Robust optimization under correlated uncertainty: Formulations and computational study

•Modeling of uncertainty correlations in robust optimization framework.•Derived robust optimization formulations under various types of uncertainty set.•Computational studies demonstrate the advantage of correlation modeling.

The uncertainty set-induced robust optimization framework has received considerable attention in the past decades. It has been extensively studied in literature and applied to address various decision-making problems. However, existing robust optimization methods generally assume that the uncertain parameters are independent. As a result, the traditional robust optimization methods may lead to a conservative solution in practice when correlations between uncertain parameters exist. In this work, we present novel results on robust optimization under correlated uncertainties that appear in a single constraint. Robust counterpart optimization formulations are derived based on various types of uncertain sets. Numerical and application examples are studied to compare the performance of robust optimization by incorporating various levels of correlation. The results demonstrate that incorporating more accurate correlation into the robust optimization formulation can lead to less conservative robust solution.