DOI QR코드

DOI QR Code

An Interactive Approach to Multiple Response Optimization

다중반응최적화를 위한 상호교호적 접근법

  • Received : 2015.05.22
  • Accepted : 2015.07.02
  • Published : 2015.08.31

Abstract

We study the problem of multiple response optimization (MRO) and focus on the selection of input levels which will produce desirable output quality. We propose an interactive multiple objective optimization approach to the input design. The earlier interactive methods utilized for MRO communicate with the decision maker only using the response variable values, in order to improve the current response values, thereby resulting in the corresponding design solution automatically. In their interaction steps of preference articulation, no account is taken of any active changes in design variable values. On the contrary, our approach permits the decision maker to change the design variable values in its interaction stage, which makes possible the consideration of the preference or economics of the design variable side. Using some typical value functions, we also demonstrate that our method converges reasonably well to the known optimal solutions.

Keywords

References

  1. 염봉진, 서순근, 윤원영, 변재현, "품질 및 신뢰성분야의 동향과 발전 방향", 대한산업공학회지, 제40권, 제6호(2014), pp.526-554. https://doi.org/10.7232/JKIIE.2014.40.6.526
  2. 이동희, 정인준, 김광재, "쌍대반응표면최적화의 방법론 및 응용", 대한산업공학회지, 제39권, 제5권(2013), pp.342-350. https://doi.org/10.7232/JKIIE.2013.39.5.342
  3. Arungpadang, T.R., 김영진, "인공신경망과 유전알고리즘 기반의 쌍대반응표면분석에 관한 연구", 대한산업공학회지, 제39권, 제5호(2013), pp.361-366. https://doi.org/10.7232/JKIIE.2013.39.5.361
  4. Barton, R.R. and K.-L. Tsui, "Multivariate yield maximization using CAD/CAE models:efficient approximations based on mean and variance," Design Theory and Methodology, Vol.31(1991), pp.31-35.
  5. Bazaraa, M.S., H.D. Sherali, and C.M. Shetty, Nonlinear programming:theory and algorithms, John Wiley and Sons, 2013.
  6. Bera, S. and I. Mukherjee, "An integrated approach based on principal component and multivariate process capability for simultaneous optimization of location and dispersion for correlated multiple response problems," Quality Engineering, Vol.25, No.3(2013), pp. 266-281. https://doi.org/10.1080/08982112.2013.765014
  7. Box, G.E. and N.R. Draper, Empirical modelbuilding and response surfaces, John Wiley and Sons, 1987.
  8. Derringer, G. and R. Suich, "Simultaneous optimization of several response variables," Journal of Quality Technology, Vol.12, No.4 (1980), pp.214-219. https://doi.org/10.1080/00224065.1980.11980968
  9. Derringer, G.C., "A balancing act-optimizing a products properties," Quality Progress, Vol. 27, No.6(1994), pp.51-58.
  10. Fogliatto, F.S. and S.L. Albin, "Variance of predicted response as an optimization criterion in multiresponse experiments," Quality Engineering, Vol.12, No.4(2000), pp.523-533. https://doi.org/10.1080/08982110008962618
  11. Geoffrion, A.M., J.S. Dyer, and A. Feinberg, "An interactive approach for multi-criterion optimization, with an application to the operation of an academic department," Management Science, Vol.19, No.4(1972), pp.357-368. https://doi.org/10.1287/mnsc.19.4.357
  12. Jeong, I.-J. and K.-J. Kim, "Interactive desirability function approach to multi-response surface optimization," International Journal of Reliability, Quality and Safety Engineering, Vol.10, No.2(2003), pp.205-217. https://doi.org/10.1142/S0218539303001093
  13. Jeong, I.-J. and K.-J. Kim, "An interactive desirability function method to multiresponse optimization," European Journal of Operational Research, Vol.195, No.2(2009), pp.412-426. https://doi.org/10.1016/j.ejor.2008.02.018
  14. Koksalan, M. and R.D. Plante, "Interactive multicriteria optimization for multiple-response product and process design," Manufacturing and Service Operations Management, Vol.5, No.4(2003), pp.334-347. https://doi.org/10.1287/msom.5.4.334.24886
  15. Khuri, A.I. and J.A. Cornell, Response surfaces: designs and analyses, CRC press, 1996.
  16. Kim, K.-J. and D.K. Lin, "Optimization of multiple responses considering both location and dispersion effects," European Journal of Operational Research, Vol.169, No.1(2006), pp.133-145. https://doi.org/10.1016/j.ejor.2004.06.020
  17. Kim, K.J. and D.K. Lin, "Simultaneous optimization of mechanical properties of steel by maximizing exponential desirability functions," Journal of the Royal Statistical Society: Series C(Applied Statistics), Vol.49, No.3 (2000), pp.311-325. https://doi.org/10.1111/1467-9876.00194
  18. Ko, Y.-H., K.-J. Kim, and C.-H. Jun, "A new loss function-based method for multiresponse optimization," Journal of Quality Technology, Vol.37, No.1(2005), pp.50-59. https://doi.org/10.1080/00224065.2005.11980300
  19. Korhonen, P., H. Moskowitz, and J. Wallenius, "Multiple criteria decision support-A review," European Journal of Operational Research, Vol.63, No.3(1992), pp.361-375. https://doi.org/10.1016/0377-2217(92)90155-3
  20. Lee, D.-H., K.-J. Kim, and M. Koksalan, "An interactive method to multiresponse surface optimization based on pairwise comparisons," IIE Transactions, Vol.44, No.1(2012), pp.13-26. https://doi.org/10.1080/0740817X.2011.564604
  21. Mollaghasemi, M. and G.W. Evans, "Multicriteria design of manufacturing systems through simulation optimization," IEEE Transactions on Systems, Man and Cybernetics, Vol.24, No.9(1994), pp.1407-1411. https://doi.org/10.1109/21.310518
  22. Montgomery, D.C. and V.M. Bettencourt, "Multiple response surface methods in computer simulation," Simulation, Vol.29, No.4 (1977), pp.113-121. https://doi.org/10.1177/003754977702900406
  23. Myers, R.H., D.C. Montgomery, and C.M. Anderson-Cook, Response surface methodology: process and product optimization using designed experiments, John Wiley and Sons, 2009.
  24. Park, K.S. and K.-J. Kim, "Optimizing multiresponse surface problems:how to use multiobjective optimization techniques," IIE Transactions, Vol.37, No.6(2005), pp.523-532. https://doi.org/10.1080/07408170590928992
  25. Park, K.S. and D.E. Shin, "Interactive multiobjective optimization approach to the inputoutput design of opening new branches," European Journal of Operational Research, Vol.220, No.2(2012), pp.530-538. https://doi.org/10.1016/j.ejor.2012.02.004
  26. Pignatiello Jr, J.J., "Strategies for robust multiresponse quality engineering," IIE transactions, Vol.25, No.3(1993), pp.5-15. https://doi.org/10.1080/07408179308964286
  27. Plante, R.D., "Multicriteria models for the allocation of design parameter targets," European Journal of Operational Research, Vol. 115, No.1(1999), pp.98-112. https://doi.org/10.1016/S0377-2217(98)00119-2
  28. Plante, R.D., "Process capability:a criterion for optimizing multiple response product and process design," IIE Transactions, Vol.33, No.6(2001), pp.497-509. https://doi.org/10.1080/07408170108936849
  29. Rees, L.P., E.R. Clayton, and B.W. Taylor, "Solving multiple response simulation models using modified response surface methodology within a lexicographic goal programming framework," IIE transactions, Vol.17, No.1(1985), pp.47-57. https://doi.org/10.1080/07408178508975271
  30. Roy, A. and J. Wallenius, "Nonlinear multiple objective optimization:An algorithm and some theory," Mathematical Programming, Vol.55, No.1/3(1992), pp.235-249. https://doi.org/10.1007/BF01581201
  31. Shah, H.K., D.C. Montgomery, and W.M. Carlyle, "Response surface modeling and optimization in multiresponse experiments using seemingly unrelated regressions," Quality Engineering, Vol.16, No.3(2004), pp.387-397. https://doi.org/10.1081/QEN-120027941
  32. Shin, W.S. and A. Ravindran, "Interactive multiple objective optimization:Survey IContinuous case," Computers and Operations Research, Vol.18, No.1(1991), pp.97-114. https://doi.org/10.1016/0305-0548(91)90046-T
  33. Vining, G.G., "A compromise approach to multiresponse optimization," Journal of Quality Technology, Vol.30, No.4(1998), pp.309-313. https://doi.org/10.1080/00224065.1998.11979867
  34. Wu, F.-C., "Optimization of correlated multiple quality characteristics using desirability function," Quality Engineering, Vol.17, No.1 (2004), pp.119-126. https://doi.org/10.1081/QEN-200028725
  35. Zellner, A., "An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias," Journal of the American statistical Association, Vol.57, No.298 (1962), pp.348-368. https://doi.org/10.1080/01621459.1962.10480664
  36. Zionts, S. and J. Wallenius, "An interactive programming method for solving the multiple criteria problem," Management Science, Vol. 22, No.6(1976), pp.652-663. https://doi.org/10.1287/mnsc.22.6.652