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

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