  In this paper, we address the problem of designing an experimental plan with
both discrete and continuous factors under fairly general parametric
statistical models. We propose a new algorithm, named ForLion, to search for
locally optimal approximate 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
present the relevant theoretical results for multinomial logit models (MLM) and
generalized linear models (GLM), and demonstrate the superiority of our
algorithm over state-of-the-art design algorithms using real-life experiments
under MLM and 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.
