New approach to robustness-based optimization with probabilistic representation of uncertainty set constructed using machine learning

Abstract

A machine learning prediction-based uncertainty set construction method is developed for capturing the true realization of uncertain variables in robustness-based optimization. A unified probabilistic approach is used in this thesis to quantify the uncertainty regardless of its form – sparse point and/or interval data to achieve better computational efficiency. Classically, the uncertainty set for robust optimization is simply chosen using expert opinion, or it might be anticipated in overly simplistic ways based on strong assumptions, whereas in this thesis, the uncertainty set is learned from complex past data. The proposed method uses machine learning prediction algorithms to construct different types of uncertainty sets containing all possible types of uncertainties in the form of sparse point and/or interval data. This thesis proposes to use a moment bounding approach to estimate the first and second moment bounds of the uncertain variables that are used as the uncertainty descriptors of the uncertainty set containing interval data. For uncertainty sets containing the mixture of point and interval data or only point data, this thesis proposes to use a worst-case maximum likelihood-based approach for the estimation of distribution parameters as well as the mean and the variance of the uncertainty set. A minimum variance portfolio optimization problem and a robustness-based multidisciplinary optimization problem are illustrated using the proposed algorithms. The numerical illustration consistently exhibited improved results in terms of portfolio risk and return compared to the existing methodologies. Several other comparative studies are also presented to demonstrate the relative attractiveness of the proposed methodologies.