Using Geometric Mean To Compute Robust Mixture Designs

Abstract

Mixture experiments involve developing a dedicated formulation for specific applications. We propose the weighted D-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. This approach finds the design that minimizes the weighted average of the volume of the confidence hyperllipsoids across a set of reduced models. When specific terms in the initial model display insignificant 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 with an interior point are robust to model misspecification.