A Robust Desirability-based Approach to Optimizing Multiple Correlated Responses

There are many real problems in which multiple responses should be optimized simultaneously by setting of process variables. One of the most common approaches for optimization of multi-response problems is the desirability function. In most real cases, there is a correlation structure between responses; therefore, ignoring the correlation may lead to incorrect results. Hence, in the present paper a robust approach, based on desirability function is provided which can consider the correlation structure in the optimization of the responses. The current study mainly aims to synthesize the ideas considering correlation structure in robust optimization through defining joint confidence interval and desirability function methods. A genetic algorithm is employed to solve the introduced problem. We have tried to enhance the effectiveness of the proposed method through some computational examples and comparisons with previous methods which are incorporated to show the applicability of the proposed approach. Also, a sensitivity analysis is provided to show the relationship between correlation and robustness in these approaches.

[1]  Ali Salmasnia,et al.  Multiple response surface optimization with correlated data , 2013 .

[2]  J. Royston.  An Extension of Shapiro and Wilk's W Test for Normality to Large Samples , 1982 .

[3]  Saurav Datta,et al.  Application of PCA-based hybrid Taguchi method for correlated multicriteria optimization of submerged arc weld: a case study , 2009 .

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

[5]  Om Prakash Yadav,et al.  Reliability‐based robust design optimization: A multi‐objective framework using hybrid quality loss function , 2010, Qual. Reliab. Eng. Int..

[6]  Wen Wan,et al.  A semiparametric technique for the multi‐response optimization problem , 2011, Qual. Reliab. Eng. Int..

[7]  J. S. Ribeiro,et al.  Simultaneous optimization of the microextraction of coffee volatiles using response surface methodology and principal component analysis , 2010 .

[8]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[9]  Zhang Liu-yang,et al.  A modified particle swarm optimization algorithm for dynamic multiresponse optimization based on goal programming approach , 2014, 2014 International Conference on Management Science & Engineering 21th Annual Conference Proceedings.

[10]  Reza Baradaran Kazemzadeh,et al.  A novel approach for optimization of correlated multiple responses based on desirability function and fuzzy logics , 2012, Neurocomputing.

[11]  Susan L. Albin,et al.  Robust Optimization of Experimentally Derived Objective Functions , 2003 .

[12]  Erwin Stinstra,et al.  Robust Optimization Using Computer Experiments , 2005, Eur. J. Oper. Res..

[13]  Zhen He,et al.  A robust desirability function method for multi-response surface optimization considering model uncertainty , 2012, Eur. J. Oper. Res..

[14]  Jing Wang,et al.  Robust optimization for multiple responses using response surface methodology , 2010 .

[15]  M. Hamada,et al.  Analyzing Experiments with Correlated Multiple Responses , 2001 .

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

[17]  Yizhong Ma,et al.  Robust parameter design of dynamic multi‐response system: a new integrated method , 2011 .

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

[19]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[20]  Jafarian Jelodar Mostafa,et al.  A Hybrid Response Surface Methodology and Simulated Annealing Algorithm: A Case Study on the Optimization of Shrinkage and Warpage of a Fuel Filter , 2011 .

[21]  Weng Kee Wong,et al.  Balancing Location and Dispersion Effects for Multiple Responses , 2013, Qual. Reliab. Eng. Int..

[22]  G. Alistair Watson.  Robust counterparts of errors-in-variables problems , 2007, Comput. Stat. Data Anal..

[23]  Mahdi Bashiri,et al.  An Optimality Probability Index for Correlated Multiple Responses , 2014 .

[24]  John J. Peterson.  A Posterior Predictive Approach to Multiple Response Surface Optimization , 2004 .

[25]  Mojtaba Salehi,et al.  A robust interactive approach to optimize correlated multiple responses , 2013 .