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