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.

翻译：本文考虑一般参数统计模型中同时包含离散因子和连续因子的实验设计问题。为在D准则下搜索最优设计，我们提出了一种名为ForLion的新算法，该算法在包含离散与连续因子的设计空间中进行穷举搜索，同时保持高效率并减少设计点数量。通过一般等价定理保证了其最优性。我们通过一个多项逻辑斯蒂模型下的真实实验展示了该算法的优势，并进一步将其特化用于广义线性模型，通过模型特定公式与迭代步骤展现了效率提升。