We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the optimal wait-and-see decisions into what we denote as the strategy. We solve multiple similar ARO instances in advance using the column and constraint generation algorithm and extract the optimal strategies to generate a training set. We train a machine learning model that predicts high-quality strategies for the here-and-now decisions, the worst-case scenarios associated with the optimal here-and-now decisions, and the wait-and-see decisions. We also introduce an algorithm to reduce the number of different target classes the machine learning algorithm needs to be trained on. We apply the proposed approach to the facility location, the multi-item inventory control and the unit commitment problems. Our approach solves ARO problems drastically faster than the state-of-the-art algorithms with high accuracy.

翻译：本文提出了一种基于机器学习的方法，用于求解涉及二元“现时决策”变量和多面体不确定集的两阶段线性自适应鲁棒优化（ARO）问题。我们将最优现时决策、与最优现时决策相关的最坏场景以及最优“观望决策”编码为所谓的策略。我们预先使用列与约束生成算法求解多个相似的ARO实例，并提取最优策略以生成训练集。我们训练一个机器学习模型，该模型能预测现时决策的高质量策略、与最优现时决策相关的最坏场景以及观望决策。同时，我们引入了一种算法来减少机器学习算法需要训练的目标类别数量。我们将所提方法应用于设施选址、多商品库存控制及机组组合问题。实验表明，该方法在保持高精度的同时，求解ARO问题的速度显著优于现有最优算法。