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.

翻译：本文研究了在相当一般参数统计模型下设计包含离散与连续因子实验的问题。我们提出了一种名为ForLion的新算法，用于搜索满足D准则的最优设计。该算法在混合因子设计空间中进行穷举搜索，同时保持高效率并减少不同实验设置的数量。其最优性由一般等价定理保证。我们通过多项逻辑模型（MLM）和广义线性模型（GLM）的实际实验，证明了该算法相较于现有最优设计算法的优越性。仿真研究表明，ForLion算法可将实验设置数量平均减少25%，或将设计相对效率平均提升17.5%。该算法有助于实验者在保持设计高效率的同时，降低时间成本、实验设备使用量及实验总成本。