Solving two-stage stochastic integer programs via representation learning.

Area of Science:

• Operations Research
• Machine Learning
• Computational Optimization

Background:

• Stochastic integer programs (SIPs) are computationally challenging due to their complexity.
• Existing methods struggle with large-scale SIP instances and diverse scenario distributions.

Purpose of the Study:

• To develop an efficient method for solving two-stage stochastic integer programs (SIPs).
• To leverage machine learning for scenario representation learning in optimization.

Main Methods:

• A conditional variational autoencoder (CVAE) using a graph convolutional network (GCN) embeds scenarios into a latent space.
• Auxiliary tasks including objective prediction and scenario contrast are used to integrate objective information.
• Gradient backpropagation refines the learned representations.

Main Results:

• Learned scenario representations significantly reduce the number of scenarios needed for SIPs.
• The approach achieves high-quality solutions within reduced computational time.
• The method demonstrates effectiveness on larger instances and varied data distributions.

Conclusions:

• The proposed CVAE-based scenario representation learning is effective for solving SIPs.
• This approach offers a computationally efficient and scalable solution for complex optimization problems.
• The technique generalizes well across different problem sizes and data characteristics.