Representation Learning for Combinatorial Optimization

Forge: Foundational Optimization
Representations from Graph Embeddings

Representational learning for combinatorial optimization. Generate embeddings from MIP instances, pre-train models, and fine-tune for downstream tasks uch as predicting integral gap, search guidance, backdoor prediction, and solver configuration.

Serdar Kadıoğlu1,2   Zohair Shafi2,3

1 Department of Computer Science, Brown University 2 AI Center of Excellence, Fidelity Investments 3 Northeastern University

Paper Code Slides 🤗 Models 🤗 Dataset

Overview

Forge (Foundational Optimization Representations from Graph Embeddings) is designed for representational learning in combinatorial optimization. It provides tools for:


Forge converts MIP instances into a bipartite graph representation (constraints ↔ variables), applies Graph Neural Networks (PyG SAGEConv) with Vector Quantization to learn compact, transferable embeddings that capture the structural properties of optimization problems.

How it Works

End-to-end workflow from MIP instances to embeddings and predictions.

Step 1
📐

MIP → MIPInfo

Parse MIP instances into feature tensors, edge indices, and edge weights using PyG COO format.

Step 2
🧠

Pre-Train

Unsupervised pre-training with graph reconstruction and VQ commitment loss on bipartite graphs.

Step 3
🎯

Fine-Tune

Fine-tune the pre-trained model for downstream tasks like integral gap prediction.

Step 4
📊

Embeddings

Generate instance, constraint, and variable-level embeddings for any MIP problem.

Models

Pre-trained and Fine-tuned models

Out-of-the-box models ready for generating instance/constraint/variable-level embeddings, and fine-tuned for downstream optimization tasks.

Zohair Shafi, Serdar Kadıoğlu

Pre-trained Models

🤗 Pre-trained MIP ModelPyG

Citation

If you use FORGE in your research, please cite our paper.

@misc{shafi2025forgefoundationaloptimizationrepresentations,
      title={FORGE: Foundational Optimization Representations from Graph Embeddings},
      author={Zohair Shafi and Serdar Kadioglu},
      year={2025},
      eprint={2508.20330},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2508.20330},
}