This paper proposes a novel data-driven robust optimization framework that leverages the power of machine learning and big data analytics for decision-making under uncertainty. By applying principal component analysis to uncertainty data, correlations between uncertain parameters are effectively captured, and latent uncertainty sources are identified. These data are then projected onto each principal component to facilitate extracting distributional information of latent uncertainties using kernel density estimation techniques. To explicitly account for asymmetric distributions, we introduce forward and backward deviation vectors into the data-driven uncertainty set, which are further incorporated into novel data-driven static and adaptive robust optimization models. The proposed framework not only significantly ameliorates the conservatism of robust optimization, but also enjoys computational efficiency and wide-ranging applicability. Three applications on optimization under uncertainty, including model predictive control, batch production scheduling, and process network planning, are presented to demonstrate the applicability of the proposed framework.

本文提出了一种新颖的数据驱动的鲁棒性优化框架，该框架利用机器学习和大数据分析的力量来进行不确定性下的决策。通过将主成分分析应用于不确定性数据，可以有效地捕获不确定性参数之间的相关性，并确定潜在的不确定性源。然后将这些数据投影到每个主成分上，以利于使用核密度估计技术提取潜在不确定性的分布信息。为了明确说明不对称分布，我们将前向和后向偏差矢量引入数据驱动的不确定性集中，然后进一步将其纳入新颖的数据驱动的静态和自适应鲁棒优化模型。所提出的框架不仅显着改善了鲁棒优化的保守性，而且具有计算效率和广泛的适用性。提出了在不确定性条件下进行优化的三种应用，包括模型预测控制，批生产计划和过程网络计划，以证明所提出框架的适用性。