Constructing model robust mixture designs via weighted G-optimality criterion

Abstract

We propose and develop a new G-optimality criterion using the concept of weighted optimality criteria and certain additional generalizations. The goal of the weighted G-optimality is to minimize a weighted average of the maximum scaled prediction variance in the design region over a set of reduced models. A genetic algorithm (GA) is used for generating the weighted G-optimal exact designs in an experimental region for mixtures. The performance of the proposed GA designs is evaluated and compared to the performance of the designs produced by our genetic algorithm and the PROC OPTEX exchange algorithm of SAS/QC. The evaluation demonstrates the advantages of GA designs over the designs generated using exchange algorithm, showing that the proposed GA designs have better model-robust properties and perform better than the designs generated by the PROC OPTEX exchange algorithm.