论文标题
在两阶段的强大优化方面的k-适应性的机器学习
Machine Learning for K-adaptability in Two-stage Robust Optimization
论文作者
论文摘要
两阶段强大的优化问题构成了最困难的优化问题类别之一。解决此类问题的解决方案方法之一是K适应性。这种方法同时寻求将场景不确定性集的最佳分配到k子集中，并优化了与这些子集相对应的决策。在通常的情况下，使用K适应性分支和结合算法来解决它，该算法需要探索成倍增长的溶液树。为了加速在这样的树木中找到高质量的解决方案，我们提出了一种基于机器学习的节点选择策略。特别是，我们基于一般两阶段的强大优化见解构建了一个功能工程方案，该方案使我们能够在已解决的B＆B树数据库上训练我们的机器学习工具，并将其应用于不同尺寸和/或类型的问题。我们在实验上表明，在对训练问题相同类型的问题进行测试时，使用我们学习的节点选择策略优于香草，随机节点选择策略，以防K值或问题大小不同于培训。
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.
