Computing efficient exact designs of experiments using integer quadratic programming

We propose a method of computing exact experimental designs by integer quadratic programming. The key idea is a suitable quadratic approximation of the criterion of D-optimality in the neighbourhood of the approximate D-optimal information matrix, which we call the criterion of Q-optimality. We demonstrate on several examples that the D-efficiency of the exact Q-optimal designs is usually very high. An important advantage of the method is that it can be applied to situations with marginal and cost constraints on the design.