Awesome Machine Learning for Combinatorial Optimization Resources

We would like to maintain a list of resources that utilize machine learning technologies to solve combinatorial optimization problems.

We mark work contributed by Thinklab with ⭐.

Maintained by members in SJTU-Thinklab: Chang Liu, Runzhong Wang, Jiayi Zhang, Zelin Zhao, Haoyu Geng, Tianzhe Wang, Wenxuan Guo, Wenjie Wu, Nianzu Yang, Ziao Guo, Yang Li, Hao Xiong, Jiale Ma, Wenzheng Pan and Junchi Yan. We also thank all contributers from the community!

We are looking for post-docs interested in machine learning especially for learning combinatorial solvers, dynamic graphs, and reinforcement learning. Please send your up-to-date resume via yanjunchi AT sjtu.edu.cn.

Content

1. Survey

2. Problems

 2.1 Travelling Salesman Problem (TSP)

 2.2 Job Shop Scheduling Problem (JSSP)

 2.3 Flow Shop Problem (FSP)

 2.4 Sorting & Ranking (Sort&Rank)

 2.5 Graph Matching (GM)

 2.6 Quadratic Assignment Problem (QAP)

 2.7 Portfolio Optimization (PortOpt)

 2.8 Maximal Cut

 2.9 Vehicle Routing Problem (VRP)

 2.10 Maximum Independent Set

 2.11 Generalization

 2.12 Orienteering Problem (OP)

 2.13 Knapsack

 2.14 Boolean Satisfiability (SAT)

 2.15 Computing Resource Allocation

 2.16 Bin Packing Problem (BPP)

 2.17 Graph Edit Distance (GED)

 2.18 Hamiltonian Cycle Problem (HCP)

 2.19 Graph Coloring

 2.20 Maximal Common Subgraph (MCS)

 2.21 Influence Maximization

 2.22 Max Clique

 2.23 Mixed Integer Programming (MIP)

 2.24 Causal Discovery

 2.25 Game Theoretic Semantics

 2.26 Differentiable Optimization

 2.27 Car Dispatch

 2.28 Electronic Design Automation (EDA)

 2.29 Conjunctive Query Containment

 2.30 Virtual Network Embedding (VNE)

 2.31 Predict+Optimize

 2.32 Optimal Power Flow

 2.33 Facility Location Problem (FLP)

 2.34 Combinatorial Drug Recommendation

 2.35 Stochastic Combinatorial Optimization

 2.36 Vertex Cover

Survey Papers

1. Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research INFORMS Journal on Computing, 1999. journal

   Kate A. Smith

2. Model-Based Search for Combinatorial Optimization: A Critical Survey. Annals of Operations Research, 2004. journal

   Mark Zlochin, Mauro Birattari, Nicolas Meuleau, Marco Dorigo

3. A Survey of Reinforcement Learning and Agent-Based Approaches to Combinatorial Optimization. Citeseer, 2012. journal

   Victor Miagkikh

4. Machine Learning Approaches to Learning Heuristics for Combinatorial Optimization Problems. Procedia Manufacturing, 2018. journal

   Sadegh Mirshekarian, Dusan Sormaz

5. Boosting combinatorial problem modeling with machine learning. IJCAI, 2018. paper

   Michele Lombardi, Michela Milano

6. Deep Reinforcement Learning as a Job Shop Scheduling Solver: A Literature Review Hybrid Intelligent Systems, 2018. journal

   Bruno Cunha, Ana M. Madureira, Benjamim Fonseca, Duarte Coelho

7. A Review of combinatorial optimization with graph neural networks. BigDIA, 2019. paper

   Tingfei Huang, Yang Ma, Yuzhen Zhou, Honglan Huang Huang, Dongmei Chen, Zidan Gong, Yao Liu

8. Machine Learning for Combinatorial Optimization: a Methodological Tour d'horizon. EJOR, 2020. journal

   Yoshua Bengio, Andrea Lodi, Antoine Prouvost

9. Reinforcement Learning for Combinatorial Optimization: A Survey. Arxiv, 2020. paper

   Nina Mazyavkina, Sergey Sviridov, Sergei Ivanov, Evgeny Burnaev

10. ⭐Learning Graph Matching and Related Combinatorial Optimization Problems. IJCAI, 2020. paper

    Junchi Yan, Shuang Yang, Edwin R. Hancock

11. Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networking. IEEE ACCESS, 2020. journal

    Natalia Vesselinova, Rebecca Steinert, Daniel F. Perez-Ramirez, Magnus Boman

12. From Shallow to Deep Interactions Between Knowledge Representation, Reasoning and Machine Learning. Arxiv, 2020. paper

    Zied Bouraoui, Antoine Cornuéjols, Thierry Denœux, Sébastien Destercke, Didier Dubois, Romain Guillaume, João Marques-Silva, Jérôme Mengin, Henri Prade, Steven Schockaert, Mathieu Serrurier, Christel Vrain

13. A Survey on Reinforcement Learning for Combinatorial Optimization. Arxiv, 2020. paper

    Yunhao Yang, Andrew Whinston

14. Research Reviews of Combinatorial Optimization Methods Based on Deep Reinforcement Learning. (in chinese) 自动化学报, 2020. journal

    Kai-Wen Li, Tao Zhang, Rui Wang, Wei-Jian Qin, Hui-Hui He, Hong Huang

15. Graph Learning for Combinatorial Optimization: A Survey of State-of-the-Art. Data Science and Engineering, 2021. journal

    Yue Peng, Byron Choi, Jianliang Xu

16. Machine Learning for Electronic Design Automation (EDA) : A Survey TODAES, 2021. journal

    Guyue Huang, Jingbo Hu, Yifan He, Jialong Liu, Mingyuan Ma, Zhaoyang Shen, Juejian Wu, Yuanfan Xu, Hengrui Zhang, Kai Zhong, others

17. ⭐A Survey for Solving Mixed Integer Programming via Machine Learning Neurocomputing, 2022. journal

    Jiayi Zhang, Chang Liu, Xijun Li, Hui-Ling Zhen, Mingxuan Yuan, Yawen Li, Junchi Yan

18. Combinatorial Optimization and Reasoning with Graph Neural Networks JMLR, 2023. journal

    Quentin Cappart, Didier Chetelat, Elias B. Khalil, Andrea Lodi, Christopher Morris, Petar Velickovic

19. Applicability of Neural Combinatorial Optimization: A Critical View TELO, 2024. journal, code

    Andoni I. Garmendia, Josu Ceberio, Alexander Mendiburu

20. Survey on Neural Routing Solvers Arxiv, 2026. paper

    Yunpeng Ba, Xi Lin, Changliang Zhou, Ruihao Zheng, Zhenkun Wang, Xinyan Liang, Zhichao Lu, Jianyong Sun, Yuhua Qian, Qingfu Zhang

Problems

Travelling Salesman Problem

Benchmark Results (Beta)

Beta feature: benchmark charts are generated from data/benchmark_results.csv. The results, sourced directly from original papers using common benchmarks, are presented to directly illustrate the evolution of performance. Runtime is normalized to 1000 instances by instance count only; hardware is not normalized. Gap charts show main-experiment points within benchmark-specific gap bounds (3.5% for TSP-500, 5% otherwise); within each baseline, slower points are shown only when they improve gap.

Uniform TSP-500

Uniform TSP-1000

1. Learning Combinatorial Optimization Algorithms over Graphs. NeurIPS, 2017. paper

   Hanjun Dai, Elias B Khalil, Yuyu Zhang, Bistra Dilkina, Le Song

2. Learning Heuristics for the TSP by Policy Gradient CPAIOR, 2018. paper, code

   Michel DeudonPierre CournutAlexandre Lacoste

3. Attention, Learn to Solve Routing Problems! ICLR, 2019. paper

   Wouter Kool, Herke Van Hoof, Max Welling

4. Learning to Solve NP-Complete Problems: A Graph Neural Network for Decision TSP. AAAI, 2019. paper

   Marcelo Prates, Pedro HC Avelar, Henrique Lemos, Luis C Lamb, Moshe Y. Vardi

5. An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem Arxiv, 2019. paper, code

   Chaitanya K. Joshi, Thomas Laurent, Xavier Bresson

6. POMO: Policy Optimization with Multiple Optima for Reinforcement Learning. NeurIPS, 2020. paper, code

   Yeong-Dae Kwon, Jinho Choo, Byoungjip Kim, Iljoo Yoon, Seungjai Min, Youngjune Gwon

7. Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances. Arxiv, 2020. paper

   Zhang-Hua Fu, Kai-Bin Qiu, Hongyuan Zha

8. A Reinforcement Learning Approach for Optimizing Multiple Traveling Salesman Problems over Graphs KBS, 2020. journal

   Yujiao Hu, Yuan Yao, Wee Sun Lee

9. Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning ACML, 2020. paper, code

   d O Costa, Paulo R, Jason Rhuggenaath, Yingqian Zhang, Alp Akcay

10. Deep Reinforcement Learning for Combinatorial Optimization: Covering Salesman Problems. IEEE Trans Cybern, 2021. journal

    Kaiwen Li, Tao Zhang, Rui Wang Yuheng Wang, Yi Han

11. The Transformer Network for the Traveling Salesman Problem IPAM, 2021. paper

    Xavier Bresson，Thomas Laurent

12. Learning Improvement Heuristics for Solving Routing Problems TNNLS, 2021. journal

    Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang, Andrew Lim

13. Reversible Action Design for Combinatorial Optimization with Reinforcement Learning Arxiv, 2021. paper

    Fan Yao, Renqin Cai, Hongning Wang

14. Solving Dynamic Traveling Salesman Problems with Deep Reinforcement Learning. TNNLS, 2021. journal

    Zizhen Zhang, Hong Liu, Meng Chu Zhou, Jiahai Wang

15. ScheduleNet: Learn to Solve Multi-agent Scheduling Problems with Reinforcement Learning Arxiv, 2021. paper

    Junyoung Park, Sanjar Bakhtiyar, Jinkyoo Park

16. DAN: Decentralized Attention-based Neural Network to Solve the MinMax Multiple Traveling Salesman Problem Arxiv, 2021. paper

    Yuhong Cao, Zhanhong Sun, Guillaume Sartoretti

17. Reinforcement Learning for Route Optimization with Robustness Guarantees IJCAI, 2021. paper

    Tobias Jacobs, Francesco Alesiani, Gulcin Ermis

18. Combining Reinforcement Learning with Lin-Kernighan-Helsgaun Algorithm for the Traveling Salesman Problem AAAI, 2021. paper, code

    Jiongzhi Zheng, Kun He, Jianrong Zhou, Yan Jin, Chu-Min Li

19. Learning to Sparsify Travelling Salesman Problem Instances CPAIOR, 2021. paper

    James Fitzpatrick, Deepak Ajwani, Paula Carroll

20. Learning TSP Requires Rethinking Generalization CP, 2021. paper, code

    Chaitanya K. Joshi, Quentin Cappart, Louis-Martin Rousseau, Thomas Laurent

21. The First AI4TSP Competition: Learning to Solve Stochastic Routing Problems Arxiv, 2022. paper, code

    Laurens Bliek, Paulo da Costa, Reza Refaei Afshar, Yingqian Zhang, Tom Catshoek, Daniel Vos, Sicco Verwer, Fynn Schmitt-Ulms, Andre Hottung, Tapan Shah, others

22. Graph Neural Network Guided Local Search for the Traveling Salesperson Problem ICLR, 2022. paper

    Benjamin Hudson, Qingbiao Li, Matthew Malencia, Amanda Prorok

23. Preference Conditioned Neural Multi-objective Combinatorial Optimization ICLR, 2022. paper

    Xi Lin, Zhiyuan Yang, Qingfu Zhang

24. Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation NeurIPS, 2022. paper, code

    Jieyi Bi, Yining Ma, Jiahai Wang, Zhiguang Cao, Jinbiao Chen, Yuan Sun, Yeow Meng Chee

25. DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems NeurIPS, 2022. paper

    Ruizhong Qiu, Zhiqing Sun, Yiming Yang

26. Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization NeurIPS, 2022. paper, code

    Minsu Kim, Junyoung Park, Jinkyoo Park

27. Simulation-guided Beam Search for Neural Combinatorial Optimization NeurIPS, 2022. paper, code

    Jinho Choo, Yeong-Dae Kwon, Jihoon Kim, Jeongwoo Jae, Andr{'e} Hottung, Kevin Tierney, Youngjune Gwon

28. Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness ICLR, 2022. paper

    Simon Geisler, Johanna Sommer, Jan Schuchardt, Aleksandar Bojchevski, Stephan Günnemann

29. ⭐LinSATNet: The Positive Linear Satisfiability Neural Networks ICML, 2023. paper, code

    Runzhong Wang, Yunhao Zhang, Ziao Guo, Tianyi Chen, Xiaokang Yang, Junchi Yan

30. Learning to CROSS exchange to solve min-max vehicle routing problems ICLR, 2023. paper

    Minjun Kim, Junyoung Park, Jinkyoo Park

31. Generalize Learned Heuristics to Solve Large-scale Vehicle Routing Problems in Real-time ICLR, 2023. paper

    Qingchun Hou, Jingwei Yang, Yiqiang Su, Xiaoqing Wang, Yuming Deng

32. ⭐ROCO: A General Framework for Evaluating Robustness of Combinatorial Optimization Solvers on Graphs ICLR, 2023. paper, code

    Han Lu, Zenan Li, Runzhong Wang, Qibing Ren, Xijun Li, Mingxuan Yuan, Jia Zeng, Xiaokang Yang, Junchi Yan

33. Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem Arxiv, 2023. paper, code

    Yan Jin, Yuandong Ding, Xuanhao Pan, Kun He, Li Zhao, Tao Qin, Lei Song, Jiang Bian

34. H-tsp: Hierarchically solving the large-scale traveling salesman problem AAAI, 2023. paper, code

    Xuanhao Pan, Yan Jin, Yuandong Ding, Mingxiao Feng, Li Zhao, Lei Song, Jiang Bian

35. Select and Optimize: Learning to solve large-scale TSP instances AISTATS, 2023. paper

    Hanni Cheng, Haosi Zheng, Ya Cong, Weihao Jiang, Shiliang Pu

36. Multi-View Graph Contrastive Learning for Solving Vehicle Routing Problems UAI, 2023. paper

    Yuan Jiang, Zhiguang Cao, Yaoxin Wu, Jie Zhang

37. Revisiting Sampling for Combinatorial Optimization ICML, 2023. paper

    Haoran, Goshvadi Katayoon, Nova Azade, Schuurmans Dale Sun, Dai Hanjun.

38. Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimization ICML, 2023. paper

    Jiwoo Son, Minsu Kim, Hyeonah Kim, Jinkyoo Park

39. Towards Omni-generalizable Neural Methods for Vehicle Routing Problems ICML, 2023. paper, code

    Zhou Jianan, Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang

40. DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization NeurIPS, 2023. paper, code

    Zhiqing Sun, Yiming Yang

41. DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization NeurIPS, 2023. paper, code

    Haoran Ye, Jiarui Wang, Zhiguang Cao, Helan Liang, Yong Li

42. Winner Takes It All: Training Performant RL Populations for Combinatorial Optimization NeurIPS, 2023. paper

    Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Cl{'e}ment Bonnet, Thomas D Barrett

43. Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods NeurIPS, 2023. paper, code

    Constantine Caramanis, Dimitris Fotakis, Alkis Kalavasis, Vasilis Kontonis, Christos Tzamos

44. Combinatorial Optimization with Policy Adaptation using Latent Space Search NeurIPS, 2023. paper

    Felix Chalumeau, Shikha Surana, Cl{'e}ment Bonnet, Nathan Grinsztajn, Arnu Pretorius, Alexandre Laterre, Thomas D Barrett

45. Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization NeurIPS, 2023. paper, code

    Jinbiao Chen, Jiahai Wang, Zizhen Zhang, Zhiguang Cao, Te Ye, Siyuan Chen

46. BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization NeurIPS, 2023. paper, code

    Darko Drakulic, Sofia Michel, Florian Mai, Arnaud Sors, Jean-Marc Andreoli

47. Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization NeurIPS, 2023. paper, code

    Fu Luo, Xi Lin, Fei Liu, Qingfu Zhang, Zhenkun Wang

48. Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement NeurIPS, 2023. paper, code

    Jinbiao Chen, Zizhen Zhang, Zhiguang Cao, Yaoxin Wu, Yining Ma, Te Ye, Jiahai Wang

49. Unsupervised Learning for Solving the Travelling Salesman Problem NeurIPS, 2023. paper

    Yimeng Min, Yiwei Bai, Carla P Gomes

50. Ensemble-based Deep Reinforcement Learning for Vehicle Routing Problems under Distribution Shift NeurIPS, 2023. paper

    Yuan Jiang, Zhiguang Cao, Yaoxin Wu, Wen Song, Jie Zhang

51. Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt NeurIPS, 2023. paper, code

    Yining Ma, Zhiguang Cao, Yeow Meng Chee

52. ⭐T2T: From Distribution Learning in Training to Gradient Search in Testing for Combinatorial Optimization NeurIPS, 2023. paper, code

    Yang Li, Jinpei Guo, Runzhong Wang, Junchi Yan

53. Reinforced Lin–Kernighan–Helsgaun Algorithms for the Traveling Salesman Problems Knowledge-Based Systems, 2023. journal, code

    Jiongzhi Zheng, Kun He, Jianrong Zhou, Yan Jin, Chu-Min Li

54. Neural Improvement Heuristics for Graph Combinatorial Optimization Problems TNNLS, 2023. journal, code

    Andoni I. Garmendia, Josu Ceberio, Alexander Mendiburu

55. GLOP: Learning Global Partition and Local Construction for Solving Large-Scale Routing Problems in Real-Time AAAI, 2024. paper, code

    Haoran Ye, Jiarui Wang, Helan Liang, Zhiguang Cao, Yong Li, Fanzhang Li

56. Distilling Autoregressive Models to Obtain High-Performance Non-autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed AAAI, 2024. paper, code

    Yubin Xiao, Di Wang, Boyang Li, Mingzhao Wang, Xuan Wu, Changliang Zhou, You Zhou

57. Position: Rethinking Post-Hoc Search-Based Neural Approaches for Solving Large-Scale Traveling Salesman Problems ICML, 2024. paper, code

    Yifan Xia, Xianliang Yang, Zichuan Liu, Zhihao Liu, Lei Song, Jiang Bian

58. MARCO: A Memory-Augmented Reinforcement Framework for Combinatorial Optimization IJCAI, 2024. paper, code

    Andoni I. Garmendia, Quentin Cappart, Josu Ceberio, Alexander Mendiburu

59. Neural Combinatorial Optimization for Robust Routing Problem with Uncertain Travel Times NeurIPS, 2024. paper

    Pei Xiao, Zizhen Zhang, Jinbiao Chen, Jiahai Wang, Zhenzhen Zhang

60. Collaboration! Towards Robust Neural Methods for Routing Problems NeurIPS, 2024. paper, code

    Jianan Zhou, Yaoxin Wu, Zhiguang Cao, Wen Song, Jie Zhang, Zhiqi Shen

61. UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems NeurIPS, 2024. paper, code

    Zhi Zheng, Changliang Zhou, Tong Xialiang, Mingxuan Yuan, Zhenkun Wang

62. Learning to Handle Complex Constraints for Vehicle Routing Problems NeurIPS, 2024. paper

    Jieyi Bi, Yining Ma, Jianan Zhou, Wen Song, Zhiguang Cao, Yaoxin Wu, Jie Zhang

63. ⭐Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization NeurIPS, 2024. paper, code

    Yang Li, Jinpei Guo, Runzhong Wang, Hongyuan Zha, Junchi Yan

64. Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model ICML, 2024. paper, code

    Fei Liu, Xialiang Tong, Mingxuan Yuan, Xi Lin, Fu Luo, Zhenkun Wang, Zhichao Lu, Qingfu Zhang

65. ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution NeurIPS, 2024. paper, code

    Haoran Ye, Jiarui Wang, Zhiguang Cao, Federico Berto, Chuanbo Hua, Haeyeon Kim, Jinkyoo Park, Guojie Song

66. Rethinking Neural Multi-Objective Combinatorial Optimization via Neat Weight Embedding ICLR, 2025. paper

    Jinbiao Chen, Zhiguang Cao, Jiahai Wang, Yaoxin Wu, Hanzhang Qin, Zizhen Zhang, Yue-Jiao Gong

67. Neural Multi-Objective Combinatorial Optimization via Graph-Image Multimodal Fusion ICLR, 2025. paper

    Jinbiao Chen, Jiahai Wang, Zhiguang Cao, Yaoxin Wu

68. Boosting Neural Combinatorial Optimization for Large-Scale Vehicle Routing Problems ICLR, 2025. paper

    Fu Luo, Xi Lin, Yaoxin Wu, Zhenkun Wang, Tong Xialiang, Mingxuan Yuan, Qingfu Zhang

69. ⭐UniCO: On Unified Combinatorial Optimization via Problem Reduction to Matrix-Encoded General TSP ICLR, 2025. paper, code

    Wenzheng Pan, Hao Xiong, Jiale Ma, Wentao Zhao, Yang Li, Junchi Yan

70. Efficient and Robust Neural Combinatorial Optimization via Wasserstein-Based Coresets ICLR, 2025. paper

    Xu Wang, Fuyou Miao, Wenjie Liu, Yan Xiong

71. ⭐Unify ML4TSP: Drawing Methodological Principles for TSP and Beyond from Streamlined Design Space of Learning and Search ICLR, 2025. paper, code

    Yang Li, Jiale Ma, Wenzheng Pan, Runzhong Wang, Haoyu Geng, Nianzu Yang, Junchi Yan

72. ⭐ML4CO-Bench-101: Benchmark Machine Learning for Classic Combinatorial Problems on Graphs NeurIPS, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

73. ⭐COExpander: Adaptive Solution Expansion for Combinatorial Optimization ICML, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

74. Large Language Models as End-to-end Combinatorial Optimization Solvers NeurIPS, 2025. paper, code

    Xia Jiang, Yaoxin Wu, Minshuo Li, Zhiguang Cao, Yingqian Zhang

75. ⭐StruDiCO: Structured Denoising Diffusion with Gradient-free Inference-stage Boosting for Memory and Time Efficient Combinatorial Optimization NeurIPS, 2025. paper, code

    Yu Wang, Yang Li, Junchi Yan, Yi Chang

76. ⭐Generation as search operator for test-time scaling of diffusion-based combinatorial optimization NeurIPS, 2025. paper, code

    Yang Li, Lvda Chen, Haonan Wang, Runzhong Wang, Junchi Yan

77. Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling ICLR, 2025. paper, code

    Yuma Ichikawa, Yamato Arai

78. BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization ICML, 2025. paper, code

    Zijun Liao, Jinbiao Chen, Debing Wang, Zizhen Zhang, Jiahai Wang

79. Neural Solver Selection for Combinatorial Optimization ICML, 2025. paper

    Chengrui Gao, Haopu Shang, Ke Xue, Chao Qian

80. Preference Optimization for Combinatorial Optimization Problems ICML, 2025. paper, code

    Mingjun Pan, Guanquan Lin, You-Wei Luo, Bin Zhu, Zhien Dai, Lijun Sun, Chun Yuan

81. PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization NeurIPS, 2025. paper, code

    Federico Berto, Chuanbo Hua, Laurin Luttmann, Jiwoo Son, Junyoung Park, Kyuree Ahn, Changhyun Kwon, Lin Xie, Jinkyoo Park

82. Differentiable extensions with rounding guarantees for combinatorial optimization over permutations NeurIPS, 2025. paper

    Robert R Nerem, Zhishang Luo, Akbar Rafiey, Yusu Wang

83. Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning NeurIPS, 2025. paper, code

    Yuanyao Chen, Rongsheng Chen, Fu Luo, Zhenkun Wang

84. Complexity Scaling Laws for Neural Models using Combinatorial Optimization NeurIPS, 2025. paper

    Lowell Weissman, Michael Krumdick, A. Lynn Abbott

85. Solving the Asymmetric Traveling Salesman Problem via Trace-Guided Cost Augmentation NeurIPS, 2025. paper

    Zhen Zhang, Javen Qinfeng Shi, Wee Sun Lee

86. Learning to Insert for Constructive Neural Vehicle Routing Solver NeurIPS, 2025. paper, code

    Fu Luo, Xi Lin, Mengyuan Zhong, Fei Liu, Zhenkun Wang, Jianyong Sun, Qingfu Zhang

87. Neural Combinatorial Optimization for Time-Dependent Traveling Salesman Problem NeurIPS, 2025. paper

    Ruixiao Yang, Chuchu Fan

88. Adversarial Generative Flow Network for Solving Vehicle Routing Problems ICLR, 2025. paper, code

    Ni Zhang, Jingfeng Yang, Zhiguang Cao, Xu Chi

89. Projecting Latent RL Actions: Towards Generalizable and Scalable Graph Combinatorial Optimization Arxiv, 2026. paper, code

    Franco Terranova, Guillermo Bernardez, Albert Cabellos-Aparicio, Nina Miolane, Abdelkader Lahmadi

90. Generalizable Heuristic Generation Through LLMs with Meta-Optimization ICLR, 2026. paper, code

    Yiding Shi, Jianan Zhou, Wen Song, Jieyi Bi, Yaoxin Wu, Zhiguang Cao, Jie Zhang

91. DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization AAMAS, 2026. paper

    Shengkai Chen, Zhiguang Cao, Jianan Zhou, Yaoxin Wu, Senthilnath Jayavelu, Zhuoyi Lin, Xiaoli Li, Shili Xiang

92. Bridging Synthetic and Real Routing Problems via LLM-Guided Instance Generation and Progressive Adaptation AAAI, 2026. paper, code

    Jianghan Zhu, Yaoxin Wu, Zhuoyi Lin, Zhengyuan Zhang, Haiyan Yin, Zhiguang Cao, Senthilnath Jayavelu, Xiaoli Li

93. EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design AAAI, 2026. paper, code

    Fei Liu, Yilu Liu, Qingfu Zhang, Xialiang Tong, Mingxuan Yuan

94. G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design Arxiv, 2026. paper, code

    Baoyun Zhao, He Wang, Liang Zeng

95. Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs ICLR, 2026. paper, code

    Filip Rydin, Attila Lischka, Jiaming Wu, Morteza Haghir Chehreghani, Balazs Kulcsar

96. ⭐MaskCO: Masked Generation Drives Effective Representation Learning and Exploiting for Combinatorial Optimization ICLR, 2026. paper, code

    Lvda Chen, Yang Li, Junchi Yan

97. Towards Efficient Constraint Handling in Neural Solvers for Routing Problems ICLR, 2026. paper, code

    Jieyi Bi, Zhiguang Cao, Jianan Zhou, Wen Song, Yaoxin Wu, Jie Zhang, Yining Ma, Cathy Wu

98. ⭐Native Adaptive Solution Expansion for Diffusion-based Combinatorial Optimization ICLR, 2026. paper

    Yu Wang, Yang Li, Jiale Ma, Junchi Yan, Yi Chang

99. ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problems ICLR, 2026. paper, code

    Zhuoli Yin, Yi Ding, Reem Khir, Hua Cai

100. FrontierCO: Real-World and Large-Scale Evaluation of Machine Learning Solvers for Combinatorial Optimization ICLR, 2026. paper, code

*Shengyu Feng, Weiwei Sun, Shanda Li, Ameet Talwalkar, Yiming Yang*

101. Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers ICLR, 2026. paper, code

*Xuanhao Pan, Chenguang Wang, Chaolong Ying, Ye XUE, Tianshu Yu*

Job Shop Scheduling Problem

1. Smart Manufacturing Scheduling With Edge Computing Using Multiclass Deep Q Network Transactions on Industrial Informatics, 2019. journal

   Chun-Cheng Lin, Der-Jiunn Deng, Yen-Ling Chih, Hsin-Ting Chiu

2. Multi-Agent Reinforcement Learning for Job Shop Scheduling in Flexible Manufacturing Systems International Conference on Artificial Intelligence for Industries (AI4I), 2019. paper

   Schirin Baer, Jupiter Bakakeu, Richard Meyes, Tobias Meisen

3. Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning. NeurIPS, 2020. paper, code

   Cong Zhang, Wen Song, Zhiguang Cao, Jie Zhang, Puay Siew Tan, Chi Xu

4. ScheduleNet: Learn to Solve Multi-agent Scheduling Problems with Reinforcement Learning Arxiv, 2021. paper

   Junyoung Park, Sanjar Bakhtiyar, Jinkyoo Park

5. Dynamic job-shop scheduling in smart manufacturing using deep reinforcement learning Computer Networks, 2021. journal

   Libing Wang, Xin Hu, Yin Wang, Sujie Xu, Shijun Ma, Kexin Yang, Zhijun Liu, Weidong Wang

6. Learning to schedule job-shop problems: Representation and policy learning using graph neural network and reinforcement learning. International Journal of Production Research, 2021. journal

   Junyoung Park, Jaehyeong Chun, Sang Hun Kim, Youngkook Kim, Jinkyoo Park

7. Explainable reinforcement learning in production control of job shop manufacturing system. International Journal of Production Research, 2021. journal

   Andreas Kuhnle, Marvin Carl May, Louis Sch?fer, Gisela Lanza

8. DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization NeurIPS, 2023. paper, code

   Haoran Ye, Jiarui Wang, Zhiguang Cao, Helan Liang, Yong Li

9. Winner Takes It All: Training Performant RL Populations for Combinatorial Optimization NeurIPS, 2023. paper

   Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Cl{'e}ment Bonnet, Thomas D Barrett

10. Combinatorial Optimization with Policy Adaptation using Latent Space Search NeurIPS, 2023. paper

    Felix Chalumeau, Shikha Surana, Cl{'e}ment Bonnet, Nathan Grinsztajn, Arnu Pretorius, Alexandre Laterre, Thomas D Barrett

11. Neural DAG Scheduling via One-Shot Priority Sampling ICLR, 2023. paper

    Wonseok Jeon, Mukul Gagrani, Burak Bartan, Weiliang Will Zeng, Harris Teague, Piero Zappi, Christopher Lott

12. Robust Scheduling with GFlowNets ICLR, 2023. paper

    David W Zhang, Corrado Rainone, Markus Peschl, Roberto Bondesan

13. Continual Task Allocation in Meta-Policy Network via Sparse Prompting ICML, 2023. paper

    Yijun, Tianyi Zhou, Jing Jiang, Guodong Long Yang, Yuhui Shi.

14. Applicability of Neural Combinatorial Optimization: A Critical View TELO, 2024. journal, code

    Andoni I. Garmendia, Josu Ceberio, Alexander Mendiburu

15. Large Language Models as End-to-end Combinatorial Optimization Solvers NeurIPS, 2025. paper, code

    Xia Jiang, Yaoxin Wu, Minshuo Li, Zhiguang Cao, Yingqian Zhang

16. BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization ICML, 2025. paper, code

    Zijun Liao, Jinbiao Chen, Debing Wang, Zizhen Zhang, Jiahai Wang

17. Multi-Action Self-Improvement for Neural Combinatorial Optimization ICLR, 2026. paper, code

    Laurin Luttmann, Lin Xie

18. ReSched: Rethinking Flexible Job Shop Scheduling from a Transformer-based Architecture with Simplified States ICLR, 2026. paper, code

    Xiangjie Xiao, Zhiguang Cao, Cong Zhang, Wen Song

19. Neural Multi-Objective Combinatorial Optimization for Flexible Job Shop Scheduling Problems ICLR, 2026. paper

    Igor G. Smit, Yaoxin Wu, Pavel Troubil, Yingqian Zhang, Wim P.M. Nuijten

Flow Shop Problem

1. Preference Optimization for Combinatorial Optimization Problems ICML, 2025. paper, code

   Mingjun Pan, Guanquan Lin, You-Wei Luo, Bin Zhu, Zhien Dai, Lijun Sun, Chun Yuan

2. PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization NeurIPS, 2025. paper, code

   Federico Berto, Chuanbo Hua, Laurin Luttmann, Jiwoo Son, Junyoung Park, Kyuree Ahn, Changhyun Kwon, Lin Xie, Jinkyoo Park

3. Multi-Action Self-Improvement for Neural Combinatorial Optimization ICLR, 2026. paper, code

   Laurin Luttmann, Lin Xie

Sorting & Ranking

1. Ranking via sinkhorn propagation Arxiv, 2011. paper

   Ryan Prescott Adams, Richard S. Zemel

2. Predict+optimise with ranking objectives: exhaustively learning linear functions IJCAI, 2019. paper

   Emir Demirovic, Peter J. Stuckey, James Bailey, Jeffrey Chan, Christopher Leckie, Kotagiri Ramamohanarao, Tias Guns

3. Stochastic Optimization of Sorting Networks via Continuous Relaxations ICLR, 2019. paper, code

   Aditya Grover, Eric Wang, Aaron Zweig, Stefano Ermon

4. Differentiable Ranking and Sorting using Optimal Transport NeurIPS, 2019. paper

   Marco Cuturi, Olivier Teboul, Jean-Philippe Vert

5. Optimizing Rank-Based Metrics With Blackbox Differentiation CVPR, 2020. paper, code

   Marin Vlastelica, Anselm Paulus, Vít Musil, Georg Martius, Michal Rolínek

6. Fast Differentiable Sorting and Ranking ICML, 2020. paper, code

   Mathieu Blondel Olivier Teboul Quentin Berthet Josip Djolonga

7. SoftSort: A Continuous Relaxation for the argsort Operator ICML, 2020. paper, code

   Sebastian Prillo, Julian Martin Eisenschlos

8. differentiable top k with optimal transport NeurIPS, 2020. paper

   Yujia Xie, Hanjun Dai, Minshuo Chen, Bo Dai, Tuo Zhao, Hongyuan Zha, Wei Wei, Tomas Pfister

9. Automatic Loss Function Search for Predict-Then-Optimize Problems with Strong Ranking Property ICLR, 2022. paper, code

   Boshi Wang, Jialin Yi, Hang Dong, Bo Qiao, Chuan Luo, Qingwei Lin

10. Decision-Focused Learning: Through the Lens of Learning to Rank ICML, 2022. paper, code

    Jayanta Mandi, Vı́ctor Bucarey, Maxime Mulamba Ke Tchomba, Tias Guns

11. PiRank-Scalable Learning To Rank via Differentiable Sorting NeurIPS, 2022. paper, code

    Robin Marcel Edwin Swezey, Aditya Grover, Bruno Charron, Stefano Ermon

12. Neural Improvement Heuristics for Graph Combinatorial Optimization Problems TNNLS, 2023. journal, code

    Andoni I. Garmendia, Josu Ceberio, Alexander Mendiburu

13. Applicability of Neural Combinatorial Optimization: A Critical View TELO, 2024. journal, code

    Andoni I. Garmendia, Josu Ceberio, Alexander Mendiburu

Graph Matching

1. Revised Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks Arxiv, 2017. paper, code

   Alex Nowak, Soledad Villar, S. Afonso Bandeira, Joan Bruna

2. Deep Learning of Graph Matching. CVPR, 2018. paper

   Andrei Zanfir, Cristian Sminchisescu

3. ⭐Learning Combinatorial Embedding Networks for Deep Graph Matching. ICCV, 2019. paper, code

   Runzhong Wang, Junchi Yan, Xiaokang Yang

4. Deep Graphical Feature Learning for the Feature Matching Problem. ICCV, 2019. paper

   Zhen Zhang, Wee Sun Lee

5. GLMNet: Graph Learning-Matching Networks for Feature Matching. Arxiv, 2019. paper

   Bo Jiang, Pengfei Sun, Jin Tang, Bin Luo

6. ⭐Learning deep graph matching with channel-independent embedding and Hungarian attention. ICLR, 2020. paper, code

   Tianshu Yu, Runzhong Wang, Junchi Yan, Baoxin Li

7. Deep Graph Matching Consensus. ICLR, 2020. paper

   Matthias Fey, Jan E. Lenssen, Christopher Morris, Jonathan Masci, Nils M. Kriege

8. ⭐Graduated Assignment for Joint Multi-Graph Matching and Clustering with Application to Unsupervised Graph Matching Network Learning. NeurIPS, 2020. paper, code

   Runzhong Wang, Junchi Yan, Xiaokang Yang

9. ⭐Combinatorial Learning of Robust Deep Graph Matching: An Embedding Based Approach. TPAMI, 2020. paper, code

   Runzhong Wang, Junchi Yan, Xiaokang Yang

10. Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers. ECCV, 2020. paper, code

    Michal Rolinek, Paul Swoboda, Dominik Zietlow, Anselm Paulus, Vit Musil, Georg Martius

11. ⭐Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching. TPAMI, 2021. paper, code

    Runzhong Wang, Junchi Yan, Xiaokang Yang

12. ⭐Deep Latent Graph Matching ICML, 2021. paper

    Tianshu Yu, Runzhong Wang, Junchi Yan, Baoxin Li

13. IA-GM: A Deep Bidirectional Learning Method for Graph Matching AAAI, 2021. paper

    Kaixuan Zhao, Shikui Tu, Lei Xu

14. Deep Graph Matching under Quadratic Constraint CVPR, 2021. paper

    Quankai Gao, Fudong Wang, Nan Xue, Jin-Gang Yu, Gui-Song Xia

15. GAMnet: Robust Feature Matching via Graph Adversarial-Matching Network MM, 2021. paper

    Bo Jiang, Pengfei Sun, Ziyan Zhang, Jin Tang, Bin Luo

16. Hypergraph Neural Networks for Hypergraph Matching ICCV, 2021. paper

    Xiaowei Liao, Yong Xu, Haibin Ling

17. Learning to Match Features with Seeded Graph Matching Network ICCV, 2021. paper

    Hongkai Chen, Zixin Luo, Jiahui Zhang, Lei Zhou, Xuyang Bai, Zeyu Hu, Chiew-Lan Tai, Long Quan

18. ⭐Appearance and Structure Aware Robust Deep Visual Graph Matching: Attack, Defense and Beyond CVPR, 2022. paper, code

    Qibing Ren, Qingquan Bao, Runzhong Wang, Junchi Yan

19. ⭐Self-supervised Learning of Visual Graph Matching ECCV, 2022. paper, code

    Chang Liu, Shaofeng Zhang, Xiaokang Yang, Junchi Yan

20. ⭐Revocable Deep Reinforcement Learning with Affinity Regularization for Outlier-Robust Graph Matching. ICLR, 2023. paper, code

    Chang Liu, Zetian Jiang, Runzhong Wang, Junchi Yan, Lingxiao Huang, Pinyan Lu

21. SeedGNN: Graph Neural Network for Supervised Seeded Graph Matching ICML, 2023. paper

    Liren Yu, Jiaming Xu, Xiaojun Lin

22. D2Match: Leveraging Deep Learning and Degeneracy for Subgraph Matching ICML, 2023. paper

    Xuan Liu, Lin Zhang, Jiaqi Sun, Yujiu Yang, Haiqing Yang

23. ⭐LinSATNet: The Positive Linear Satisfiability Neural Networks ICML, 2023. paper, code

    Runzhong Wang, Yunhao Zhang, Ziao Guo, Tianyi Chen, Xiaokang Yang, Junchi Yan

24. LVM-Med: Learning Large-Scale Self-Supervised Vision Models for Medical Imaging via Second-order Graph Matching NeurIPS, 2023. paper, code

    Duy MH Nguyen, Hoang Nguyen, Nghiem T Diep, Tan N Pham, Tri Cao, Binh T Nguyen, Paul Swoboda, Nhat Ho, Shadi Albarqouni, Pengtao Xie, others

25. Improving Graph Matching with Positional Reconstruction Encoder-Decoder Network NeurIPS, 2023. paper

    Yixiao Zhou, Ruiqi Jia, Hongxiang Lin, Hefeng Quan, Yumeng Zhao, Xiaoqing Lyu

26. Learning to Prune Instances of Steiner Tree Problem in Grap INOC, 2024. paper, code

    Jiwei Zhang, Dena Tayebi, Saurabh Ray, Deepak Ajwani

Quadratic Assignment Problem

1. Revised Note on Learning Algorithms for Quadratic Assignment with Graph Neural Networks Arxiv, 2017. paper, code

   Alex Nowak, Soledad Villar, S. Afonso Bandeira, Joan Bruna

2. ⭐Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching. TPAMI, 2021. paper, code

   Runzhong Wang, Junchi Yan, Xiaokang Yang

3. ⭐Revocable Deep Reinforcement Learning with Affinity Regularization for Outlier-Robust Graph Matching. ICLR, 2023. paper, code

   Chang Liu, Zetian Jiang, Runzhong Wang, Junchi Yan, Lingxiao Huang, Pinyan Lu

4. ⭐Towards Quantum Machine Learning for Constrained Combinatorial Optimization: a Quantum QAP Solver ICML, 2023. paper

   Xinyu Ye, Ge Yan, Junchi Yan

5. Differentiable extensions with rounding guarantees for combinatorial optimization over permutations NeurIPS, 2025. paper

   Robert R Nerem, Zhishang Luo, Akbar Rafiey, Yusu Wang

Portfolio Optimization

1. ⭐LinSATNet: The Positive Linear Satisfiability Neural Networks ICML, 2023. paper, code

   Runzhong Wang, Yunhao Zhang, Ziao Guo, Tianyi Chen, Xiaokang Yang, Junchi Yan

2. Integrating prediction in mean-variance portfolio optimization Quantitative Finance, 2023. paper

   Andrew Butler, Roy H Kwon

3. ⭐Towards One-shot Neural Combinatorial Solvers: Theoretical and Empirical Notes on the Cardinality-Constrained Case ICLR, 2023. paper, code

   Runzhong Wang, Li Shen, Yiting Chen, Junchi Yan, Xiaokang Yang, Dacheng Tao

Maximal Cut

1. Learning Combinatorial Optimization Algorithms over Graphs. NeurIPS, 2017. paper

   Hanjun Dai, Elias B Khalil, Yuyu Zhang, Bistra Dilkina, Le Song

2. Exploratory Combinatorial Optimization with Reinforcement Learning. AAAI, 2020. paper

   Thomas LBarrett, William Clements, Jakob Foerster, Alex Lvovsky

3. Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs. NeurIPS, 2020. paper

   Nikolaos Karalias, Andreas Loukas

4. Reversible Action Design for Combinatorial Optimization with Reinforcement Learning Arxiv, 2021. paper

   Fan Yao, Renqin Cai, Hongning Wang

5. LeNSE: Learning To Navigate Subgraph Embeddings for Large-Scale Combinatorial Optimisation ICML, 2022. paper, code

   David Ireland, G. Montana

6. Learning to Solve Combinatorial Graph Partitioning Problems via Efficient Exploration Arxiv, 2022. paper, code

   Thomas D Barrett, Christopher WF Parsonson, Alexandre Laterre

7. Revisiting Sampling for Combinatorial Optimization ICML, 2023. paper

   Haoran, Goshvadi Katayoon, Nova Azade, Schuurmans Dale Sun, Dai Hanjun.

8. Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods NeurIPS, 2023. paper, code

   Constantine Caramanis, Dimitris Fotakis, Alkis Kalavasis, Vasilis Kontonis, Christos Tzamos

9. Neural Improvement Heuristics for Graph Combinatorial Optimization Problems TNNLS, 2023. journal, code

   Andoni I. Garmendia, Josu Ceberio, Alexander Mendiburu

10. Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets NeurlPS, 2023. paper, code

    Dinghuai Zhang, Hanjun Dai, Nikolay Malkin, Aaron Courville, Yoshua Bengio, Ling Pan

11. Variational Annealing on Graphs for Combinatorial Optimization NeurlPS, 2023. paper, code

    Sebastian Sanokowski, Wilhelm Franz Berghammer, Sepp Hochreiter, Sebastian Lehner

12. DISCS: A Benchmark for Discrete Sampling NeurlPS, 2023. paper, code

    Katayoon Goshvadi, Haoran Sun, Xingchao Liu, Azade Nova, Ruqi Zhang, Will Sussman Grathwohl, Dale Schuurmans, Hanjun Dai

13. MARCO: A Memory-Augmented Reinforcement Framework for Combinatorial Optimization IJCAI, 2024. paper, code

    Andoni I. Garmendia, Quentin Cappart, Josu Ceberio, Alexander Mendiburu

14. Controlling Continuous Relaxation for Combinatorial Optimization NeurlPS, 2024. paper

    Yuma Ichikawa

15. Distributed Constrained Combinatorial Optimization leveraging Hypergraph Neural Networks Nature Machine Intelligence, 2024. paper, code

    Nasimeh Heydaribeni, Xinrui Zhan, Ruisi Zhang, Tina Eliassi-Rad, Farinaz Koushanfar

16. Efficient Combinatorial Optimization via Heat Diffusion NeurIPS, 2024. paper, code

    Hengyuan Ma, Wenlian Lu, Jianfeng Feng

17. A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization ICML, 2024. paper, code

    Sebastian Sanokowski, Sepp Hochreiter, Sebastian Lehner

18. ⭐ML4CO-Bench-101: Benchmark Machine Learning for Classic Combinatorial Problems on Graphs NeurIPS, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

19. ⭐COExpander: Adaptive Solution Expansion for Combinatorial Optimization ICML, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

20. Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics ICLR, 2025. paper

    Sebastian Sanokowski, Wilhelm Franz Berghammer, Haoyu Peter Wang, Martin Ennemoser, Sepp Hochreiter, Sebastian Lehner

21. Learning to Explore and Exploit with GNNs for Unsupervised Combinatorial Optimization ICLR, 2025. paper, code

    Utku Umur Acikalin, Aaron M. Ferber, Carla P. Gomes

22. Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling ICLR, 2025. paper, code

    Yuma Ichikawa, Yamato Arai

23. Regularized Langevin Dynamics for Combinatorial Optimization ICML, 2025. paper, code

    Shengyu Feng, Yiming Yang

24. Projecting Latent RL Actions: Towards Generalizable and Scalable Graph Combinatorial Optimization Arxiv, 2026. paper, code

    Franco Terranova, Guillermo Bernardez, Albert Cabellos-Aparicio, Nina Miolane, Abdelkader Lahmadi

Vehicle Routing Problem

1. Learning to Perform Local Rewriting for Combinatorial Optimization. NeurIPS, 2019. paper, code

   Xinyun Chen, Yuandong Tian

2. Deep Reinforcement Learning for the Electric Vehicle Routing Problem with Time Windows. Arxiv, 2020. paper

   Bo Lin, Bissan Ghaddar, Jatin Nathwani

3. Efficiently Solving the Practical,Vehicle Routing Problem: A Novel Joint Learning Approach. KDD, 2020. paper

   Lu Duan, Yang Zhan, Haoyuan Hu, Yu Gong, Jiangwen Wei, Xiaodong Zhang, Yinghui Xu

4. Reinforcement Learning with Combinatorial Actions: An Application to Vehicle Routing NeurIPS, 2020. paper, code

   Arthur Delarue, Ross Anderson, Christian Tjandraatmadja

5. A Learning-based Iterative Method for Solving Vehicle Routing Problems ICLR, 2020. paper

   Hao Lu, Xingwen Zhang, Shuang Yang

6. Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem Arxiv, 2020. paper

   Andre Hottung, Kevin Tierney

7. Learning Improvement Heuristics for Solving Routing Problems TNNLS, 2021. journal

   Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang, Andrew Lim

8. Reinforcement Learning for Route Optimization with Robustness Guarantees IJCAI, 2021. paper

   Tobias Jacobs, Francesco Alesiani, Gulcin Ermis

9. Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problems. AAAI, 2021. paper, code

   Liang Xin, Wen Song, Zhiguang Cao, Jie Zhang

10. Analytics and Machine Learning in Vehicle Routing Research Arxiv, 2021. paper

    Ruibin Bai, Xinan Chen, Zhi-Long Chen, Tianxiang Cui, Shuhui Gong, Wentao He, Xiaoping Jiang, Huan Jin, Jiahuan Jin, Graham Kendall, others

11. RP-DQN: An application of Q-Learning to Vehicle Routing Problems Arxiv, 2021. paper

    Ahmad Bdeir, Simon Boeder, Tim Dernedde, Kirill Tkachuk, Jonas K Falkner, Lars Schmidt-Thieme

12. Deep Policy Dynamic Programming for Vehicle Routing Problems Arxiv, 2021. paper

    Wouter Kool, Herke van Hoof, Joaquim Gromicho, Max Welling

13. Learning to Delegate for Large-scale Vehicle Routing NeurIPS, 2021. paper

    Sirui Li, Zhongxia Yan, Cathy Wu

14. Learning a Latent Search Space for Routing Problems using Variational Autoencoders ICLR, 2021. paper

    Andre Hottung, Bhanu Bhandari, Kevin Tierney

15. Preference Conditioned Neural Multi-objective Combinatorial Optimization ICLR, 2022. paper

    Xi Lin, Zhiyuan Yang, Qingfu Zhang

16. Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation NeurIPS, 2022. paper, code

    Jieyi Bi, Yining Ma, Jiahai Wang, Zhiguang Cao, Jinbiao Chen, Yuan Sun, Yeow Meng Chee

17. Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization NeurIPS, 2022. paper, code

    Minsu Kim, Junyoung Park, Jinkyoo Park

18. Simulation-guided Beam Search for Neural Combinatorial Optimization NeurIPS, 2022. paper, code

    Jinho Choo, Yeong-Dae Kwon, Jihoon Kim, Jeongwoo Jae, Andr{'e} Hottung, Kevin Tierney, Youngjune Gwon

19. Learning to CROSS exchange to solve min-max vehicle routing problems ICLR, 2023. paper

    Minjun Kim, Junyoung Park, Jinkyoo Park

20. Generalize Learned Heuristics to Solve Large-scale Vehicle Routing Problems in Real-time ICLR, 2023. paper

    Qingchun Hou, Jingwei Yang, Yiqiang Su, Xiaoqing Wang, Yuming Deng

21. Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimization ICML, 2023. paper

    Jiwoo Son, Minsu Kim, Hyeonah Kim, Jinkyoo Park

22. Towards Omni-generalizable Neural Methods for Vehicle Routing Problems ICML, 2023. paper, code

    Zhou Jianan, Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang

23. DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization NeurIPS, 2023. paper, code

    Haoran Ye, Jiarui Wang, Zhiguang Cao, Helan Liang, Yong Li

24. Winner Takes It All: Training Performant RL Populations for Combinatorial Optimization NeurIPS, 2023. paper

    Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Cl{'e}ment Bonnet, Thomas D Barrett

25. Combinatorial Optimization with Policy Adaptation using Latent Space Search NeurIPS, 2023. paper

    Felix Chalumeau, Shikha Surana, Cl{'e}ment Bonnet, Nathan Grinsztajn, Arnu Pretorius, Alexandre Laterre, Thomas D Barrett

26. Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization NeurIPS, 2023. paper, code

    Jinbiao Chen, Jiahai Wang, Zizhen Zhang, Zhiguang Cao, Te Ye, Siyuan Chen

27. BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization NeurIPS, 2023. paper, code

    Darko Drakulic, Sofia Michel, Florian Mai, Arnaud Sors, Jean-Marc Andreoli

28. Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization NeurIPS, 2023. paper, code

    Fu Luo, Xi Lin, Fei Liu, Qingfu Zhang, Zhenkun Wang

29. Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement NeurIPS, 2023. paper, code

    Jinbiao Chen, Zizhen Zhang, Zhiguang Cao, Yaoxin Wu, Yining Ma, Te Ye, Jiahai Wang

30. Ensemble-based Deep Reinforcement Learning for Vehicle Routing Problems under Distribution Shift NeurIPS, 2023. paper

    Yuan Jiang, Zhiguang Cao, Yaoxin Wu, Wen Song, Jie Zhang

31. Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt NeurIPS, 2023. paper, code

    Yining Ma, Zhiguang Cao, Yeow Meng Chee

32. Learning to Prune Electric Vehicle Routing Problems LION, 2023. paper

    James Fitzpatrick, Deepak Ajwani, Paula Carroll

33. GLOP: Learning Global Partition and Local Construction for Solving Large-Scale Routing Problems in Real-Time AAAI, 2024. paper, code

    Haoran Ye, Jiarui Wang, Helan Liang, Zhiguang Cao, Yong Li, Fanzhang Li

34. Distilling Autoregressive Models to Obtain High-Performance Non-autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed AAAI, 2024. paper, code

    Yubin Xiao, Di Wang, Boyang Li, Mingzhao Wang, Xuan Wu, Changliang Zhou, You Zhou

35. Neural Combinatorial Optimization for Robust Routing Problem with Uncertain Travel Times NeurIPS, 2024. paper

    Pei Xiao, Zizhen Zhang, Jinbiao Chen, Jiahai Wang, Zhenzhen Zhang

36. Collaboration! Towards Robust Neural Methods for Routing Problems NeurIPS, 2024. paper, code

    Jianan Zhou, Yaoxin Wu, Zhiguang Cao, Wen Song, Jie Zhang, Zhiqi Shen

37. UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems NeurIPS, 2024. paper, code

    Zhi Zheng, Changliang Zhou, Tong Xialiang, Mingxuan Yuan, Zhenkun Wang

38. A Scalable Learning Approach for the Capacitated Vehicle Routing Problem Computers and Operations Research, 2024. journal

    James Fitzpatrick, Deepak Ajwani, Paula Carroll

39. A Neural Column Generation Approach to the Vehicle Routing Problem with Two-Dimensional Loading and Last-In-First-Out Constraints IJCAI, 2024. paper, code

    Yifan Xia, Xiangyi Zhang

40. MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts ICML, 2024. paper, code

    Jianan Zhou, Zhiguang Cao, Yaoxin Wu, Wen Song, Yining Ma, Jie Zhang, Xu Chi

41. DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems ICML, 2024. paper

    Zhi Zheng, Shunyu Yao, Zhenkun Wang, Xialiang Tong, Mingxuan Yuan, Ke Tang

42. Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model ICML, 2024. paper, code

    Fei Liu, Xialiang Tong, Mingxuan Yuan, Xi Lin, Fu Luo, Zhenkun Wang, Zhichao Lu, Qingfu Zhang

43. ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution NeurIPS, 2024. paper, code

    Haoran Ye, Jiarui Wang, Zhiguang Cao, Federico Berto, Chuanbo Hua, Haeyeon Kim, Jinkyoo Park, Guojie Song

44. Rethinking Neural Multi-Objective Combinatorial Optimization via Neat Weight Embedding ICLR, 2025. paper

    Jinbiao Chen, Zhiguang Cao, Jiahai Wang, Yaoxin Wu, Hanzhang Qin, Zizhen Zhang, Yue-Jiao Gong

45. Boosting Neural Combinatorial Optimization for Large-Scale Vehicle Routing Problems ICLR, 2025. paper

    Fu Luo, Xi Lin, Yaoxin Wu, Zhenkun Wang, Tong Xialiang, Mingxuan Yuan, Qingfu Zhang

46. ⭐ML4CO-Bench-101: Benchmark Machine Learning for Classic Combinatorial Problems on Graphs NeurIPS, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

47. ⭐COExpander: Adaptive Solution Expansion for Combinatorial Optimization ICML, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

48. Large Language Models as End-to-end Combinatorial Optimization Solvers NeurIPS, 2025. paper, code

    Xia Jiang, Yaoxin Wu, Minshuo Li, Zhiguang Cao, Yingqian Zhang

49. Neural Solver Selection for Combinatorial Optimization ICML, 2025. paper

    Chengrui Gao, Haopu Shang, Ke Xue, Chao Qian

50. Preference Optimization for Combinatorial Optimization Problems ICML, 2025. paper, code

    Mingjun Pan, Guanquan Lin, You-Wei Luo, Bin Zhu, Zhien Dai, Lijun Sun, Chun Yuan

51. A Mixed-Curvature based Pre-training Paradigm for Multi-Task Vehicle Routing Solver ICML, 2025. paper

    Suyu Liu, Zhiguang Cao, Shanshan Feng, Yew-Soon Ong

52. SHIELD: Multi-task Multi-distribution Vehicle Routing Solver with Sparsity and Hierarchy ICML, 2025. paper

    Yong Liang Goh, Zhiguang Cao, Yining Ma, Jianan Zhou, Mohammed Haroon Dupty, Wee Sun Lee

53. PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization NeurIPS, 2025. paper, code

    Federico Berto, Chuanbo Hua, Laurin Luttmann, Jiwoo Son, Junyoung Park, Kyuree Ahn, Changhyun Kwon, Lin Xie, Jinkyoo Park

54. CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention ICML, 2025. paper, code

    Han Li, Fei Liu, Zhi Zheng, Yu Zhang, Zhenkun Wang

55. Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees NeurIPS, 2025. paper, code

    Fu Luo, Yaoxin Wu, Zhi Zheng, Zhenkun Wang

56. Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning NeurIPS, 2025. paper, code

    Yuanyao Chen, Rongsheng Chen, Fu Luo, Zhenkun Wang

57. Learning to Insert for Constructive Neural Vehicle Routing Solver NeurIPS, 2025. paper, code

    Fu Luo, Xi Lin, Mengyuan Zhong, Fei Liu, Zhenkun Wang, Jianyong Sun, Qingfu Zhang

58. MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver NeurIPS, 2025. paper

    Yuepeng Zheng, Fu Luo, Zhenkun Wang, Yaoxin Wu, Yu Zhou

59. Rethinking Light Decoder-based Solvers for Vehicle Routing Problems ICLR, 2025. paper, code

    Ziwei Huang, Jianan Zhou, Zhiguang Cao, Yixin Xu

60. Adversarial Generative Flow Network for Solving Vehicle Routing Problems ICLR, 2025. paper, code

    Ni Zhang, Jingfeng Yang, Zhiguang Cao, Xu Chi

61. Generalizable Heuristic Generation Through LLMs with Meta-Optimization ICLR, 2026. paper, code

    Yiding Shi, Jianan Zhou, Wen Song, Jieyi Bi, Yaoxin Wu, Zhiguang Cao, Jie Zhang

62. DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization AAMAS, 2026. paper

    Shengkai Chen, Zhiguang Cao, Jianan Zhou, Yaoxin Wu, Senthilnath Jayavelu, Zhuoyi Lin, Xiaoli Li, Shili Xiang

63. Bridging Synthetic and Real Routing Problems via LLM-Guided Instance Generation and Progressive Adaptation AAAI, 2026. paper, code

    Jianghan Zhu, Yaoxin Wu, Zhuoyi Lin, Zhengyuan Zhang, Haiyan Yin, Zhiguang Cao, Senthilnath Jayavelu, Xiaoli Li

64. EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design AAAI, 2026. paper, code

    Fei Liu, Yilu Liu, Qingfu Zhang, Xialiang Tong, Mingxuan Yuan

65. Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLM ICLR, 2026. paper, code

    Rongjie Zhu, Cong Zhang, Zhiguang Cao

66. RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization ICLR, 2026. paper, code

    Jiwoo Son, Zhikai Zhao, Federico Berto, Chuanbo Hua, Zhiguang Cao, Changhyun Kwon, Jinkyoo Park

67. Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs ICLR, 2026. paper, code

    Shuangchun Gui, Suyu Liu, Xuehe Wang, Zhiguang Cao

68. RADAR: Learning to Route with Asymmetry-aware Distance Representations ICLR, 2026. paper, code

    Hang Yi, Ziwei Huang, Yining Ma, Zhiguang Cao

69. Combination-of-Experts with Knowledge Sharing for Cross-Task Vehicle Routing Problems ICLR, 2026. paper, code

    Zikang Yu, Jinbiao Chen, Jiahai Wang

70. An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems ICLR, 2026. paper, code

    Ni Zhang, Zhiguang Cao, Jianan Zhou, Cong Zhang, Yew-Soon Ong

71. Learning to Segment for Vehicle Routing Problems ICLR, 2026. paper, code

    Wenbin Ouyang, Sirui Li, Yining Ma, Cathy Wu

72. G-LNS: Generative Large Neighborhood Search for LLM-Based Automatic Heuristic Design Arxiv, 2026. paper, code

    Baoyun Zhao, He Wang, Liang Zeng

73. Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphs ICLR, 2026. paper, code

    Filip Rydin, Attila Lischka, Jiaming Wu, Morteza Haghir Chehreghani, Balazs Kulcsar

74. ⭐MaskCO: Masked Generation Drives Effective Representation Learning and Exploiting for Combinatorial Optimization ICLR, 2026. paper, code

    Lvda Chen, Yang Li, Junchi Yan

75. Towards Efficient Constraint Handling in Neural Solvers for Routing Problems ICLR, 2026. paper, code

    Jieyi Bi, Zhiguang Cao, Jianan Zhou, Wen Song, Yaoxin Wu, Jie Zhang, Yining Ma, Cathy Wu

76. ⭐Native Adaptive Solution Expansion for Diffusion-based Combinatorial Optimization ICLR, 2026. paper

    Yu Wang, Yang Li, Jiale Ma, Junchi Yan, Yi Chang

77. Multi-Action Self-Improvement for Neural Combinatorial Optimization ICLR, 2026. paper, code

    Laurin Luttmann, Lin Xie

78. Multiagent Environments for Vehicle Routing Problems INFORMS Journal on Computing, 2026. paper, code

    Ricardo Gama, Ricardo Cunha, Daniel Fuertes, Carlos R. del-Blanco, Hugo L. Fernandes

Maximum Independent Set

1. Combinatorial Optimization with Graph Convolutional Networks and Guided Tree Search. NeurIPS, 2018. paper

   Zhuwen Li, Qifeng Chen, Vladlen Koltun

2. Learning What to Defer for Maximum Independent Sets ICML, 2020. paper

   Sungsoo Ahn, Younggyo Seo, Jinwoo Shin

3. Distributed Scheduling Using Graph Neural Networks ICASSP, 2021. paper

   Zhongyuan Zhao, Gunjan Verma, Chirag Rao, Ananthram Swami, Santiago Segarra

4. Solving Graph-based Public Good Games with Tree Search and Imitation Learning NeurlPS, 2021. paper

   Victor-Alexandru Darvariu, Stephen Hailes, Mirco Musolesi

5. NN-Baker: A Neural-network Infused Algorithmic Framework for Optimization Problems on Geometric Intersection Graphs NeurlPS, 2021. paper

   Evan McCarty, Qi Zhao, Anastasios Sidiropoulos, Yusu Wang

6. What's Wrong with Deep Learning in Tree Search for Combinatorial Optimization ICLR, 2022. paper, code

   Maximilian Bother, Otto Kissig, Martin Taraz, Sarel Cohen, Karen Seidel, Tobias Friedrich

7. Optimistic tree search strategies for black-box combinatorial optimization NeurlPS, 2022. paper

   Cedric Malherbe, Antoine Grosnit, Rasul Tutunov, Haitham Bou Ammar, Jun Wang

8. ⭐ROCO: A General Framework for Evaluating Robustness of Combinatorial Optimization Solvers on Graphs ICLR, 2023. paper, code

   Han Lu, Zenan Li, Runzhong Wang, Qibing Ren, Xijun Li, Mingxuan Yuan, Jia Zeng, Xiaokang Yang, Junchi Yan

9. Revisiting Sampling for Combinatorial Optimization ICML, 2023. paper

   Haoran, Goshvadi Katayoon, Nova Azade, Schuurmans Dale Sun, Dai Hanjun.

10. DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization NeurIPS, 2023. paper, code

    Zhiqing Sun, Yiming Yang

11. ⭐T2T: From Distribution Learning in Training to Gradient Search in Testing for Combinatorial Optimization NeurIPS, 2023. paper, code

    Yang Li, Jinpei Guo, Runzhong Wang, Junchi Yan

12. Unsupervised Learning for Combinatorial Optimization Needs Meta Learning ICLR, 2023. paper, code

    Haoyu Wang, Pan Li

13. Graph-based Deterministic Policy Gradient for Repetitive Combinatorial Optimization Problems ICLR, 2023. paper, code

    Zhongyuan Zhao, Ananthram Swami, Santiago Segarra

14. Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets NeurlPS, 2023. paper, code

    Dinghuai Zhang, Hanjun Dai, Nikolay Malkin, Aaron Courville, Yoshua Bengio, Ling Pan

15. Variational Annealing on Graphs for Combinatorial Optimization NeurlPS, 2023. paper, code

    Sebastian Sanokowski, Wilhelm Franz Berghammer, Sepp Hochreiter, Sebastian Lehner

16. Maximum Independent Set: Self-Training through Dynamic Programming NeurlPS, 2023. paper, code

    Lorenzo Brusca, Lars CPM Quaedvlieg, Stratis Skoulakis, Grigorios G Chrysos, Volkan Cevher

17. DISCS: A Benchmark for Discrete Sampling NeurlPS, 2023. paper, code

    Katayoon Goshvadi, Haoran Sun, Xingchao Liu, Azade Nova, Ruqi Zhang, Will Sussman Grathwohl, Dale Schuurmans, Hanjun Dai

18. MARCO: A Memory-Augmented Reinforcement Framework for Combinatorial Optimization IJCAI, 2024. paper, code

    Andoni I. Garmendia, Quentin Cappart, Josu Ceberio, Alexander Mendiburu

19. ⭐Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimization NeurIPS, 2024. paper, code

    Yang Li, Jinpei Guo, Runzhong Wang, Hongyuan Zha, Junchi Yan

20. Controlling Continuous Relaxation for Combinatorial Optimization NeurlPS, 2024. paper

    Yuma Ichikawa

21. Distributed Constrained Combinatorial Optimization leveraging Hypergraph Neural Networks Nature Machine Intelligence, 2024. paper, code

    Nasimeh Heydaribeni, Xinrui Zhan, Ruisi Zhang, Tina Eliassi-Rad, Farinaz Koushanfar

22. Efficient Combinatorial Optimization via Heat Diffusion NeurlPS, 2024. paper

    Hengyuan Ma, Wenlian Lu, Jianfeng Feng

23. A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimization ICML, 2024. paper, code

    Sebastian Sanokowski, Sepp Hochreiter, Sebastian Lehner

24. ⭐ML4CO-Bench-101: Benchmark Machine Learning for Classic Combinatorial Problems on Graphs NeurIPS, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

25. ⭐COExpander: Adaptive Solution Expansion for Combinatorial Optimization ICML, 2025. paper, code

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

26. Large Language Models as End-to-end Combinatorial Optimization Solvers NeurIPS, 2025. paper, code

    Xia Jiang, Yaoxin Wu, Minshuo Li, Zhiguang Cao, Yingqian Zhang

27. ⭐StruDiCO: Structured Denoising Diffusion with Gradient-free Inference-stage Boosting for Memory and Time Efficient Combinatorial Optimization NeurIPS, 2025. paper, code

    Yu Wang, Yang Li, Junchi Yan, Yi Chang

28. ⭐Generation as search operator for test-time scaling of diffusion-based combinatorial optimization NeurIPS, 2025. paper, code

    Yang Li, Lvda Chen, Haonan Wang, Runzhong Wang, Junchi Yan

29. Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics ICLR, 2025. paper

    Sebastian Sanokowski, Wilhelm Franz Berghammer, Haoyu Peter Wang, Martin Ennemoser, Sepp Hochreiter, Sebastian Lehner

30. Learning to Explore and Exploit with GNNs for Unsupervised Combinatorial Optimization ICLR, 2025. paper, code

    Utku Umur Acikalin, Aaron M. Ferber, Carla P. Gomes

31. Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling ICLR, 2025. paper, code

    Yuma Ichikawa, Yamato Arai

32. Continuous Parallel Relaxation for Finding Diverse Solutions in Combinatorial Optimization Problems TMLR, 2025. journal, code

    Yuma Ichikawa, Hiroaki Iwashita

33. Regularized Langevin Dynamics for Combinatorial Optimization ICML, 2025. paper, code

    Shengyu Feng, Yiming Yang

34. Geometric Algorithms for Neural Combinatorial Optimization with Constraints NeurIPS, 2025. paper

    Nikolaos Karalias, Akbar Rafiey, Yifei Xu, Zhishang Luo, Behrooz Tahmasebi, Connie Jiang, Stefanie Jegelka

35. ⭐MaskCO: Masked Generation Drives Effective Representation Learning and Exploiting for Combinatorial Optimization ICLR, 2026. paper, code

    Lvda Chen, Yang Li, Junchi Yan

36. ⭐ConRep4CO: Contrastive Representation Learning of Combinatorial Optimization Instances across Types ICLR, 2026. paper, code

    Ziao Guo, Yang Li, Shiyue Wang, Junchi Yan

37. ⭐Native Adaptive Solution Expansion for Diffusion-based Combinatorial Optimization ICLR, 2026. paper

    Yu Wang, Yang Li, Jiale Ma, Junchi Yan, Yi Chang

38. FrontierCO: Real-World and Large-Scale Evaluation of Machine Learning Solvers for Combinatorial Optimization ICLR, 2026. paper, code

    Shengyu Feng, Weiwei Sun, Shanda Li, Ameet Talwalkar, Yiming Yang

Generalization

1. It's Not What Machines Can Learn It's What We Cannot Teach ICML, 2020. paper

   Gal Yehuda, Moshe Gabel, Assaf Schuster

2. Learning TSP Requires Rethinking Generalization CP, 2021. paper, code

   Chaitanya K. Joshi, Quentin Cappart, Louis-Martin Rousseau, Thomas Laurent

3. Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness ICLR, 2022. paper

   Simon Geisler, Johanna Sommer, Jan Schuchardt, Aleksandar Bojchevski, Stephan Günnemann

4. Learning for Robust Combinatorial Optimization: Algorithm and Application INFOCOM, 2022. journal

   Zhihui Shao, Jianyi Yang, Cong Shen, Shaolei Ren

5. ⭐ROCO: A General Framework for Evaluating Robustness of Combinatorial Optimization Solvers on Graphs ICLR, 2023. paper, code

   Han Lu, Zenan Li, Runzhong Wang, Qibing Ren, Xijun Li, Mingxuan Yuan, Jia Zeng, Xiaokang Yang, Junchi Yan

6. Towards Omni-generalizable Neural Methods for Vehicle Routing Problems ICML, 2023. paper, code

   Zhou Jianan, Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang

7. Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model ICML, 2024. paper, code

   Fei Liu, Xialiang Tong, Mingxuan Yuan, Xi Lin, Fu Luo, Zhenkun Wang, Zhichao Lu, Qingfu Zhang

8. ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution NeurIPS, 2024. paper, code

   Haoran Ye, Jiarui Wang, Zhiguang Cao, Federico Berto, Chuanbo Hua, Haeyeon Kim, Jinkyoo Park, Guojie Song

9. GOAL: A Generalist Combinatorial Optimization Agent Learner ICLR, 2025. paper

   Darko Drakulic, Sofia Michel, Jean-Marc Andreoli

10. OPTFM: A Scalable Multi-View Graph Transformer for Hierarchical Pre-Training in Combinatorial Optimization NeurIPS, 2025. paper

    Hao Yuan, Wenli Ouyang, Changwen Zhang, Congrui Li, Yong Sun

11. Projecting Latent RL Actions: Towards Generalizable and Scalable Graph Combinatorial Optimization Arxiv, 2026. paper, code

    Franco Terranova, Guillermo Bernardez, Albert Cabellos-Aparicio, Nina Miolane, Abdelkader Lahmadi

Orienteering Problem

1. A reinforcement learning approach to the orienteering problem with time windows Computers & Operations Research, 2021. paper, code

   Ricardo Gama, Hugo L. Fernandes

2. Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimization ICML, 2023. paper

   Jiwoo Son, Minsu Kim, Hyeonah Kim, Jinkyoo Park

3. DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization NeurIPS, 2023. paper, code

   Haoran Ye, Jiarui Wang, Zhiguang Cao, Helan Liang, Yong Li

4. UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems NeurIPS, 2024. paper, code

   Zhi Zheng, Changliang Zhou, Tong Xialiang, Mingxuan Yuan, Zhenkun Wang

Knapsack

1. A Pointer Network Based Deep Learning Algorithm for 0-1 Knapsack Problem ICACI, 2018. paper

   Shenshen Gu, Hao Tao

2. An Investigation into Prediction + Optimisation for the Knapsack Problem CPAIOR, 2019. paper

   Emir Demirovic, Peter J. Stuckey, James Bailey, Jeffrey Chan, Chris Leckie, Kotagiri Ramamohanarao, Tias Guns

3. A Novel Method to Solve Neural Knapsack Problems ICML, 2021. paper

   Duanshun Li, Jing Liu, Dongeun Lee, Ali Seyedmazloom, Giridhar Kaushik, Kookjin Lee, Noseong Park

4. Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size AAAI, 2021. paper

   Christoph Hertrich, Martin Skutella

5. DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization NeurIPS, 2023. paper, code

   Haoran Ye, Jiarui Wang, Zhiguang Cao, Helan Liang, Yong Li

6. Winner Takes It All: Training Performant RL Populations for Combinatorial Optimization NeurIPS, 2023. paper

   Nathan Grinsztajn, Daniel Furelos-Blanco, Shikha Surana, Cl{'e}ment Bonnet, Thomas D Barrett

7. Efficient Meta Neural Heuristic for Multi-Objective Combinatorial Optimization NeurIPS, 2023. paper, code

   Jinbiao Chen, Jiahai Wang, Zizhen Zhang, Zhiguang Cao, Te Ye, Siyuan Chen

8. BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimization NeurIPS, 2023. paper, code

   Darko Drakulic, Sofia Michel, Florian Mai, Arnaud Sors, Jean-Marc Andreoli

9. Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement NeurIPS, 2023. paper, code

   Jinbiao Chen, Zizhen Zhang, Zhiguang Cao, Yaoxin Wu, Yining Ma, Te Ye, Jiahai Wang

10. Rethinking Neural Multi-Objective Combinatorial Optimization via Neat Weight Embedding ICLR, 2025. paper

    Jinbiao Chen, Zhiguang Cao, Jiahai Wang, Yaoxin Wu, Hanzhang Qin, Zizhen Zhang, Yue-Jiao Gong

11. Approximation algorithms for combinatorial optimization with predictions ICLR, 2025. paper

    Antonios Antoniadis, Marek Elias, Adam Polak, Moritz Venzin

Boolean Satisfiability

1. Graph neural networks and boolean satisfiability. Arxiv, 2017. paper

   Benedikt Bünz, Matthew Lamm.

2. Learning a SAT solver from single-bit supervision. Arxiv, 2018. paper, code

   Daniel Selsam, Benedikt Bünz Matthew Lamm, Leonardo de Moura Percy Liang, David L. Dill.

3. Machine learning-based restart policy for CDCL SAT solvers. SAT, 2018. paper

   Jia Hui Liang, Minu Mathew Chanseok Oh, Chunxiao Li Ciza Thomas, Vijay Ganesh.

4. Learning to solve circuit-SAT: An unsupervised differentiable approach. ICLR, 2019. paper, code

   Saeed, Sergiy Matusevych Amizadeh, Markus Weimer.

5. Learning Local Search Heuristics for Boolean Satisfiability. NeurIPS, 2019. paper, code

   Emre Yolcu, Barnabas Poczos

6. Improving SAT solver heuristics with graph networks and reinforcement learning. Arxiv, 2019. paper

   Vitaly Kurin, Shimon Whiteson Saad Godil, Bryan Catanzaro.

7. Graph neural reasoning may fail in certifying boolean unsatisfiability. Arxiv, 2019. paper

   Ziliang Chen, Zhanfu Yang.

8. Guiding high-performance SAT solvers with unsat-core predictions. SAT, 2019. paper

   Daniel Selsam, Nikolaj Bjørner.

9. G2SAT: Learning to Generate SAT Formulas. NeurIPS, 2019. paper, code

   Jiaxuan, Haoze Wu, Clark Barrett, Raghuram Ramanujan You, Jure Leskovec.

10. Learning Heuristics for Quantified Boolean Formulas through Reinforcement Learning. Arxiv, 2019. paper, code

    Gil Lederman, Edward A. Lee Markus N. Rabe, Sanjit A. Seshia.

11. Enhancing SAT solvers with glue variable predictions. Arxiv, 2020. paper

    Jesse Michael. Han

12. Can Q-Learning with Graph Networks Learn a Generalizable Branching Heuristic for a SAT Solver? NeurIPS, 2020. paper

    Shimon Whiteson

13. Online Bayesian Moment Matching based SAT Solver Heuristics. ICML, 2020. paper, code

    Haonan, Saeed Nejati, George Trimponias, Pascal Poupart Duan, Vijay Ganesh.

14. Learning Clause Deletion Heuristics with Reinforcement Learning. AITP, 2020. paper

    Pashootan, Gil Lederman, Yuhuai Wu, Roger Grosse Vaezipoor, Fahiem Bacchus.

15. Classification of SAT problem instances by machine learning methods. CEUR, 2020. paper

    Márk, Zijian Győző Yang Danisovszky, Gábor Kusper.

16. Predicting Propositional Satisfiability via End-to-End Learning. AAAI, 2020. paper

    Chris Cameron, Jason Hartford Rex Chen, Kevin Leyton-Brown.

17. Neural heuristics for SAT solving. Arxiv, 2020. paper

    Sebastian, Michał Łuszczyk Jaszczur, Henryk Michalewski.

18. NLocalSAT: Boosting Local Search with Solution Prediction. Arxiv, 2020. paper, code

    Wenjie, Zeyu Sun, Qihao Zhu, Ge Li, Shaowei Cai, Yingfei Xiong Zhang, Lu Zhang.

19. Optimistic tree search strategies for black-box combinatorial optimization NeurlPS, 2022. paper

    Cedric Malherbe, Antoine Grosnit, Rasul Tutunov, Haitham Bou Ammar, Jun Wang

20. Goal-Aware Neural SAT Solver. IJCNN, 2022. paper

    Emils Ozolins, Andis Draguns Karlis Freivalds, Ronalds Zakovskis Eliza Gaile, Sergejs Kozlovics.

21. NeuroComb: Improving SAT Solving with Graph Neural Networks. Arxiv, 2022. paper

    Wenxi Wang, Mohit Tiwari Yang Hu, Kenneth McMillan Sarfraz Khurshid, Risto Miikkulainen.

22. On the Performance of Deep Generative Models of Realistic SAT Instances. SAT, 2022. paper

    Iván, Pablo Mesejo Garzón, Jesús Giráldez-Cru.

23. DeepSAT: An EDA-Driven Learning Framework for SAT. Arxiv, 2022. paper

    Min, Zhengyuan Shi, Qiuxia Lai, Sadaf Khan Li, Qiang Xu.

24. SATformer: Transformers for SAT Solving. Arxiv, 2022. paper

    Zhengyuan Shi, Sadaf Khan Min Li, Mingxuan Yuan Hui-Ling Zhen, Qiang Xu.

25. Augment with Care: Contrastive Learning for Combinatorial Problems. ICML, 2022. paper, code

    Haonan, Pashootan Vaezipoor, Max B. Paulus, Yangjun Ruan Duan, Chris J. Maddison

26. NSNet: A General Neural Probabilistic Framework for Satisfiability Problems NeurIPS, 2022. paper

    Zhaoyu Li, Xujie Si

27. Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions NeurIPS, 2022. paper

    Nikolaos Karalias, Joshua Robinson, Andreas Loukas, Stefanie Jegelka

28. Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustness ICLR, 2022. paper

    Simon Geisler, Johanna Sommer, Jan Schuchardt, Aleksandar Bojchevski, Stephan Günnemann

29. Let the Flows Tell: Solving Graph Combinatorial Optimization Problems with GFlowNets NeurlPS, 2023. paper, code

    Dinghuai Zhang, Hanjun Dai, Nikolay Malkin, Aaron Courville, Yoshua Bengio, Ling Pan

30. ⭐HardSATGEN: Understanding the Difficulty of Hard SAT Formula Generation and A Strong Structure-Hardness-Aware Baseline KDD, 2023. paper, code

    Yang Li, Xinyan Chen, Wenxuan Guo, Xijun Li, Wanqian Luo, Junhua Huang, Hui-Ling Zhen, Mingxuan Yuan, Junchi Yan

31. Distributed Constrained Combinatorial Optimization leveraging Hypergraph Neural Networks Nature Machine Intelligence, 2024. paper, code

    Nasimeh Heydaribeni, Xinrui Zhan, Ruisi Zhang, Tina Eliassi-Rad, Farinaz Koushanfar

32. Efficient Combinatorial Optimization via Heat Diffusion NeurlPS, 2024. paper

    Hengyuan Ma, Wenlian Lu, Jianfeng Feng

33. Efficient Combinatorial Optimization via Heat Diffusion NeurIPS, 2024. paper, code

    Hengyuan Ma, Wenlian Lu, Jianfeng Feng

34. ⭐UniCO: On Unified Combinatorial Optimization via Problem Reduction to Matrix-Encoded General TSP ICLR, 2025. paper, code

    Wenzheng Pan, Hao Xiong, Jiale Ma, Wentao Zhao, Yang Li, Junchi Yan

Computing Resource Allocation

1. Resource Management with Deep Reinforcement Learning. HotNets, 2016. paper

   Hongzi Mao, Mohammad Alizadeh, Ishai Menache, Srikanth Kandula

2. Learning to Perform Local Rewriting for Combinatorial Optimization. NeurIPS, 2019. paper, code

   Xinyun Chen, Yuandong Tian

3. Learning Scheduling Algorithms for Data Processing Clusters SIGCOMM, 2019. paper, code

   Hongzi Mao, Malte Schwarzkopf, Bojja Shaileshh Venkatakrishnan, Zili Meng, Mohammad Alizadeh

4. Smart Resource Allocation for Mobile Edge Computing: A Deep Reinforcement Learning Approach IEEE Transactions on Emerging Topics in Computing, 2019. Paper

   Lei Zhao Jiadai, Nei Kato Jiajia Liu

5. A Two-stage Framework and Reinforcement Learning-based Optimization Algorithms for Complex Scheduling Problems Arxiv, 2021. paper

   Yongming He, Guohua Wu, Yingwu Chen, Witold Pedrycz

6. ⭐A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs NeurIPS, 2021. paper, code

   Runzhong Wang, Zhigang Hua, Gan Liu, Jiayi Zhang, Junchi Yan, Feng Qi, Shuang Yang, Jun Zhou, Xiaokang Yang

7. Projecting Latent RL Actions: Towards Generalizable and Scalable Graph Combinatorial Optimization Arxiv, 2026. paper, code

   Franco Terranova, Guillermo Bernardez, Albert Cabellos-Aparicio, Nina Miolane, Abdelkader Lahmadi

Bin Packing Problem

1. Small Boxes Big Data: A Deep Learning Approach to Optimize Variable Sized Bin Packing BigDataService, 2017. paper

   Feng Mao, Edgar Blanco, Mingang Fu, Rohit Jain, Anurag Gupta, Sebastien Mancel, Rong Yuan, Stephen Guo, Sai Kumar, Yayang Tian

2. Solving a New 3D Bin Packing Problem with Deep Reinforcement Learning Method Arxiv, 2017. paper

   Haoyuan Hu, Xiaodong Zhang, Xiaowei Yan, Longfei Wang, Yinghui Xu

3. Best Arm Identification in Multi-armed Bandits with Delayed Feedback PMLR, 2018. paper

   Aditya Grover, Todor Markov, Peter Attia, Norman Jin, Nicolas Perkins, Bryan Cheong, Michael Chen, Zi Yang, Stephen Harris, William Chueh, others

4. Ranked Reward: Enabling Self-Play Reinforcement Learning for Combinatorial Optimization Alexandre Arxiv, 2018. paper

   Alexandre Laterre, Yunguan Fu, Mohamed Khalil Jabri, Alain-Sam Cohen, David Kas, Karl Hajjar, Torbjorn S Dahl, Amine Kerkeni, Karim Beguir

5. A Multi-task Selected Learning Approach for Solving 3D Bin Packing Problem. AAMAS, 2019. paper

   Lu Duan, Haoyuan Hu, Yu Qian, Yu Gong, Xiaodong Zhang, Yinghui Xu, Jiangwen Wei

6. A Data-Driven Approach for Multi-level Packing Problems in Manufacturing Industry KDD, 2019. paper

   Lei Chen, Xialiang Tong, Mingxuan Yuan, Jia Zeng, Lei Chen

7. Solving Packing Problems by Conditional Query Learning OpenReview, 2019. paper

   Dongda Li, Changwei Ren, Zhaoquan Gu, Yuexuan Wang, Francis Lau

8. RePack: Dense Object Packing Using Deep CNN with Reinforcement Learning CACS, 2019. paper

   Yu-Cheng Chu, Horng-Horng Lin

9. Reinforcement learning driven heuristic optimization Arxiv, 2019. paper

   Qingpeng Cai, Will Hang, Azalia Mirhoseini, George Tucker, Jingtao Wang, Wei Wei

10. A Generalized Reinforcement Learning Algorithm for Online 3D Bin-Packing. AAAI Workshop, 2020. paper

    Richa Verma, Aniruddha Singhal, Harshad Khadilkar, Ansuma Basumatary, Siddharth Nayak, Harsh Vardhan Singh, Swagat Kumar, Rajesh Sinha

11. Robot Packing with Known Items and Nondeterministic Arrival Order. TASAE, 2020. paper

    Fan Wang, Kris Hauser

12. TAP-Net: Transport-and-Pack using Reinforcement Learning. TOG, 2020. paper, code

    Ruizhen Hu, Juzhan Xu, Bin Chen, Minglun Gong, Hao Zhang, Hui Huang

13. Simultaneous Planning for Item Picking and Placing by Deep Reinforcement Learning IROS, 2020. paper

    Tatsuya Tanaka, Toshimitsu Kaneko, Masahiro Sekine, Voot Tangkaratt, Masashi Sugiyama

14. Monte Carlo Tree Search on Perfect Rectangle Packing Problem Instances GECCO, 2020. paper

    Igor Pejic, Daan van den Berg

15. PackIt: A Virtual Environment for Geometric Planning ICML, 2020. paper, code

    Ankit Goyal, Jia Deng

16. Online 3D Bin Packing with Constrained Deep Reinforcement Learning. AAAI, 2021. paper, code

    Hang Zhao, Qijin She, Chenyang Zhu, Yin Yang, Kai Xu

17. Learning Practically Feasible Policies for Online 3D Bin Packing Arxiv, 2021. paper

    Hang Zhao, Chenyang Zhu, Xin Xu, Hui Huang, Kai Xu

18. Attend2Pack: Bin Packing through Deep Reinforcement Learning with Attention ICML Workshop, 2021. paper

    Jingwei Zhang, Bin Zi, Xiaoyu Ge

19. Solving 3D bin packing problem via multimodal deep reinforcement learning AAMAS, 2021. paper

    Yuan, Zhiguang Cao Jiang, Jie Zhang

20. Learning to Solve 3-D Bin Packing Problem via Deep Reinforcement Learning and Constraint Programming IEEE transactions on cybernetics, 2021. paper

    Yuan Jiang, Zhiguang Cao, Jie Zhang

21. Learning to Pack: A Data-Driven Tree Search Algorithm for Large-Scale 3D Bin Packing Problem CIKM, 2021. paper

    Qianwen Zhu, Xihan Li, Zihan Zhang, Zhixing Luo, Xialiang Tong, Mingxuan Yuan, Jia Zeng

22. Learning Efficient Online 3D Bin Packing on Packing Configuration Trees. ICLR, 2022. paper

    Hang Zhao, Kai Xu

23. Improved Algorithms for Multi-period Multi-class Packing Problemswith Bandit Feedback ICML, 2023. paper

    Wonyoung Kim, Garud Iyengar, Assaf Zeevi

24. Adjustable Robust Reinforcement Learning for Online 3D Bin Packing NeurIPS, 2023. paper

    Yuxin Pan, Yize Chen, Fangzhen Lin

25. A Neural Column Generation Approach to the Vehicle Routing Problem with Two-Dimensional Loading and Last-In-First-Out Constraints IJCAI, 2024. paper, code

    Yifan Xia, Xiangyi Zhang

26. Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model ICML, 2024. paper, code

    Fei Liu, Xialiang Tong, Mingxuan Yuan, Xi Lin, Fu Luo, Zhenkun Wang, Zhichao Lu, Qingfu Zhang

27. ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution NeurIPS, 2024. paper, code

    Haoran Ye, Jiarui Wang, Zhiguang Cao, Federico Berto, Chuanbo Hua, Haeyeon Kim, Jinkyoo Park, Guojie Song

28. Generalizable Heuristic Generation Through LLMs with Meta-Optimization ICLR, 2026. paper, code

    Yiding Shi, Jianan Zhou, Wen Song, Jieyi Bi, Yaoxin Wu, Zhiguang Cao, Jie Zhang

29. DRAGON: LLM-Driven Decomposition and Reconstruction Agents for Large-Scale Combinatorial Optimization AAMAS, 2026. paper

    Shengkai Chen, Zhiguang Cao, Jianan Zhou, Yaoxin Wu, Senthilnath Jayavelu, Zhuoyi Lin, Xiaoli Li, Shili Xiang

30. EoH-S: Evolution of Heuristic Set using LLMs for Automated Heuristic Design AAAI, 2026. paper, code

    Fei Liu, Yilu Liu, Qingfu Zhang, Xialiang Tong, Mingxuan Yuan

Graph Edit Distance

1. SimGNN - A Neural Network Approach to Fast Graph Similarity Computation WSDM, 2019. paper, code

   Yunsheng Bai, Hao Ding, Song Bian, Ting Chen, Yizhou Sun, Wei Wang

2. Graph Matching Networks for Learning the Similarity of Graph Structured Objects ICML, 2019. paper, code

   Yujia Li, Chenjie Gu, Thomas Dullien, Oriol Vinyals, Pushmeet Kohli

3. Convolutional Embedding for Edit Distance SIGIR, 2020. paper, code

   Xinyan Dai, Xiao Yan, Kaiwen Zhou, Yuxuan Wang, Han Yang, James Cheng

4. Learning-Based Efficient Graph Similarity Computation via Multi-Scale Convolutional Set Matching AAAI, 2020. paper, code

   Yunsheng Bai, Hao Ding, Ken Gu, Yizhou Sun, Wei Wang

5. ⭐A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs NeurIPS, 2021. paper, code

   Runzhong Wang, Zhigang Hua, Gan Liu, Jiayi Zhang, Junchi Yan, Feng Qi, Shuang Yang, Jun Zhou, Xiaokang Yang

6. ⭐Combinatorial Learning of Graph Edit Distance via Dynamic Embedding. CVPR, 2021. paper, code

   Runzhong Wang, Tianqi Zhang, Tianshu Yu, Junchi Yan, Xiaokang Yang

7. Gelato: Graph Edit Distance via Autoregressive Neural Combinatorial Optimization ICLR, 2026. paper, code

   Paolo Pellizzoni, Till Hendrik Schulz, Karsten Borgwardt

Hamiltonian Cycle Problem

1. ⭐A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphs NeurIPS, 2021. paper, code

   Runzhong Wang, Zhigang Hua, Gan Liu, Jiayi Zhang, Junchi Yan, Feng Qi, Shuang Yang, Jun Zhou, Xiaokang Yang

2. ⭐UniCO: On Unified Combinatorial Optimization via Problem Reduction to Matrix-Encoded General TSP ICLR, 2025. paper, code

   Wenzheng Pan, Hao Xiong, Jiale Ma, Wentao Zhao, Yang Li, Junchi Yan

3. VSAL: A Vision Solver with Adaptive Layouts for Graph Property Detection WWW, 2026. paper, code

   Jiahao Xie, Guangmo Tong

Graph Coloring

1. Deep Learning-based Hybrid Graph-Coloring Algorithm for Register Allocation. Arxiv, 2019. paper

   Dibyendu Das, Shahid Asghar Ahmad, Kumar Venkataramanan

2. Neural Models for Output-Space Invariance in Combinatorial Problems ICLR, 2022. paper

   Yatin Nandwani, Vidit Jain, Parag Singla, others

3. Enhancing Column Generation by a Machine-Learning-Based Pricing Heuristic for Graph Coloring AAAI, 2022. paper, code

   Yunzhuang, Yuan Sun, Xiaodong Li, Andrew Craig Eberhard Shen, Andreas T. Ernst.

4. Learning to Generate Columns with Application to Vertex Coloring ICLR, 2023. paper, code

   Yuan Sun, Andreas T Ernst, Xiaodong Li, Jake Weiner

5. Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling ICLR, 2025. [paper](https: