Optimal design of mixture experiments
19 October 2015
University of Antwerp, Promotiezaal Grauwzusters - Lange Sint-Annastraat 7 - 2000 Antwerp
Utami Dyah Syafitri
Prof Peter Goos
PhD defence Utami Dyah Syafitri - Faculty of Applied Economics
A mixture experiment is an experiment in which the experimental factors are ingredients of a mixture, and the response depends only on the relative proportions of the ingredients. Special features of mixture experiments are the two main constraints that the levels of the experimental factors all lie between zero and one, and that the sum of the levels of all experimental factors is one.
In this dissertation, we discuss and address two main topics. The first topic is inspired by the fact that, although mixture experiments usually are intended to predict the response(s) for all possible formulations of the mixture and to identify optimal proportions for each of the ingredients, little research has been done concerning their I-optimal design. In this dissertation, we provide the first detailed overview of the literature on the I-optimal design of mixture experiments and identify several contradictions. We present I-optimal continuous designs for various Scheffé models and contrast them with the published results.
The second topic is related to additional constraints in mixture experiments. The problems are inspired by De Ketelaere, Goos, and Brijs (2011) who discuss a baking experiment. In some cases, the available stock of certain ingredients is limited. This type of constraint substantially complicates the search for optimal designs for mixture experiments. We propose a variable neighborhood descent algorithm to tackle the problem.
Another problem in the baking experiment is that, in order to create "new" flours to bake bread from, the experimenters not only used the pure flours but they also mixed the sample flours. The experiment was complicated because the chemical component proportions could not be manipulated directly, but only indirectly, by mixing the sample flours. To tackle the problem, we propose a modified coordinate-exchange algorithm.