Using a Modified Genetic Algorithm to Find Feasible Regions of a Desirability Function

The multi-response optimization (MRO) problem in response surface methodology is quite common in applications. Most of the MRO techniques such as the desirability function method by Derringer and Suich are utilized to find one or several optimal solutions. However, in fact, practitioners usually prefer to identify all of the near-optimal solutions, or all feasible regions, because some feasible regions may be more desirable than others based on practical considerations. In this paper, with benefits from the stochastic property of a genetic algorithm (GA), we present an innovative procedure using a modified GA (MGA), a computational efficient GA with a local directional search incorporated into the GA process, to approximately generate all feasible regions for the desirability function without the limitation of the number of factors in the design space. The procedure is illustrated through a case study. The MGA is also compared to other commonly used methods for determining the set of feasible regions. Using Monte Carlo simulations with two benchmark functions and a case study, it is shown that the MGA can more efficiently determine the set of feasible regions than the GA, grid methods, and the Nelder-Mead simplex algorithm.