A non‐approximate method for generating G$G$‐optimal RSM designs

Abstract

We present a nonapproximate computational method for generating ‐optimal designs in response surface methodology (RSM) settings using Gloptipoly, a global polynomial optimizer. Traditional approaches use a grid approximation for computing a candidate design's ‐score. Gloptipoly can find the global optimum of high‐order polynomials thus making it suitable for computing a design's ‐score, that is, its maximum scaled prediction variance, which, for second‐order models, is a quartic polynomial function of the experimental factors. We demonstrate the efficacy and performance of our method through comprehensive application to well‐published examples, and illustrate, for the first time, its application to generating ‐optimal designs supporting models of order greater than 2. This work represents the first non‐approximate computational approach to solving the ‐optimal design problem. This advancement opens new possibilities for finding ‐optimal designs beyond second‐order RSM models.