Stochastic coordinate-exchange optimal designs with complex constraints

Abstract The paper provides a method to construct the exact optimal experimental designs for both physical and computer experiments with any regular or irregularly constrained design space. We modify the original greedy coordinate-exchange algorithm into the stochastic version by adding the random selection of the “bad” coordinates that can be exchanged for “better” values to improve the optimal design criterion. More importantly, we adapt it to accommodate the non-convex or disconnected constrained design space. We implement the stochastic coordinate-exchange (SCE) algorithm for D- and linear- (A- and I-) optimal designs for physical experiments, and -optimal space-filling designs for computer experiments.

**摘要**：本文提供了一种为具有任何规则或不规则约束设计空间的物理实验和计算机实验构建精确最优实验设计的方法。我们通过添加对可交换为“更好”值的“不良”坐标的随机选择，将原始的贪心坐标交换算法修改为随机版本，以改进最优设计准则。更重要的是，我们对其进行调整以适应非凸或不连通的约束设计空间。我们针对物理实验的D - 最优和线性（A - 和I - ）最优设计以及计算机实验的最优空间填充设计实现了随机坐标交换（SCE）算法。