A novel approach for optimization of correlated multiple responses based on desirability function and fuzzy logics

Many real world applications consist of finding optimal inputs (design variables) to the system that yields in desirable values for stochastic outputs (Responses). Several studies in the literature have suggested approaches addressing these problems but most of them assume that the responses are independent and their variances are constant over the experimental space. Furthermore, in many situations the relationship between the response variables and design variables is too complex to be efficiently estimated using traditional surface fitting approaches. In this paper, a method is presented for optimizing the problem of correlated multiple responses where relationship among response and design variables is highly nonlinear by means of Neuro-Fuzzy and principal component analysis derived desirability function. As another advantage over existing works, we have relaxed the assumption that variance of each response is invariant over the feasible region. Finally, effectiveness of the proposed method is illustrated through a numerical example.