Decision making for interactive optimization of correlated desirability functions

Optimizing multi-response problems has become an increasingly relevant issue when more than one correlated product quality characteristic must be assessed simultaneously in a complicated manufacturing process. This study proposes new interactive multi criteria method for determining the best levels of the decision variables needed to simultaneously optimization of response variables. Initially principal component analysis (PCA) is conducted on the response values to obtain a set of uncorrelated component. Then, we obtain initial design solution by solving model which aims to identify control variables which minimizes maximal deviation of the normalized mean and the standard deviation of all the responses from their target values within the experimental region. In next step, the desirability functions of principal components are maximized using G-D-F algorithm. Finally optimal step size is obtained from technique for order preference by similarity to ideal solution (TOPSIS) and then if the new solution is not satisfactory this solution is improved by repeating algorithm.