Optimal design of experiments for non-linear response surface models

Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a non-linear model in these factors. This non-linear model can be mechanistic, empirical or a hybrid of the two. Motivated by experiments in chemical engineering, we focus on D-optimal designs for multifactor non-linear response surfaces in general. To find and study optimal designs, we first implement conventional point and co-ordinate exchange algorithms. Next, we develop a novel multiphase optimization method to construct D-optimal designs with improved properties. The benefits of this method are demonstrated by application to two experiments involving non-linear regression models. The designs obtained are shown to be considerably more informative than designs obtained by using traditional design optimality algorithms.