In this paper, we consider experiments involving both discrete factors and continuous factors under general parametric statistical models. To search for optimal designs under the D-criterion, we propose a new algorithm, called the ForLion algorithm, which performs an exhaustive search in a design space with discrete and continuous factors while keeping high efficiency and a reduced number of design points. Its optimality is guaranteed by the general equivalence theorem. We show its advantage using a real-life experiment under multinomial logistic models, and further specialize the algorithm for generalized linear models to show the improved efficiency with model-specific formulae and iterative steps.
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