Simultaneous Optimization of Response Surfaces: Using Variance Weighted Gradient

In the literature, several method for solving multiple response simultaneous optimizations problems have been adopted such as desirability function approach, weighted mean square error approach etc. In this study a variance weighted gradient approach is developed for a simultaneous optimization of an n-variate polynomial response functions defined on a single feasible region. This method uses properties of line-equations in obtaining the optimizers for each response function. These optimizers are successively added to the initial design points and the search continues. The addition of these points contributes to the quick convergence of the method to the desired optima. It was observed that, at each iteration, as the optimizers are added to the previous design, the variance functions decreases in all directions of search.