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Recognizing and hedging uncertainty by novel integrated algorithms: Validated by data-driven robust optimization
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DOI：10.1016/j.cor.2025.107364.png)
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Abstract
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Depicting and hedging uncertainty in practice are still challenging in operational research and the related fields, aiming at making ‘optimal’ decisions in an uncertain environment. In views of robustness and conservatism, robust optimization (RO) and distributionally robust optimization (DRO) are among existing popular approaches, displaying their respective advantages in terms of applicability and computability. In this paper, a novel data-driven multi-center uncertainty set is proposed to describe uncertainty. Instead of a pre-specified one, our uncertainty sets are constructed directly from data by integrating two machine-learning methods and the cutting plane strategy. Specifically, nonnegative matrix factorization (NMF), as an unsupervised learning technique, is leveraged to identify potential multi-center feature of data. The kernel-density-estimation method (KDE) is employed to adaptively capture the distributional information of each data cluster, and cutting planes are used to further tighten the uncertainty set by removing the redundant empty regions. Efficiency and superiority of such an uncertainty set over existing methods are demonstrated by the numerical simulation and the nice properties of its induced RO models, maintaining two salient advantages of RO and DRO: Computational tractability of RO and the ability of DRO in utilizing distributional structure. For example, it can efficiently identify the outliers in data and the samples in minority clusters; All the induced RO models can be efficiently solved, and achieve similar robustness and conservatism to those by the DRO method within much less computing time. Application in management problems of green hydrogen supply chains with uncertain demand and carbon cap-and-trade policy further validates the practical values of the induced RO method.
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