# The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights

arXiv: https://arxiv.org/abs/2203.02433 · HTML: https://mlsanity.com/paper/2203.02433/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 4 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Born Again Neural Networks](https://mlsanity.com/paper/1805.04770/) (2018)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search](https://mlsanity.com/paper/1810.10659/) (2018)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Hybrid Models for Learning to Branch](https://mlsanity.com/paper/2006.15212/) (2020)
- [Learning to Branch](https://mlsanity.com/paper/1803.10150/) (2018)
- [Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization](https://mlsanity.com/paper/2006.01610/) (2020)
- [Ecole: A Gym-like Library for Machine Learning in Combinatorial Optimization Solvers](https://mlsanity.com/paper/2011.06069/) (2020)
- [Learning to Run challenge solutions: Adapting reinforcement learning methods for neuromusculoskeletal environments](https://mlsanity.com/paper/1804.00361/) (2018)

## Built on by (most cited first, 30 of 39)

- [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)
- [MILP-StuDio: MILP Instance Generation via Block Structure Decomposition](https://mlsanity.com/paper/2410.22806/) (2024)
- [Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming](https://mlsanity.com/paper/2503.01129/) (2025)
- [Distributional MIPLIB: a Multi-Domain Library for Advancing ML-Guided MILP Methods](https://mlsanity.com/paper/2406.06954/) (2024)
- [Learning to Configure Separators in Branch-and-Cut](https://mlsanity.com/paper/2311.05650/) (2023)
- [Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation](https://mlsanity.com/paper/2310.14161/) (2023)
- [Learning To Dive In Branch And Bound](https://mlsanity.com/paper/2301.09943/) (2023)
- [Learning to Stop Cut Generation for Efficient Mixed-Integer Linear Programming](https://mlsanity.com/paper/2401.17527/) (2024)
- [LLMs for Cold-Start Cutting Plane Separator Configuration](https://mlsanity.com/paper/2412.12038/) (2024)
- [Multi-task Representation Learning for Mixed Integer Linear Programming](https://mlsanity.com/paper/2412.14409/) (2024)
- [Riemannian Optimization on Relaxed Indicator Matrix Manifold](https://mlsanity.com/paper/2503.20505/) (2025)
- [Reinforcement Learning for Node Selection in Branch-and-Bound](https://mlsanity.com/paper/2310.00112/) (2023)
- [Model Uncertainty in Evolutionary Optimization and Bayesian Optimization: A Comparative Analysis](https://mlsanity.com/paper/2403.14413/) (2024)
- [CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Prediction](https://mlsanity.com/paper/2511.09209/) (2025)
- [LLM4Branch: Large Language Model for Discovering Efficient Branching Policies of Integer Programs](https://mlsanity.com/paper/2605.10401/) (2026)
- [Exact Combinatorial Optimization with Temporo-Attentional Graph Neural Networks](https://mlsanity.com/paper/2311.13843/) (2023)
- [An Efficient Unsupervised Framework for Convex Quadratic Programs via Deep Unrolling](https://mlsanity.com/paper/2412.01051/) (2024)
- [When GNNs meet symmetry in ILPs: an orbit-based feature augmentation approach](https://mlsanity.com/paper/2501.14211/) (2025)
- [RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domains](https://mlsanity.com/paper/2511.02331/) (2025)
- [Structured Q-learning For Antibody Design](https://mlsanity.com/paper/2209.04698/) (2022)
- [Are Your Generated Instances Truly Useful? GenBench-MILP: A Benchmark Suite for MILP Instance Generation](https://mlsanity.com/paper/2505.24779/) (2025)
- [Principled Data Augmentation for Learning to Solve Quadratic Programming Problems](https://mlsanity.com/paper/2506.01728/) (2025)
- [Constraint Matters: Multi-Modal Representation for Reducing Mixed-Integer Linear programming](https://mlsanity.com/paper/2508.18742/) (2025)
- [TreeDQN: Sample-Efficient Off-Policy Reinforcement Learning for Combinatorial Optimization](https://mlsanity.com/paper/2306.05905/) (2023)
- [Threshold-aware Learning to Generate Feasible Solutions for Mixed Integer Programs](https://mlsanity.com/paper/2308.00327/) (2023)
- [RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs](https://mlsanity.com/paper/2411.19517/) (2024)
- [BenLOC: A Benchmark for Learning to Configure MIP Optimizers](https://mlsanity.com/paper/2506.02752/) (2025)
- [A General Neural Backbone for Mixed-Integer Linear Optimization via Dual Attention](https://mlsanity.com/paper/2601.04509/) (2026)
- [GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs](https://mlsanity.com/paper/2606.23299/) (2026)

## Abstract (arXiv)

Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have focused on solving problem instances in isolation, ignoring that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning as a new approach for solving combinatorial problems, either directly as solvers or by enhancing exact solvers. Based on this context, the ML4CO aims at improving state-of-the-art combinatorial optimization solvers by replacing key heuristic components. The competition featured three challenging tasks: finding the best feasible solution, producing the tightest optimality certificate, and giving an appropriate solver configuration. Three realistic datasets were considered: balanced item placement, workload apportionment, and maritime inventory routing. This last dataset was kept anonymous for the contestants.