Optimal Design of Experiments for Nonlinear Response Surface Models

TL;DR

This paper develops a novel multiphase optimization method for designing D-optimal experiments in nonlinear response surface models, improving the informativeness of experimental designs in chemical engineering applications.

Contribution

It introduces a new multiphase algorithm for constructing D-optimal designs, outperforming traditional methods in nonlinear multifactor experiments.

Findings

The new method produces more informative experimental designs.

Application to chemical engineering experiments demonstrates improved design quality.

Designs obtained are significantly better than those from conventional algorithms.

Abstract

Many chemical and biological experiments involve multiple treatment factors and 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. 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 and coordinate exchange algorithms. Next, we develop a novel multiphase optimisation method to construct D-optimal designs with improved properties. The benefits of this method are demonstrated by application to two experiments involving nonlinear regression models. The designs obtained are shown to be considerably more informative than designs obtained using traditional design optimality algorithms.