Fast Computation of Exact G-Optimal Designs Via I_λ-Optimality

Exact G-optimal designs have rarely, if ever, been employed in practical applications. One reason for this is that, due to the computational difficulties involved, no statistical software system currently provides capabilities for constructing them. Two algorithms for exact G-optimal design construction of small designs involving one to three factors have been discussed in the literature: one employing a genetic algorithm and one employing a coordinate-exchange algorithm. However, these algorithms are extremely computer intensive in small experiments and do not scale beyond two or three factors. In this article, we develop a new method for constructing exact G-optimal designs using the integrated variance criterion, I_λ-optimality. We show that with careful selection of the weight function, a difficult exact G-optimal design construction problem can be converted to an equivalent exact I_λ-optimal design problem, which is easily and quickly solved. We illustrate the use of the algorithm for full quadratic models in one to five factors. The MATLAB codes used to implement our algorithm and the exact G-optimal designs produced by the algorithm for each test case are available online as supplementary material.