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.