TA algorithms for D-optimal OofA Mixture designs

Abstract

In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. This classical experiment has been studied for a long time, but little attention has been given to the addition order of the components. In an Order-of-Addition (OofA) Mixture experiment, the response depends on both the mixture proportions of components and their order of addition. The overall goal of the OofA Mixture experiment is to identify the addition order and mixture proportions that produce an optimal response. Methodology for constructing full OofA Mixture designs is discussed, but the size of these full designs increases rapidly as m increases. A Threshold Accepting (TA) algorithm is used to find a subset of n rows of the full OofA Mixture design that maximize the D-optimality criterion, reducing the number of required runs. Neighborhood structures are proposed for OofA simplex lattice and general mixture designs. The TA algorithm is compared with the well-known Fedorov algorithm, and recommendations for the use of this algorithm are provided.