Mixed-integer linear programming for computing optimal experimental designs

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.