Optimal design of multifactor experiments via grid exploration

We propose an algorithm for computing efficient approximate experimental designs that can be applied in the case of very large grid-like design spaces. Such a design space typically corresponds to the set of all combinations of multiple genuinely discrete factors or densely discretized continuous factors. The proposed algorithm alternates between two key steps: (1) the construction of exploration sets composed of star-shaped components and separate, highly informative design points and (2) the application of a conventional method for computing optimal approximate designs on medium-sized design spaces. For a given design, the star-shaped components are constructed by selecting all points that differ in at most one coordinate from some support point of the design. Because of the reliance on these star sets, we call our algorithm the galaxy exploration method (GEX). We demonstrate that GEX significantly outperforms several state-of-the-art algorithms when applied to D-optimal design problems for linear, generalized linear and nonlinear regression models with continuous and mixed factors. Importantly, we provide a free R code that permits direct verification of the numerical results and allows researchers to easily compute optimal or nearly optimal experimental designs for their own statistical models.