A novel set-induced robust optimization model under correlated uncertainty: a comparative theoretical and computational study

Abstract

In practical scenarios, optimization problems frequently involve uncertain parameters that exhibit correlated fluctuations. The widely adopted set-induced robust optimization approach is employed to address correlated uncertainty in environments with limited data. This approach focuses on deriving a deterministic reformulation of the original uncertain optimization problem, ensuring that the constructed solution remains feasible for all potential realizations of input parameters within a predefined uncertainty set. However, this approach often yields overly conservative solutions. In this study, an innovative uncertainty set is developed to mitigate the over-conservatism associated with the set-induced robust optimization approach under correlated uncertainty. Moreover, from the proposed description of data uncertainty, a robust linear reformulation of the original uncertain optimization problem is established to strike a balance between conservativeness and optimality. Computational studies exploring production planning optimization programs demonstrate the superior performance of the proposed robust model over other alternatives, considering various levels of correlation among uncertain parameters.