Interactive weighting of bias and variance in dual response surface optimization

In dual response surface optimization, minimizing weighted mean squared error (WMSE) is a simple yet effective way of obtaining a satisfactory solution. To minimize WMSE, the weights of the squared bias and variance should be determined in advance. Determining the weights in accordance with the decision maker (DM)'s preference structure regarding the tradeoffs between the two responses is critical and difficult. In this study, we develop an interactive weighting method where the DM provides his/her preference information in the form of pairwise comparisons. Our method estimates the weights based on the pairwise comparisons in an interactive manner. The method obtains a satisfactory solution through several pairwise comparisons in the case examples that we tested.

[1]  Derek J. Pike,et al.  Empirical Model‐building and Response Surfaces. , 1988 .

[2]  G. Geoffrey Vining,et al.  A Compromise Approach to Multiresponse Optimization , 1998 .

[3]  Young-Hyun Ko,et al.  A New Loss Function-Based Method for Multiresponse Optimization , 2005 .

[4]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[5]  Dennis K. J. Lin,et al.  Bayesian analysis for weighted mean‐squared error in dual response surface optimization , 2010, Qual. Reliab. Eng. Int..

[6]  R. L. Keeney,et al.  Decisions with Multiple Objectives: Preferences and Value Trade-Offs , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[7]  Byung Rae Cho,et al.  Robust design models for customer-specified bounds on process parameters , 2006 .

[8]  L. Tang,et al.  A Unified Approach for Dual Response Surface Optimization , 2002 .

[9]  Kwang-Jae Kim,et al.  A posterior preference articulation approach to dual-response-surface optimization , 2009 .

[10]  Dong-Hee Lee,et al.  A posterior preference articulation approach to multiresponse surface optimization , 2009, Eur. J. Oper. Res..

[11]  Joseph J. Pignatiello,et al.  STRATEGIES FOR ROBUST MULTIRESPONSE QUALITY ENGINEERING , 1993 .

[12]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

[13]  R. H. Myers,et al.  Response Surface Techniques for Dual Response Systems , 1973 .

[14]  Peter R. Nelson,et al.  Dual Response Optimization via Direct Function Minimization , 1996 .

[15]  C. Hwang.  Multiple Objective Decision Making - Methods and Applications: A State-of-the-Art Survey , 1979 .

[16]  Wanzhu Tu,et al.  Dual response surface optimization , 1995 .

[17]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[18]  新家 健精.  Decisions with Multiple Objectives Preferences and Value tradeoffs : by Ralph L. Keeney, Howard Raiffa John Willey , 1981 .

[19]  Murat Köksalan,et al.  Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions , 1995 .

[20]  In-Jun Jeong,et al.  Optimal Weighting of Bias and Variance in Dual Response Surface Optimization , 2005 .

[21]  Dennis K. J. Lin,et al.  Dual Response Surface Optimization: A Fuzzy Modeling Approach , 1998 .

[22]  G. Geoffrey Vining,et al.  Combining Taguchi and Response Surface Philosophies: A Dual Response Approach , 1990 .

[23]  C George,et al.  A Balancing Act: Optimizing a Product's Properties , 1994 .