We show that the optimal exact design of experiment on a finite design space can be computed via mixed-integer linear programming (MILP) for a wide class of optimality criteria, including the criteria of A-, I-, G- and MV-optimality. The key idea of the MILP formulation is the McCormick relaxation, which critically depends on finite interval bounds for the elements of the covariance matrix corresponding to an optimal exact design. We provide both analytic and algorithmic constructions of such bounds. Finally, we demonstrate some unique advantages of the MILP approach and illustrate its performance in selected experimental design settings.

翻译：我们证明，在有限设计空间上，对于包括A-最优性、I-最优性、G-最优性和MV-最优性准则在内的广泛最优性准则类，最优精确实验设计可通过混合整数线性规划（MILP）计算得出。该MILP公式的关键在于McCormick松弛，而这一松弛的关键依赖于与最优精确设计对应的协方差矩阵元素上的有限区间界。我们提供了此类界的解析构造与算法构造。最后，我们展示了MILP方法的一些独特优势，并说明了其在选定实验设计场景中的性能表现。