Using a genetic algorithm to generate D s -optimal designs for mixture experiments in a simplex region

Abstract

We propose and develop a genetic algorithm(GA) to generate Ds-optimal or near-optimal mixture designs of a simplex region that maximizes the Ds-criterion while simultaneously guaranteeing an acceptable D-efficiency for the mixture experiments. Our method does not need a candidate set which makes it possible to select points throughout a continuous region. Two new GAs are developed to handle specific subsets of quadratic and special cubic mixture model terms. Summaries of GA designs are reported for 3 and 4 mixture components. The performance of GA designs is assessed in comparisons with the designs generated from an exchange algorithm (EA) and SAS Proc OPTEX computer generated designs (CGDs). The results show that the Ds-criterion values of the GA designs for all percentage of D-efficiency were greater than or equal to those of the EA and SAS Proc OPTEX designs(CGDs). This suggests that the GA is a effective method for generating subset optimal designs for mixture experiments.