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.

基于机器学习的方法解决了具有二阶段线性适应鲁棒优化问题中的两个关键问题：二值即时变量和多面体不确定性集。我们通过将最优即时决策、与最优即时决策相关的最差情况以及最优观望决策编码为策略来进行求解。使用列生成和约束生成算法为多个相似的适应鲁棒优化实例提供预先求解，并提取最优策略生成训练集。我们训练了一个机器学习模型，该模型用于预测即时决策、与最优即时决策相关的最差情况以及观望决策的高质量策略。我们还介绍了一种算法来减少机器学习算法需要训练的不同目标类别的数量。我们将所提出的方法应用于设施选址、多项存货控制和机组投资问题，相比于最先进的算法，我们的方法在极短的时间内以高准确性解决了适应鲁棒优化问题。