ForLion: A New Algorithm for D-optimal Designs under General Parametric Statistical Models with Mixed Factors

In this paper, we address the problem of designing an experiment with both discrete and continuous factors under fairly general parametric statistical models. We propose a new algorithm, named ForLion, to search for optimal designs under the D-criterion. The algorithm performs an exhaustive search in a design space with mixed factors while keeping high efficiency and reducing the number of distinct experimental settings. Its optimality is guaranteed by the general equivalence theorem. We demonstrate its superiority over state-of-the-art design algorithms using real-life experiments under multinomial logistic models (MLM) and generalized linear models (GLM). Our simulation studies show that the ForLion algorithm could reduce the number of experimental settings by 25% or improve the relative efficiency of the designs by 17.5% on average. Our algorithm can help the experimenters reduce the time cost, the usage of experimental devices, and thus the total cost of their experiments while preserving high efficiencies of the designs.