Machine Learning for K-adaptability in Two-stage Robust Optimization
This work addresses a specific bottleneck in optimization for researchers and practitioners dealing with two-stage robust problems, offering an incremental improvement over existing methods.
The paper tackles the computational challenge of solving two-stage robust optimization problems via the K-adaptability branch-and-bound algorithm, which involves exploring exponentially growing solution trees, by proposing a machine learning-based node selection strategy that accelerates finding high-quality solutions. The result shows that this learned strategy outperforms a random node selection strategy on problems of the same type, even when the K-value or problem size differs from training, with experimental validation.
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.