A Novel Weighted Data-Driven Robust Optimization Approach for Creating Adjustable Uncertainty Sets

Abstract

Robust optimization provides a progressive and efficient approach to dealing with uncertainty which applies to various optimization problems. However, most existing robust optimization approaches generate a unique uncertainty set for each level of conservatism, disregarding supplementary information such as predicted values. This paper proposes a new weighted data-driven robust optimization approach for creating adjustable uncertainty sets. The proposed approach enables the adjustment of the boundary reduction rate of uncertainty sets, effectively pulling uncertainty sets towards areas of higher density or towards the predicted points. Additionally, a multi-stage clustering algorithm is proposed to fully cover the areas around the predicted point. A regularization parameter search algorithm is also developed to tune the conservatism degree. The numerical results indicate that by weighting historical data, adjustable uncertainty sets with the same fraction of data coverage can be created that ensures the feasibility of the model and reduces the extra conservatism.