Hedging Against Uncertainty in Process Planning: A Data-Driven Adaptive Nested Robust Optimization Approach

Abstract

Abstract We propose a data-driven adaptive robust optimization (ARO) framework that leverages big data in process 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 ARO. 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 further proposed for the resulting problem that cannot be solved directly by any off-the-shelf optimization solvers. The effectiveness and advantages of the framework and solution algorithm are demonstrated through an application in process network planning.