Two-stage robust optimization problems constitute one of the hardest optimization problem classes. One of the solution approaches to this class of problems is K-adaptability. This approach simultaneously seeks the best partitioning of the uncertainty set of scenarios into K subsets, and optimizes decisions corresponding to each of these subsets. In general case, it is solved using the K-adaptability branch-and-bound algorithm, which requires exploration of exponentially-growing solution trees. To accelerate finding high-quality solutions in such trees, we propose a machine learning-based node selection strategy. In particular, we construct a feature engineering scheme based on general two-stage robust optimization insights that allows us to train our machine learning tool on a database of resolved B&B trees, and to apply it as-is to problems of different sizes and/or types. We experimentally show that using our learned node selection strategy outperforms a vanilla, random node selection strategy when tested on problems of the same type as the training problems, also in case the K-value or the problem size differs from the training ones.
翻译:两阶段强力优化问题构成了最难处理的问题类别之一。 解决这类问题的方法之一是 K 适应性。 这个方法同时寻求将不确定的情景组合最佳地分成K子集,并优化与这些子集相应的决定。 一般来说,它使用K适应性分支和约束算法来解决,这需要探索指数增长的解决方案树。 为了加速在这种树上找到高质量的解决方案,我们提出了一个基于机器学习的节点选择战略。 特别是,我们根据一般的两阶段强力优化洞察力, 建立一个功能工程计划, 使我们能够在已解决的B和B树数据库中培训我们的机器学习工具, 并将其作为不同大小和/或类型的问题加以应用。 我们实验性地显示, 使用我们所学的节点选择策略, 超越了与培训问题相同类型的问题测试时的香草、 随机节点选择战略, 也有可能在K值或问题大小与培训问题不同的情况下进行测试。