Solving two-stage stochastic integer programs via representation learning

Solving stochastic integer programs (SIPs) is extremely intractable due to the high computational complexity. To solve two-stage SIPs efficiently, we propose a conditional variational autoencoder (CVAE) for scenario representation learning. A graph convolutional network (GCN) based VAE embeds scenarios into a low-dimensional latent space, conditioned on the deterministic context of each instance. With the latent representations of stochastic scenarios, we perform two auxiliary tasks: objective prediction and scenario contrast, which predict scenario objective values and the similarities between them, respectively. These tasks further integrate objective information into the representations through gradient backpropagation. Experiments show that the learned scenario representations can help reduce scenarios in SIPs, facilitating high-quality solutions in a short computational time. This superiority generalizes well to instances of larger sizes, more scenarios, and various distributions.