Robust multi-response surface optimization: a posterior preference approach

This paper discusses the use of multi-response surface optimization (MRSO) to select the preferred solutions from among various non-dominated solutions (NDS). Since MSRO often involves conflicting responses, the decision-maker's (DM) preference information should be included in the model in order to choose the preferred solutions. In some approaches this information is added to the model after the problem is solved. In contrast, this paper proposes a three-stage method for solving the problem. In the first stage, a robust approach is used to construct a regression model. In the second phase, non-dominated solutions are generated by the ε-constraint approach. The robust solutions obtained in the third phase are NDS that are more likely to be Pareto solutions during consecutive iterations. A simulation study is then presented to show the effective performance of the proposed approach. Finally, a numerical example from the literature is brought in to demonstrate the efficiency and applicability of the proposed methodology.