mlsanityData to 7 Oct 2026

Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon

arXiv 1811.06128 ↗First posted 15 Nov 2018cs.LG stat.MLcited by 612

Not on the map. Why?

Abstract (arXiv)

This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems, state-of-the-art algorithms rely on handcrafted heuristics for making decisions that are otherwise too expensive to compute or mathematically not well defined. Thus, machine learning looks like a natural candidate to make such decisions in a more principled and optimized way. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail a methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task.

Key facts. Cited by 612 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Nov 2018.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 89; 2022: 88; 2023: 97; 2024: 111; 2025: 119; 2026: 108.

612 papers.

Sort:

By area:

  1. 2021Graph Neural Networks with Learnable Structural and Positional Representationscited by 326
  2. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  3. 2024ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolutioncited by 266
  4. 2024Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Modelcited by 258
  5. 2021Learning to Optimize: A Primer and A Benchmarkcited by 206
  6. 2021DC3: A learning method for optimization with hard constraintscited by 181
  7. 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
  8. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  9. 2022The CLRS Algorithmic Reasoning Benchmarkcited by 103
  10. 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 102
  11. 2021Implicit MLE: Backpropagating Through Discrete Exponential Family Distributionscited by 97
  12. 2021Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applicationscited by 96
38 more
  1. 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 89
  2. 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
  3. 2022Tutorial on amortized optimizationcited by 83
  4. 2023A Survey of Contextual Optimization Methods for Decision Making under Uncertaintycited by 81
  5. 2023BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimizationcited by 80
  6. 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
  7. 2021Graph Neural Network Guided Local Search for the Traveling Salesperson Problemcited by 70
  8. 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
  9. 2024MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Expertscited by 69
  10. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
  11. 2023Robust Scheduling with GFlowNetscited by 67
  12. 2024A Systematic Survey on Large Language Models for Algorithm Designcited by 65
  13. 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 61
  14. 2022Self-Supervised Primal-Dual Learning for Constrained Optimizationcited by 60
  15. 2022Winner Takes It All: Training Performant RL Populations for Combinatorial Optimizationcited by 57
  16. 2023Unsupervised Learning for Solving the Travelling Salesman Problemcited by 57
  17. 2022Pareto Set Learning for Neural Multi-objective Combinatorial Optimizationcited by 56
  18. 2021Towards Lower Bounds on the Depth of ReLU Neural Networkscited by 55
  19. 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
  20. 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
  21. 2023Jumanji: a Diverse Suite of Scalable Reinforcement Learning Environments in JAXcited by 52
  22. 2023Algorithm Evolution Using Large Language Modelcited by 52
  23. 2024Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalizationcited by 49
  24. 2021Learning to Select Cuts for Efficient Mixed-Integer Programmingcited by 48
  25. 2022MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solverscited by 48
  26. 2024GraphArena: Evaluating and Exploring Large Language Models on Graph Computationcited by 48
  27. 2021Constructions in combinatorics via neural networkscited by 46
  28. 2021Variational Neural Annealingcited by 45
  29. 2022Learning to branch with Tree MDPscited by 45
  30. 2022A Survey for Solving Mixed Integer Programming via Machine Learningcited by 44
  31. 2023Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Modelcited by 44
  32. 2023H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problemcited by 43
  33. 2025Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimizationcited by 43
  34. 2021Learning a Large Neighborhood Search Algorithm for Mixed Integer Programscited by 41
  35. 2022Equivariant quantum circuits for learning on weighted graphscited by 41
  36. 2023Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNetscited by 40
  37. 2022On Representing Linear Programs by Graph Neural Networkscited by 39
  38. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39

50 most cited of 612 All 612 (JSON)