Abstract
Mixed-integer linear programs (MILP) model many real-world decision problems, motivating machine-learning methods that exploit recurring structure to accelerate MILP solving. MILPs can admit many equivalent formulations: integrality-preserving changes of variables and the addition of redundant constraints can alter their formulations while preserving the optimization problem. We leverage these reformulations as a source of self-supervision for learning general-purpose representations of MILP variables and constraints. We characterize the affine reformulations that are valid for every input instance, and distinguish re-descriptions, which leave variables unchanged, from substitutions, which transform them predictably. Building on equivariant self-supervised learning, we introduce ReMILP (reformulation-contrastive MILP representation learning), which jointly trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables. Without solver-derived labels, ReMILP learns representations that exhibit the intended invariance and equivariance on unseen problem classes. Across binary solution, constraint activity and integrality gap prediction, these representations carry task-relevant information when frozen and provide a useful initialization for fine-tuning.
Keywords
Subject
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Bouaneni, O., Bail, M. L., Elliker, C., Jenny, M., & Vanier, S. (2026). Reformulation-Contrastive Learning for Mixed Integer Programs. https://omanscience.com/en/articles/reformulation-contrastive-learning-for-mixed-integer-programs
MLA 9
Bouaneni, Ousema, et al. "Reformulation-Contrastive Learning for Mixed Integer Programs." https://omanscience.com/en/articles/reformulation-contrastive-learning-for-mixed-integer-programs.
Chicago (author–date)
Bouaneni, Ousema, Mathis Le Bail, Clément Elliker, Maël Jenny, and Sonia Vanier. 2026. "Reformulation-Contrastive Learning for Mixed Integer Programs." https://omanscience.com/en/articles/reformulation-contrastive-learning-for-mixed-integer-programs.
Harvard
Bouaneni, O., Bail, M. L., Elliker, C., Jenny, M. and Vanier, S. (2026) 'Reformulation-Contrastive Learning for Mixed Integer Programs', Available at: https://omanscience.com/en/articles/reformulation-contrastive-learning-for-mixed-integer-programs.
Vancouver
Bouaneni O, Bail ML, Elliker C, Jenny M, Vanier S. Reformulation-Contrastive Learning for Mixed Integer Programs. https://omanscience.com/en/articles/reformulation-contrastive-learning-for-mixed-integer-programs
IEEE
O. Bouaneni, M. L. Bail, C. Elliker, M. Jenny, and S. Vanier, "Reformulation-Contrastive Learning for Mixed Integer Programs," https://omanscience.com/en/articles/reformulation-contrastive-learning-for-mixed-integer-programs.