Multiresponse Optimization and Pareto Frontiers

Methods that can capture evenly distributed solutions along the Pareto frontier are useful for multiresponse optimization problems because they provide a large variety of alternative solutions to the decision maker from among a set of nondominated solutions. However, methods often used for optimizing dual and multiple dual response problems have been rarely evaluated in terms of their ability to capture those solutions. This article provides this information by evaluating a global criterion–based method and the popular weighted mean square error method. Convex and nonconvex response surfaces were considered, and results of the methods were compared with those of a lexicographic approach on the basis of two examples from the literature. Regarding the results, it is shown that the user can be successful in capturing Pareto solutions in convex and nonconvex regions using the global criterion–based method. Moreover, it is shown that the starting point affects the distribution of solutions along the Pareto frontier but is not pivotal to obtain a complete representation of the Pareto frontier. For this purpose, it is necessary to decrease the weight increment and to compute for more solutions. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  Kwang-Jae Kim,et al.  Optimizing multi-response surface problems: How to use multi-objective optimization techniques , 2005 .

[2]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[3]  Srikrishna Madhumohan Govindaluri,et al.  Robust design modeling with correlated quality characteristics using a multicriteria decision framework , 2007 .

[4]  Nuno Ricardo Costa,et al.  Desirability function approach: A review and performance evaluation in adverse conditions , 2011 .

[5]  S. Masala,et al.  Product/process improvement by integrated physical and simulation experiments: a case study in the textile industry , 2008, Qual. Reliab. Eng. Int..

[6]  A. Bessaudou,et al.  Calculation of weights from equal satisfaction surfaces , 2008 .

[7]  N. Doganaksoy,et al.  Joint Optimization of Mean and Standard Deviation Using Response Surface Methods , 2003 .

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

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

[10]  Reza Baradaran Kazemzadeh,et al.  PROMETHEE: A comprehensive literature review on methodologies and applications , 2010, Eur. J. Oper. Res..

[11]  Daniel D. Frey,et al.  Adaptive One-Factor-at-a-Time Experimentation and Expected Value of Improvement , 2006, Technometrics.

[12]  Surajit Pal,et al.  Multi-Response Optimization Using Multiple Regression–Based Weighted Signal-to-Noise Ratio (MRWSN) , 2010 .

[13]  Ray D. Rhew,et al.  Adapting second-order response surface designs to specific needs , 2008, Qual. Reliab. Eng. Int..

[14]  Heidi A. Taboada,et al.  Multi-objective scheduling problems: Determination of pruned Pareto sets , 2008 .

[15]  Dennis K. J. Lin,et al.  Dual-Response Surface Optimization: A Weighted MSE Approach , 2004 .

[16]  A. Messac,et al.  Required Relationship Between Objective Function and Pareto Frontier Orders: Practical Implications , 2001 .

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

[18]  Christine M. Anderson-Cook,et al.  A Graphical Approach for Assessing Optimal Operating Conditions in Robust Design , 2009 .

[19]  Wei Chen,et al.  Exploration of the effectiveness of physical programming in robust design , 2000 .

[20]  Onur Köksoy,et al.  A nonlinear programming solution to robust multi-response quality problem , 2008, Appl. Math. Comput..

[21]  Martín Tanco,et al.  Practical applications of design of experiments in the field of engineering: a bibliographical review , 2008, Qual. Reliab. Eng. Int..

[22]  Byung Rae Cho,et al.  Studies on a biobjective robust design optimization problem , 2009 .

[23]  Daniele Romano,et al.  Robust design via simulation experiments: a modified dual response surface approach , 2008, Qual. Reliab. Eng. Int..

[24]  Dylan Jones,et al.  A practical weight sensitivity algorithm for goal and multiple objective programming , 2011, Eur. J. Oper. Res..

[25]  Alejandro Heredia-Langner,et al.  A Genetic Algorithm Approach to Multiple-Response Optimization , 2004 .

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

[27]  John J. Peterson,et al.  A Bayesian Reliability Approach to Multiple Response Optimization with Seemingly Unrelated Regression Models , 2009 .

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

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

[30]  R. Marler,et al.  Function-transformation methods for multi-objective optimization , 2005 .

[31]  Dennis K. J. Lin,et al.  Optimization of multiple responses considering both location and dispersion effects , 2006, Eur. J. Oper. Res..

[32]  Nuno Ricardo Costa,et al.  Multiple response optimization: a global criterion‐based method , 2010 .

[33]  In-Jun Jeong,et al.  An interactive desirability function method to multiresponse optimization , 2009, Eur. J. Oper. Res..

[34]  Ralph E. Steuer,et al.  An interactive weighted Tchebycheff procedure for multiple objective programming , 1983, Math. Program..

[35]  Dennis K. J. Lin,et al.  Multiresponse systems optimization using a goal attainment approach , 2004 .

[36]  Patrick Guillaume,et al.  Robust optimization of an airplane component taking into account the uncertainty of the design parameters , 2009, Qual. Reliab. Eng. Int..

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

[38]  Lee-Ing Tong,et al.  Optimization of multi-response processes using the VIKOR method , 2007 .

[39]  Byung Rae Cho,et al.  Development of a sequential optimization procedure for robust design and tolerance design within a bi-objective paradigm , 2008 .

[40]  Anthony C. Atkinson,et al.  Multiresponse optimization with consideration of probabilistic covariates , 2011, Qual. Reliab. Eng. Int..

[41]  R. Marler,et al.  The weighted sum method for multi-objective optimization: new insights , 2010 .

[42]  Ali Haydar Kayhan,et al.  Hybridizing the harmony search algorithm with a spreadsheet ‘Solver’ for solving continuous engineering optimization problems , 2009 .

[43]  Kwang-Jae Kim,et al.  A case study on modeling and optimizing photolithography stage of semiconductor fabrication process , 2010, Qual. Reliab. Eng. Int..

[44]  Zuomin Dong,et al.  Trends, features, and tests of common and recently introduced global optimization methods , 2010 .

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

[46]  Glynn J. Sundararaj,et al.  Ability of Objective Functions to Generate Points on Nonconvex Pareto Frontiers , 2000 .

[47]  Byung Rae Cho,et al.  Another view of dual response surface modeling and optimization in robust parameter design , 2009 .

[48]  Janet K. Allen,et al.  A review of robust design methods for multiple responses , 2005 .

[49]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[50]  Paul L. Goethals,et al.  The development of a robust design methodology for time‐oriented dynamic quality characteristics with a target profile , 2011, Qual. Reliab. Eng. Int..

[51]  Chiuh-Cheng Chyu,et al.  Optimization of robust design for multiple quality characteristics , 2004 .

[52]  Achille Messac,et al.  MULTIOBJECTIVE OPTIMIZATION: CONCEPTS AND METHODS , 2007 .

[53]  Juscelino Almeida Dias,et al.  Laboratoire D'analyse Et Modélisation De Systèmes Pour L'aide À La Décision Cahier Du Lamsade 274 Electre Tri-c: a Multiple Criteria Sorting Method Based on Characteristic Reference Actions Electre Tri-c: a Multiple Criteria Sorting Method Based on Characteristic Reference Actions , 2022 .

[54]  Kathrin Klamroth,et al.  Norm-based approximation in multicriteria programming , 2002 .

[55]  R. F. Scrutton DEFORMATION IN THE SHEAR ZONE IN METAL CUTTING, A COMPARATIVE REVIEW , 1965 .

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

[57]  Mahdi Bashiri,et al.  A general framework for multiresponse optimization problems based on goal programming , 2008, Eur. J. Oper. Res..

[58]  Wei Chen,et al.  Quality utility : a Compromise Programming approach to robust design , 1999 .

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