Optimal Design of Nonlinear Multifactor Experiments
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Most chemical and biological experiments involve multiple treatment factors. Often, it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two, as long as it describes the unknown mechanism behind the response surface. Motivated by experiments in chemical engineering, we focus on D-optimal design for multifactor nonlinear response surfaces in general. In order to find and study optimal designs, we first implement conventional point (coordinate) exchange algorithms. Moreover, we develop a novel multiphase optimisation method to construct D-optimal designs with improved properties that are illustrated in our results. The benefits of this method are demonstrated by application to two experiments. For each case, highly efficient and feasible designs are found and tailored to the nonlinear regression models. Such designs can be easily used for comprehensive mechanism studies and are shown to be considerably more informative than standard designs.
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