Machine learning-based data-driven robust optimization approach under uncertainty

Abstract

On the basis of the machine learning ability to analyze massive data, we propose a new concept suitable for data-driven robust optimization, and design two new methods for constructing data-driven uncertainty sets. Partial least squares (PLS) or kernel principal component analysis (KPCA) is selected to capture the underlying uncertainties and correlation of uncertain data, and the projection of uncertain data on each principal component is obtained. Then, the probability distribution information of project data is extracted via robust kernel density estimation (RKDE). Considering the applicability of PLS to linear data for the idea of canonical correlation analysis and the bias of KPCA to nonlinear data due to kernel function, guidelines for selecting an appropriate method are presented in terms of the linear and nonlinear degree between data. The measurement indicators are Pearson correlation coefficient, mutual information and nonlinear coefficient. The induced robust counterpart framework not only alleviates excessive conservatism, but also significantly improves the robustness, which has the advantages of easy implementation and high computational efficiency. Through a numerical example and two application cases, the effectiveness of the proposed framework is illustrated.