: Diseño de Experimentos Industriales, Edit. Universidad Técnica Federico Santa María, Valparaíso, Chile (2005)
Bravo, D.B.: Desarrollo de una Herramienta basada en Algoritmos Genéticos para resolver problemas de Diseño Robusto en Sistemas Multivariados. Master thesis, Universidad Adolfo Ibáñez (2005)
Del Castillo E., Montgomery D.C. and McCarville D.R. (1996). Modified desirability functions for multiple response optimization. J. Qual. Technol. 28: 337–345
Golberg, D.E.: Genetic Algorithm in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA(1989)
Haupt R.L. and Haupt S.E. (2004). Practical Genetic Algorithms. Wiley, New Jersey
Holland, J.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor, MI (1974)
Kackar R.N. and Shoemaker A.C. (1986). Robust design: a cost effective method for improving manufacturing processes. AT&T Tech. J. 65(2): 39–50
Leon R., Schoemaker A.C. and Kackar R.N. (1987). Performance measures independent of adjustment: an explanation and extension of Taguchi’s signal to noise ratios (with discussions). Technometrics 29(3): 253–285
Maghsoodloo S. and Chang C. (2001). Quadratic loss functions and SNR for a bivariate response. J. Manuf. Syst. 20(1): 1–12
Myers R.H. and Montgomery D.C. (2002). Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Wiley, New York, NY
Ortiz F., Simpson J., Heredia-Langner A. and Pigniatello J. Jr., (2004). A genetic algorithm Approach to multiple—response optimization. J. Qual. Technol. 36(4): 432–449
Pignatiello J. Jr.,(1988). An overview of the strategy and tactics of Taguchi. IIE Trans. 20(3): 247–254
Roy R.K.: Design of Experiments Using the Taguchi Approach, 1st edn. J. Wiley & Sons, New York, NY (2001)
Taguchi, G.: Systems of Experimental Design, vol. 1 and 2, 4th edn. American Supplier Institute, Dearborn, MI (1991)
Vandenbrande, W.: Make love, not war: combining DOE and Taguchi, ASQ’s 54th annual quality congress. In: Proceedings, pp. 450–456 (2000)
Yuan, Y.: Multiple Imputation for Missing Data: Concepts and New Development. SAS Institute Inc., Rockville MD (2006)
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Allende, H., Bravo, D. & Canessa, E. Robust design in multivariate systems using genetic algorithms. Qual Quant 44, 315–332 (2010). https://doi.org/10.1007/s11135-008-9201-z
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DOI: https://doi.org/10.1007/s11135-008-9201-z