Optimization of Weighted Correlated Multiple Responses Using a probabilistic index

Dealing with more than one response in the process optimization is a great issue in these recent years, so multiple response optimization studies have been grown in the published works. In the common problems, there are some input variables which can affect output responses but optimization can be more complex and more real when the responses have correlation with each other. In such problems analyst should consider the correlation structure in addition to input variables effects. In some cases, responses variables may emerge from another distributions rather than normal in which can be analyzed by the proposed method. Moreover, in some problems, response variables may have different importance for the decision maker. In this study, we try to propose an efficient method to find the best treatment in an experimental design which its correlated responses have different weights, either cardinal or ordinal ones. Also a heuristic method was proposed to deal with problems that have considerable number of correlated responses or treatments. The results of some numerical examples confirm the validity of the proposed method. Moreover a real case about Tehran air pollution is studied to show theapplicability of the proposed method in the real problems.