Using geometric mean to compute robust mixture designs

Mixture experiments involve developing a dedicated formulation for specific applications. We propose the weighted optimality criterion using the geometric mean as the objective function for the genetic algorithms. We generate a robust mixture design using genetic algorithms (GAs) of which the region of interest is an irregularly shaped polyhedral region formed by constraints on proportions of the mixture component. When specific terms in the initial model display unimportant effects, it is assumed that they are removed. The design generation objective requires model robustness across the set of the reduced models of the design. Proposing an alternative way to tackle the problem, we find that the proposed GA designs based on G- or/and IV-efficiency are robust to model misspecification.