Leveraging big data for adaptive robust optimization of scheduling under uncertainty

Abstract

In this paper, we propose a data-driven outlier-insensitive adaptive robust optimization framework that leverages big data in industries. A Bayesian nonparametric model - the Dirichlet process mixture model - is adopted to extract the information embedded within uncertainty data via a variational inference algorithm. We then devise data-driven uncertainty sets for adaptive robust optimization. This Bayesian nonparametric model is seamlessly integrated with adaptive optimization approach through a novel four-level robust optimization framework. This framework explicitly considers the correlation, asymmetry and multimode of uncertainty data, and as a result generates less conservative solutions. Additionally, this framework is robust not only to parameter variations, but also to data outliers. An efficient tailored column-and-constraint generation algorithm is proposed for the resulting problem that cannot be solved by any off-the-shelf optimization solvers. The effectiveness and advantages of the modeling framework and solution algorithm are demonstrated through an industrial application in batch process scheduling.