Designing experiments for robust-optimization problems: the V s -optimality criterion

Abstract

We suggest an experimentation strategy for the robust design of empirically fitted models. The suggested approach is used to design experiments that minimize the variance of the optimal robust solution. The new design-of-experiment optimality criterion, termed V s-optimal, prioritizes the estimation of a model's coefficients, such that the variance of the optimal solution is minimized by the performed experiments. It is discussed how the proposed criterion is related to known optimality criteria. We present an analytical formulation of the suggested approach for linear models and a numerical procedure for higher-order or nonpolynomial models. In comparison with conventional robust-design methods, our approach provides more information on the robust solution by numerically generating its multidimensional distribution. Moreover, in a case study, the proposed approach results in a better robust solution in comparison with these standard methods.

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