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Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm

Year 2015, Volume: 28 Issue: 2, 321 - 330, 05.01.2015

Abstract

In multi-response studies, optimization and decision making are two crucial stages for obtaining a satisfactory solution. Generally, multiple responses are aggregated in a single objective function and the optimization result is considered as a compromise solution for all the responses. However, this approach does not meet required targets of all the responses simultaneously. In this study, Non-dominated Sorting Genetic Algorithm-II (NSGA-II), a well-known posterior preference articulation approach, is adapted with penalty function approach to optimize multiple responses with constraints. Then, the obtained non-dominated solutions are evaluated to make decision for the best satisfactory solution. In order to achieve the decision making stage, a fuzzy clustering based algorithm, fuzzy c-means (FCM), and a mostly used multi criteria decision making (MCDM) method, technique for order preference by similarity to an ideal solution (TOPSIS), are preferred. The selected combination of the NSGA-II with FCM and TOPSIS are performed on a real world data set given in the literature and results are discussed. The results show the applicability of the FCM for decision making in multiple responses. It can be said that the FCM makes easier the selection of a compromise solution in the non-dominated solution set by using membership degrees of each solution to the clusters without removing any non-dominated solution.

References

  • Box, G. E. P., Hunter, W. G., Macgregor, J. F. and Erjavec, J., “Some Problems Associated with the Analysis of Multiresponse Data”, Technometrics, 15(1): 33-51, (1973).
  • Zellner, A., “An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias", American Statistical Association Journal, 57: 348–368, (1962).
  • Shah, H. K., Montgomery, D. C. and Carlyle, W. M., “Response Surface Modeling and Optimization in Multiresponse
  • Unrelated Regressions”, Quality Engineering, 16(3): 387–397, (2004). Using
  • Seemingly 4. Liao, H. C., “Multi-response optimization using weighted principal component”, International Journal of Advanced Manufacturing Technology, 27: 720–725, (2006).
  • Wang, C. H., “Dynamic multi-response optimization using principal component analysis and multiple criteria evaluation of the grey relation model”, Journal of Advanced Manufacturing Technology, 32: 617-624, (2007).
  • Šibalija, T. V. and Majstorović, V. D., “Novel Approach to Multi-Response Optimisation for Correlated Responses”, FME Transactions, 38: 39- 48, (2010).
  • Biles, W. E., “A response surface method for experimental
  • process”, Industrial and Engineering Chemistry Process Design and Development, 14(2): 152-158, (1975). of
  • multi-response 8. Derringer, G. and Suich, R., “Simultaneous optimization of several response variables”, Journal of Quality Technology, 12(4): 214–219, (1980).
  • Derringer, G., “A Balancing Act: Optimizing a Product’s Properties”, Quality Progress, 27: 51–58, (1994).
  • Kim, K. and Lin, D., “Simultaneous optimization of multiple responses by maximizing exponential desirability functions”, Applied Statistics (Journal of the Royal Statistical Society: Series C), 49(3): 311-325, (2000).
  • Jeong, I. J. and Kim, K. J., “An interactive desirability function method to multiresponse optimization”, European Journal of Operational Research, 195: 412-426, (2009).
  • He, Z., Zhu, P., Wang, J. and Park, S. H., “Robust multi-response parameter design based on RSM”, Asian Journal on Quality, 10(3): 1-11, (2009).
  • He, Z., Wang, J., Oh, J. and Park, S. H., “Robust optimization for multiple responses using response surface methodology”, Applied Stochastic Models in Business and Industry, 26(2): 157-171, (2010).
  • He, Z., Zhu, P. F. and Park, S. H., “A robust desirability function method for multi-response surface
  • uncertainty”, European Journal of Operational Research, 221: 241-247, (2012).
  • model 15. Khuri, A. I. and Conlon, M., “Simultaneous optimization of multiple responses represented by polynomial regression functions”, Technometrics, 23(4): 363-375, (1981).
  • Pignatiello, J., “Strategies for robust multiresponse quality engineering”, IIE Transactions, 25(3), 5– 15, (1993).
  • Ames, A., Mattucci, N., McDonald, S., Szonyi, G. and Hawkins, D., “Quality loss function for optimization across multiple response surfaces”, Journal of Quality Technology, 29(3): 339–346, (1997).
  • Vining, G., “A compromise approach to multiresponse optimization”, Journal of Quality Technology, 30: 309–313, (1998).
  • Ko, Y., Kim, K. and Jun, C., “A new loss function- based method for multiresponse optimization”, Journal of Quality Technology, 37(1): 50–59, (2005).
  • Park, K. S. and Kim, K.J., “Optimizing multi- response surface problems: How to use multi- objective
  • Transactions, 37: 523-532, (2005). techniques”,
  • IIE Dreo, J., Petrowski, A., Siarry, P. and Taillard, E., Metaheuristics For Hard Optimization Methods and Case Studies, Springer-Verlag, Berlin, (2006).
  • Deb, K., Multi-Objective Optimization Using Evolutionary Algorithms, John-Wiley and Sons, New York, (2004).
  • Lee, D. H., Kim, K. J. and Köksalan, M., “A posterior preference articulation approach to multiresponse surface optimization”, European Journal of Operational Research, 210: 301–309, (2011). 24. Miettinen,
  • Optimization, Kluwer, Boston, (1999).
  • Multiobjective 25. Khuri, A. and Cornell, J., Response Surfaces: Designs and Analyses. Dekker, New York, (1996).
  • Kaveh, A., Kalateh-Ahani, M. and Fahimi-Farzani, M., “Constructability optimal design of reinforced concrete retaining walls using a multi-objective genetic algorithm”, Structucal Engineering and Mechanics, 47(2): 227-245, (2013).
  • Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T., “Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation, 6: 182-197, (2002).
Year 2015, Volume: 28 Issue: 2, 321 - 330, 05.01.2015

Abstract

References

  • Box, G. E. P., Hunter, W. G., Macgregor, J. F. and Erjavec, J., “Some Problems Associated with the Analysis of Multiresponse Data”, Technometrics, 15(1): 33-51, (1973).
  • Zellner, A., “An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias", American Statistical Association Journal, 57: 348–368, (1962).
  • Shah, H. K., Montgomery, D. C. and Carlyle, W. M., “Response Surface Modeling and Optimization in Multiresponse
  • Unrelated Regressions”, Quality Engineering, 16(3): 387–397, (2004). Using
  • Seemingly 4. Liao, H. C., “Multi-response optimization using weighted principal component”, International Journal of Advanced Manufacturing Technology, 27: 720–725, (2006).
  • Wang, C. H., “Dynamic multi-response optimization using principal component analysis and multiple criteria evaluation of the grey relation model”, Journal of Advanced Manufacturing Technology, 32: 617-624, (2007).
  • Šibalija, T. V. and Majstorović, V. D., “Novel Approach to Multi-Response Optimisation for Correlated Responses”, FME Transactions, 38: 39- 48, (2010).
  • Biles, W. E., “A response surface method for experimental
  • process”, Industrial and Engineering Chemistry Process Design and Development, 14(2): 152-158, (1975). of
  • multi-response 8. Derringer, G. and Suich, R., “Simultaneous optimization of several response variables”, Journal of Quality Technology, 12(4): 214–219, (1980).
  • Derringer, G., “A Balancing Act: Optimizing a Product’s Properties”, Quality Progress, 27: 51–58, (1994).
  • Kim, K. and Lin, D., “Simultaneous optimization of multiple responses by maximizing exponential desirability functions”, Applied Statistics (Journal of the Royal Statistical Society: Series C), 49(3): 311-325, (2000).
  • Jeong, I. J. and Kim, K. J., “An interactive desirability function method to multiresponse optimization”, European Journal of Operational Research, 195: 412-426, (2009).
  • He, Z., Zhu, P., Wang, J. and Park, S. H., “Robust multi-response parameter design based on RSM”, Asian Journal on Quality, 10(3): 1-11, (2009).
  • He, Z., Wang, J., Oh, J. and Park, S. H., “Robust optimization for multiple responses using response surface methodology”, Applied Stochastic Models in Business and Industry, 26(2): 157-171, (2010).
  • He, Z., Zhu, P. F. and Park, S. H., “A robust desirability function method for multi-response surface
  • uncertainty”, European Journal of Operational Research, 221: 241-247, (2012).
  • model 15. Khuri, A. I. and Conlon, M., “Simultaneous optimization of multiple responses represented by polynomial regression functions”, Technometrics, 23(4): 363-375, (1981).
  • Pignatiello, J., “Strategies for robust multiresponse quality engineering”, IIE Transactions, 25(3), 5– 15, (1993).
  • Ames, A., Mattucci, N., McDonald, S., Szonyi, G. and Hawkins, D., “Quality loss function for optimization across multiple response surfaces”, Journal of Quality Technology, 29(3): 339–346, (1997).
  • Vining, G., “A compromise approach to multiresponse optimization”, Journal of Quality Technology, 30: 309–313, (1998).
  • Ko, Y., Kim, K. and Jun, C., “A new loss function- based method for multiresponse optimization”, Journal of Quality Technology, 37(1): 50–59, (2005).
  • Park, K. S. and Kim, K.J., “Optimizing multi- response surface problems: How to use multi- objective
  • Transactions, 37: 523-532, (2005). techniques”,
  • IIE Dreo, J., Petrowski, A., Siarry, P. and Taillard, E., Metaheuristics For Hard Optimization Methods and Case Studies, Springer-Verlag, Berlin, (2006).
  • Deb, K., Multi-Objective Optimization Using Evolutionary Algorithms, John-Wiley and Sons, New York, (2004).
  • Lee, D. H., Kim, K. J. and Köksalan, M., “A posterior preference articulation approach to multiresponse surface optimization”, European Journal of Operational Research, 210: 301–309, (2011). 24. Miettinen,
  • Optimization, Kluwer, Boston, (1999).
  • Multiobjective 25. Khuri, A. and Cornell, J., Response Surfaces: Designs and Analyses. Dekker, New York, (1996).
  • Kaveh, A., Kalateh-Ahani, M. and Fahimi-Farzani, M., “Constructability optimal design of reinforced concrete retaining walls using a multi-objective genetic algorithm”, Structucal Engineering and Mechanics, 47(2): 227-245, (2013).
  • Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T., “Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II”, IEEE Transactions on Evolutionary Computation, 6: 182-197, (2002).
There are 31 citations in total.

Details

Primary Language English
Journal Section Statistics
Authors

Özlem Türkşen

Publication Date January 5, 2015
Published in Issue Year 2015 Volume: 28 Issue: 2

Cite

APA Türkşen, Ö. (2015). Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm. Gazi University Journal of Science, 28(2), 321-330.
AMA Türkşen Ö. Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm. Gazi University Journal of Science. June 2015;28(2):321-330.
Chicago Türkşen, Özlem. “Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm”. Gazi University Journal of Science 28, no. 2 (June 2015): 321-30.
EndNote Türkşen Ö (June 1, 2015) Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm. Gazi University Journal of Science 28 2 321–330.
IEEE Ö. Türkşen, “Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm”, Gazi University Journal of Science, vol. 28, no. 2, pp. 321–330, 2015.
ISNAD Türkşen, Özlem. “Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm”. Gazi University Journal of Science 28/2 (June 2015), 321-330.
JAMA Türkşen Ö. Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm. Gazi University Journal of Science. 2015;28:321–330.
MLA Türkşen, Özlem. “Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm”. Gazi University Journal of Science, vol. 28, no. 2, 2015, pp. 321-30.
Vancouver Türkşen Ö. Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm. Gazi University Journal of Science. 2015;28(2):321-30.