Design space definition is one of the key parts in pharmaceutical research and development. In this article, we propose a novel solution strategy to explicitly describe the design space without recourse decisions. First, to smooth the boundary, the Kreisselmeier–Steinhauser (KS) function is applied to aggregate all inequality constraints. Next, for creating a surrogate polynomial model of the KS function, we focus on finding sampling points on the boundary of KS space. After performing Latin hypercube sampling (LHS), two methods are presented to efficiently expand the boundary points, that is, line projection to the boundary through any two feasible LHS points and perturbation around the adaptive sampling points. Finally, a symbolic computation method, cylindrical algebraic decomposition, is applied to transform the surrogate model into a series of explicit and triangular subsystems, which can be converted to describe the KS space. Two case studies show the efficiency of the proposed algorithm.

中文翻译：

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通过自适应采样和符号计算设计空间描述

设计空间定义是药物研发的关键部分之一。在本文中，我们提出了一种新颖的解决方案策略来明确描述设计空间而无需追索决策。首先，为了平滑边界，应用 Kreisselmeier-Steinhauser (KS) 函数来聚合所有不等式约束。接下来，为了创建 KS 函数的代理多项式模型，我们专注于在 KS 空间的边界上寻找采样点。在执行拉丁超立方体采样（LHS）之后，提出了两种有效扩展边界点的方法，即通过任意两个可行的LHS点向边界线投影和自适应采样点周围的扰动。最后，一种符号计算方法，圆柱代数分解，用于将代理模型转化为一系列显式和三角形的子系统，这些子系统可以转换为描述 KS 空间。两个案例研究表明了所提出算法的效率。