Data-driven contextual robust optimization based on support vector clustering

Abstract

Support vector clustering (SVC) is an effective data-driven method to construct uncertainty sets in robust optimization (RO). However, it cannot appropriately address varying uncertainty in a contextually uncertain environment. In this work, we propose a new contextual RO (CRO) scheme, where an efficient contextual uncertainty set called kNN-SVC is developed to capture the correlation between covariates and uncertainty. Using the k-nearest neighbors (kNN) to select a subset of historical observations, contextual information can be integrated into SVC uncertainty sets, thereby alleviating conservatism while inheriting merits of SVC such as polytopic representability and ease of manipulating robustness. Besides, using only a fraction of data samples ensures low computational costs. Numerical examples demonstrate the performance improvement of the proposed kNN-SVC uncertainty set over conventional sets without considering contextual information. An industrial case of gasoline blending shows the usefulness of the proposed approach in producing robust decisions against linearization errors in nonlinear blending.