Deep Learning for Two-Stage Robust Integer Optimization (2310.04345v3)

Abstract: Robust optimization is an established framework for modeling optimization problems with uncertain parameters. While static robust optimization is often criticized for being too conservative, two-stage (or adjustable) robust optimization (2RO) provides a less conservative alternative by allowing some decisions to be made after the uncertain parameters have been revealed. Unfortunately, in the case of integer decision variables, existing solution methods for 2RO typically fail to solve large-scale instances, limiting the applicability of this modeling paradigm to simple cases. We propose Neur2RO, a deep-learning-augmented instantiation of the column-and-constraint-generation (CCG) algorithm, which expands the applicability of the 2RO framework to large-scale instances with integer decisions in both stages. A custom-designed neural network is trained to estimate the optimal value and feasibility of the second-stage problem. The network can be incorporated into CCG, leading to more computationally tractable subproblems in each of its iterations. The resulting algorithm enjoys approximation guarantees which depend on the neural network's prediction error. In our experiments, Neur2RO produces high-quality solutions quickly, outperforming state-of-the-art methods on two-stage knapsack, capital budgeting, and facility location problems. Compared to existing methods, which often run for hours, Neur2RO finds better solutions in a few seconds or minutes. Our code is available at https://github.com/khalil-research/Neur2RO.