# SRG: Score-based Relaxation-guided Generation for Mixed Integer Linear Programming

arXiv: https://arxiv.org/abs/2603.24033 · HTML: https://mlsanity.com/paper/2603.24033/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 32 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 17 of 17)

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- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Optimization with Non-Differentiable Constraints with Applications to Fairness, Recall, Churn, and Other Goals](https://mlsanity.com/paper/1809.04198/) (2018)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2302.05636/) (2023)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming](https://mlsanity.com/paper/2401.17527/) (2024)
- [A Comprehensive Survey of Linear, Integer, and Mixed-Integer Programming Approaches for Optimizing Resource Allocation in 5G and Beyond Networks](https://mlsanity.com/paper/2502.15585/) (2025)

## Abstract (arXiv)

We propose Score-based Relaxation-guided Generation (SRG), a generative framework based on an approximate formulation of relaxation-guided stochastic differential equations (SDEs) for mixed-integer linear programming. SRG employs a Transformer-based score network that incorporates feasibility and optimality signals into score modeling, encouraging the learned generative model to place more probability mass on feasible, high-quality regions of the solution space. At inference time, SRG directly samples diverse candidate solutions from the learned score model without requiring any additional guidance module. These candidates are then used to construct compact trust-region subproblems for standard MILP solvers. Across multiple public benchmarks, SRG matches or improves upon the solution quality of the strongest learning-based baselines, with particularly strong gains in challenging candidate-generation settings. Moreover, SRG shows promising zero-shot transferability to unseen cross-scale and cross-problem instances, improving solver objectives and reducing search time in several cases through higher-quality initial candidates and compact trust-region search.