When Robust Statistics Meets with Robust Optimization: Data-Driven Batch Process Scheduling in The Presence of Outliers

We propose a novel data-driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M-estimation. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over-conservatism. Robust kernel density estimation is employed to extract probability distributions from uncertainty data via a kernelized iteratively re-weighted least squares algorithm. A data driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, in order to organically integrate the multistage ARO framework With uncertainty data. Based on this uncertainty set, we further develop an exact robust counterpart in its general form. To illustrate the applicability of the proposed framework, an application in batch process scheduling is presented.