# Multi-task Representation Learning for Mixed Integer Linear Programming

arXiv: https://arxiv.org/abs/2412.14409 · HTML: https://mlsanity.com/paper/2412.14409/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 57 references that are in the map.
- First posted on arXiv 18 Dec 2024.

## Builds on (most cited first, 29 of 29)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [MiniGPT-v2: large language model as a unified interface for vision-language multi-task learning](https://mlsanity.com/paper/2310.09478/) (2023)
- [End-to-End Multi-Task Learning with Attention](https://mlsanity.com/paper/1803.10704/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (2022)
- [Learning to Schedule Heuristics in Branch-and-Bound](https://mlsanity.com/paper/2103.10294/) (2021)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [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)
- [Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning](https://mlsanity.com/paper/2302.01578/) (2023)
- [The SCIP Optimization Suite 9.0](https://mlsanity.com/paper/2402.17702/) (2024)
- [Learning to Compare Nodes in Branch and Bound with Graph Neural Networks](https://mlsanity.com/paper/2210.16934/) (2022)
- [Towards Foundation Models for Mixed Integer Linear Programming](https://mlsanity.com/paper/2410.08288/) (2024)
- [Machine Learning Augmented Branch and Bound for Mixed Integer Linear Programming](https://mlsanity.com/paper/2402.05501/) (2024)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Learning to Search via Retrospective Imitation](https://mlsanity.com/paper/1804.00846/) (2018)
- [Finding Backdoors to Integer Programs: A Monte Carlo Tree Search Framework](https://mlsanity.com/paper/2110.08423/) (2021)
- [Optimization Over Trained Neural Networks: Taking a Relaxing Walk](https://mlsanity.com/paper/2401.03451/) (2024)
- [CAMBranch: Contrastive Learning with Augmented MILPs for Branching](https://mlsanity.com/paper/2402.03647/) (2024)
- [Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions](https://mlsanity.com/paper/2301.07966/) (2023)
- [Learning Pseudo-Backdoors for Mixed Integer Programs](https://mlsanity.com/paper/2106.05080/) (2021)
- [Instance-wise algorithm configuration with graph neural networks](https://mlsanity.com/paper/2202.04910/) (2022)
- [Automatic MILP Solver Configuration By Learning Problem Similarities](https://mlsanity.com/paper/2307.00670/) (2023)

## Built on by (most cited first, 7 of 7)

- [FORGE: Foundational Optimization Representations from Graph Embeddings](https://mlsanity.com/paper/2508.20330/) (2025)
- [ParBalans: Parallel Multi-Armed Bandits-based Adaptive Large Neighborhood Search](https://mlsanity.com/paper/2508.06736/) (2025)
- [ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programs](https://mlsanity.com/paper/2512.10211/) (2025)
- [Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2508.03030/) (2025)
- [Imitation Learning for Combinatorial Optimisation under Uncertainty](https://mlsanity.com/paper/2601.05383/) (2026)
- [Reformulation-Contrastive Learning for Mixed Integer Programs](https://mlsanity.com/paper/2610.00730/) (2026)
- [Sequence-Structured Decision Learning for Branch-and-Bound in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2610.14835/) (2026)

## Abstract (arXiv)

Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant potential in improving MILP-solving efficiency. However, these methods typically rely on separate offline data collection and training processes, which limits their scalability and adaptability. This paper introduces the first multi-task learning framework for ML-guided MILP solving. The proposed framework provides MILP embeddings helpful in guiding MILP solving across solvers (e.g., Gurobi and SCIP) and across tasks (e.g., Branching and Solver configuration). Through extensive experiments on three widely used MILP benchmarks, we demonstrate that our multi-task learning model performs similarly to specialized models within the same distribution. Moreover, it significantly outperforms them in generalization across problem sizes and tasks.