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.

翻译：本文研究了在相当通用的参数统计模型下，同时包含离散与连续因子的实验设计问题。我们提出了一种名为ForLion的新算法，用于在D最优准则下搜索局部最优近似设计。该算法在混合因子的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。我们针对多项Logit模型（MLM）和广义线性模型（GLM）给出了相关理论结果，并通过MLM和GLM下的实际实验证明了本算法相较于现有先进设计算法的优越性。模拟研究表明，ForLion算法平均可减少25%的实验设置数量，或将设计的相对效率提升17.5%。本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，从而减少实验总成本。