Robust Optimal Desirability Approach for Multiple Responses Optimization with Multiple Productions Scenarios

Document Type : Research Paper


shahed university


An optimal desirability function method is proposed to optimize multiple responses in multiple production scenarios, simultaneously. In dynamic environments, changes in production requirements in each condition create different production scenarios. Therefore, in multiple production scenarios like producing in several production lines with different technologies in a factory, various fitted response models are obtained for each response according to their related conditions. In order to consider uncertainty in these models, confidence interval of fitted responses has been defined in the proposed method. This method uses all values in the confidence region of model outputs to define the robustness measure. This method has been applied on the traditional desirability function of each scenario in order to get the best setting of controllable variables for all scenarios simultaneously. To achieve this, the Imperialist Competitive Algorithm has been used to find the robust optimal controllable factors setting. The reported results and analysis of the proposed method confirm efficiency of the proposed approach in a dynamic environment.


1. Atashpaz-Gargari, E. & Lucas, C. (2007). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialistic competition. Evolutionary Computation. CEC. IEEE Congress.
2. Bashiri, M. & Bagheri, M. (2013). "Using Imperialist competitive algorithm optimization in multi-response nonlinear programming."International Journal of Industiral Engineering & Producion Research, 24(3) 229-235.
3. Ch'ng, C., S. Quah & H. Low. (2005). "A new approach for multiple-response optimization."Quality Engineering, 17(4): 621-626.
4. Costa, N. R., J. Lourenço & Z. L. Pereira (2011). "Desirability function approach: A review and performance evaluation in adverse conditions."Chemometrics and Intelligent Laboratory Systems, 107(2) 234-244.
5. Das, P. & S. Sengupta. (2010). "Composite desirability index in cases of negative and zero desirability."Journal of Management Research, 10(1): 25-38.
6. Derringer, G. (1980). "Simultaneous optimization of several response variables."Journal of Quality Technology, 12(4): 214-219.
7. Derringer, G.C. (1994). "A balancing act-optimizing a products properties."Quality Progress, 27(6) 51-58.
8. Ghasemi, M., S. Ghavidel, M. M. Ghanbarian, H. R. Massrur & M. Gharibzadeh. (2014). "Application of imperialist competitive algorithm with its modified techniques for multi-objective optimal power flow problem: A comparative study."
Information Sciences, 281: 225-247.
9. He, Z., J. Wang, J. Oh & S. H. Park (2010). "Robust optimization for multiple responses using response surface methodology."Applied Stochastic Models in Business and Industry, 26(2) 157-171.
10. He, Z., P.F. Zhu & S.H. Park. (2012). "A robust desirability function method for multi-response surface optimization considering model uncertainty."European Journal of Operational Research, 221(1) 241-247.
11. Jeong, I.J. & K.J. Kim. (2003). "Interactive desirability function approach to multi-response surface optimization."
International Journal of Reliability, Quality and Safety Engineering, 10(02) 205-217.
12. Jeong, I.J. & K.J. Kim. (2009). "An interactive desirability function method to multiresponse optimization."European Journal of Operational Research, 195(2) 412-426.
13. Kim, K.J. & D. K. Lin. (2000). "Simultaneous optimization of mechanical properties of steel by maximizing exponential desirability functions."Journal of the Royal Statistical Society.Series C(Applied Statistics), 49(3) 311-325.
14. Lee, M.S. & K.J. Kim. (2007). "Expected desirability function: consideration of both location and dispersion effects in desirability function approach."Quality Technology & Quantitative Management, 4(3) 365-377.
15. Montgomery, D. C. (2005). Design and Analysis of Experiments, sixth ed. Wiley, New and York.
16. Ortiz, F., J. R. Simpson, J. J. Pignatiello & A. Heredia-Langner (2004). "A genetic algorithm approach to multiple-response optimization."Journal of Quality Technology, 36(4) 432-450.
17. Ribardo, C. & T. T. Allen (2003). "An alternative desirability function for achieving ‘six sigma’quality."Quality and Reliability Engineering International 19(3): 227-240.
18. Wu, F.C. (2004). "Optimization of correlated multiple quality characteristics using desirability function."Quality Engineering, 17(1) 119-126.