A semiparametric technique for the multi-response optimization problem

Multi-response optimization (MRO) in response surface methodology (RSM) is quite common in applications. Before the optimization phase, appropriate fitted models for each response are required. A common problem is model misspecification and occurs when any of the models built for the responses are misspecified resulting in an erroneous optimal solution. The model robust regression technique, a semiparametric method, has been shown to be more robust to misspecification than either parametric or nonparametric methods. In this study, we propose the use of model robust regression to improve the quality of model estimation and adapt its fits of each response to the desirability function approach, one of the most popular MRO techniques. A case study and simulation studies are presented to illustrate the procedure and to compare the semiparametric method with the parametric and nonparametric methods. The results show that model robust regression performs much better than the other two methods in terms of model comparison criteria in most situations during the modeling stage. In addition, the simulated optimization results for model robust regression are more reliable during the optimization stage.