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 machine learning models that predict 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. The models can be applied to problems with varying dimensions. We also introduce novel methods to expedite training data generation and 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.

中文翻译：

---

两阶段自适应鲁棒优化的机器学习方法


我们提出了一种基于机器学习的方法来解决具有二元此时此地变量和多面体不确定性集的两阶段线性自适应鲁棒优化（ARO）问题。我们将此时此刻的最佳决策、与此时此刻的最佳决策相关的最坏情况以及最佳观望决策编码为我们所说的策略。我们使用列和约束生成算法提前解决多个相似的 ARO 实例，并提取最优策略来生成训练集。我们训练机器学习模型，预测此时此刻决策的高质量策略、与最佳此时此刻决策相关的最坏情况场景以及观望决策。这些模型可以应用于不同维度的问题。我们还引入了新的方法来加快训练数据的生成并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、多项目库存控制和单位承诺问题。我们的方法解决 ARO 问题的速度比最先进的算法快得多，并且具有高精度。