A GLOBAL OPTIMIZATION METHOD FOR MULTIPLE RESPONSE OPTIMIZATION PROBLEMS

The multiple response optimization problem has been studied extensively. However, most existing methods only find locally optimal solutions to the concerned optimization problem. Several methods were proposed which tried to find a globally optimal solution of the problem, but there is no theoretical guarantee to obtain a globally optimal solution. In this paper, we investigate a global optimization method for the problem of a chemical process studied by Myers et al. which involves two input variables and three responses of interest. Based on the fitted polynomial functions of three responses, this multiple response problem is reformulated as a polynomial optimization problem where the primary response is objective while the other responses are put into constraints. We obtain a globally optimal solution to the concerned polynomial optimization problem when requirements of non-primary responses and experimental region are given. The satisfactory optimal designs can be obtained by adjusting non-primary responses appropriately. The method we proposed can be implemented easily, and it obtains a globally optimal solution to the multiple response optimization problem we considered.