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 Job Shop Scheduling Problem (JSSP)	2.2 Flow Shop Problem (FSP)
2.3 Sorting & Ranking (Sort&Rank)	2.4 Graph Matching (GM)
2.5 Quadratic Assignment Problem (QAP)	2.6 Travelling Salesman Problem (TSP)
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

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

    Laurin Luttmann, Lin Xie

17. 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

Flow Shop Problem

1. 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

Travelling Salesman Problem

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. 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

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

    Jinbiao Chen, Jiahai Wang, Zhiguang Cao, Yaoxin Wu

66. 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

67. ⭐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

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

    Xu Wang, Fuyou Miao, Wenjie Liu, Yan Xiong

69. ⭐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

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

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

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

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

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

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

73. ⭐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

74. ⭐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

75. 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

76. 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

77. 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

78. 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

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

    Baoyun Zhao, He Wang, Liang Zeng

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

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

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

    Lvda Chen, Yang Li, Junchi Yan

82. 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

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

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

84. 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

85. 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

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

    Yuma Ichikawa, Yamato Arai

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

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. 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

41. 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

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

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

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

    Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

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

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

45. 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

46. 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

47. 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

48. 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

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

    Rongjie Zhu, Cong Zhang, Zhiguang Cao

50. 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

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

    Shuangchun Gui, Suyu Liu, Xuehe Wang, Zhiguang Cao

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

    Hang Yi, Ziwei Huang, Yining Ma, Zhiguang Cao

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

    Zikang Yu, Jinbiao Chen, Jiahai Wang

54. 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

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

    Wenbin Ouyang, Sirui Li, Yining Ma, Cathy Wu

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

    Baoyun Zhao, He Wang, Liang Zeng

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

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

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

    Lvda Chen, Yang Li, Junchi Yan

59. 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

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

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

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

    Laurin Luttmann, Lin Xie

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

    Lvda Chen, Yang Li, Junchi Yan

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

    Ziao Guo, Yang Li, Shiyue Wang, Junchi Yan

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

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

34. 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

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

    Yuma Ichikawa, Yamato Arai

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

    Yuma Ichikawa, Hiroaki Iwashita

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

   Darko Drakulic, Sofia Michel, Jean-Marc Andreoli

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

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. 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

27. 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

28. 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, code

   Yuma Ichikawa, Yamato Arai

Maximal Common Subgraph

1. Fast Detection of Maximum Common Subgraph via Deep Q-Learning. Arxiv, 2020. paper

   Yunsheng Bai, Derek Xu, Alex Wang, Ken Gu, Xueqing Wu, Agustin Marinovic, Christopher Ro, Yizhou Sun, Wei Wang

Influence Maximization

1. Learning Heuristics over Large Graphs via Deep Reinforcement Learning. NeurIPS, 2020. paper

   Akash Mittal, Anuj Dhawan, Sahil Manchanda, Sourav Medya, Sayan Ranu, Ambuj Singh

2. Controlling Graph Dynamics with Reinforcement Learning and Graph Neural Networks. ICML, 2021. paper

   Eli A. Meirom, Haggai Maron, Shie Mannor, Gal Chechik

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

   David Ireland, G. Montana

4. ⭐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

5. Deep Graph Representation Learning and Optimization for Influence Maximization ICML, 2023. paper

   Chen Ling, Junji Jiang, Junxiang Wang, My T. Thai, Lukas Xue, James Song, Meikang Qiu, Liang Zhao

Max Clique

1. Can Hybrid Geometric Scattering Networks Help Solve the Maximum Clique Problem NeurIPS, 2022. paper, code

   Yimeng Min, Frederik Wenkel, Michael Perlmutter, Guy Wolf

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

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

3. 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

4. Learning fine-grained search space pruning and heuristics for combinatorial optimization. Journal of Heuristics, 2023. journal

   Juho Lauri, Sourav Dutta, Marco Grassia, Deepak Ajwani

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

   Sebastian Sanokowski, Sepp Hochreiter, Sebastian Lehner

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

   Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

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

   Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

8. 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

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

   Antonios Antoniadis, Marek Elias, Adam Polak, Moritz Venzin

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

    Ziao Guo, Yang Li, Shiyue Wang, Junchi Yan

Mixed Integer Programming

1. Sequential model-based optimization for general algorithm configuration International conference on learning and intelligent optimization, 2011. journal

   Frank Hutter, Holger H Hoos, Kevin Leyton-Brown

2. Non-model-based Search Guidance for Set Partitioning Problems AAAI, 2012. paper

   Serdar Kadioglu, Yuri Malitsky, Meinolf Sellmann

3. A Aupervised Machine Learning Approach to Variable Branching in Branch-and-bound Citeseer, 2014. journal

   Alejandro Marcos Alvarez, Quentin Louveaux, Louis Wehenkel

4. Learning to Search in Branch-and-Bound Algorithms NeurlPS, 2014. paper

   He He, Hal Daume III, Jason M Eisner

5. Learningto Branch in Mixed Integer Programming AAAI, 2016. paper

   E. B. Khalil, P. L. Bodic, L. Song, G. Nemhauser, B. Dilkina

6. Dash: Dynamic Approach for Switching Heuristics European Journal of Operational Research, 2016. journal

   Giovanni Di Liberto, Serdar Kadioglu, Kevin Leo, Yuri Malitsky

7. Learning When to Use a Decomposition International conference on AI and OR techniques in constraint programming for combinatorial optimization problems, 2017. journal

   Markus Kruber, L{\u}bbecke Marco E, Parmentier Axel

8. Learning to Run Heuristics in Tree Search IJCAI, 2017. paper

   Elias B Khalil, Bistra Dilkina, George L Nemhauser, Shabbir Ahmed, Yufen Shao

9. Exact Combinatorial Optimization with Graph Convolutional Neural Networks NeurlPS, 2019. paper, code

   Maxime Gasse, Didier Chetelat, Nicola Ferroni, Laurent Charlin, Andrea Lodi

10. Improving Learning to Branch via Reinforcement Learning NeurIPS Workshop, 2020. paper

    Haoran Sun, Wenbo Chen, Hui Li, Le Song

11. Reinforcement learning for variable selection in a branch and bound algorithm International Conference on Integration of Constraint Programming, 2020. journal

    Marc Etheve, Zacharie Al{`e}s, C{^o}me Bissuel, Olivier Juan, Safia Kedad-Sidhoum

12. Random sampling and machine learning to understand good decompositions Annals of Operations Research, 2020. journal

    Saverio Basso, Alberto Ceselli, Andrea Tettamanzi

13. Hybrid Models for Learning to Branch NeurlPS, 2020. paper, code

    Prateek Gupta, Maxime Gasse, Elias B Khalil, M Pawan Kumar, Andrea Lodi, Yoshua Bengio

14. Reinforcement Learning for Integer Programming: Learning to Cut ICML, 2020. paper

    Yunhao Tang, Shipra Agrawal, Yuri Faenza

15. Solving Mixed Integer Programs Using Neural Networks Arxiv, 2020. paper

    Vinod Nair, Sergey Bartunov, Felix Gimeno, Ingrid von Glehn, Pawel Lichocki, Ivan Lobov, Brendan O'Donoghue, Nicolas Sonnerat, Christian Tjandraatmadja, Pengming Wang, others

16. Learning Efficient Search Approximation in Mixed Integer Branch and Bound Arxiv, 2020. paper

    Kaan Yilmaz, Neil Yorke-Smith

17. Learning a Large Neighborhood Search Algorithm for Mixed Integer Programs Arxiv, 2020. paper

    Nicolas Sonnerat, Pengming Wang, Ira Ktena, Sergey Bartunov, Vinod Nair

18. A General Large Neighborhood Search Framework for Solving Integer Linear Programs NeurlPS, 2020. paper

    Jialin Song, Ravi Lanka, Yisong Yue, Bistra Dilkina

19. Neural Large Neighborhood Search NeurlPS Workshop, 2020. paper

    Vinod Nair, Mohammad Alizadeh, others

20. Accelerating Primal Solution Findings for Mixed Integer Programs Based on Solution Prediction AAAI, 2020. paper

    Jian-Ya, Chao Zhang, Lei Shen, Shengyin Li, Bing Wang, Yinghui Xu Ding, Le Song

21. CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints Arxiv, 2021. paper, code

    Anselm Paulus, Michal Rolinek, Vit Musil, Brandon Amos, Georg Martius

22. Reinforcement Learning for (Mixed) Integer Programming: Smart Feasibility Pump ICML Workshop, 2021. paper

    Meng Qi, Mengxin Wang, Zuo-Jun Shen

23. Parameterizing Branch-and-Bound Search Trees to Learn Branching Policies AAAI, 2021. paper, code

    Giulia Zarpellon, Jason Jo, Andrea Lodi, Yoshua Bengio

24. Learning to Select Cuts for Efficient Mixed-Integer Programming Arxiv, 2021. journal

    Zeren Huang, Kerong Wang, Furui Liu, Hui-ling Zhen, Weinan Zhang, Mingxuan Yuan, Jianye Hao, Yong Yu, Jun Wang

25. Confidence Threshold Neural Diving NeurIPS ML4CO Competition Workshop, 2021. paper

    Taehyun Yoon

26. Learning large neighborhood search policy for integer programming NeurlPS, 2021. paper

    Yaoxin Wu, Wen Song, Zhiguang Cao, Jie Zhang

27. Generative Deep Learning for Decision Making in Gas Networks Arxiv, 2021. paper

    Lovis Anderson, Mark Turner, Thorsten Koch

28. Offline Constraint Screening for Online Mixed-integer Optimization Arxiv, 2021. paper

    Asunción Jiménez-Cordero, Juan Miguel Morales, Salvador Pineda

29. Mixed Integer Programming versus Evolutionary Computation for Optimizing a Hard Real-World Staff Assignment Problem ICAPS, 2021. paper

    Jannik Peters, Daniel Stephan, Isabel Amon, Hans Gawendowicz, Julius Lischeid, Lennart Salabarria, Jonas Umland, Felix Werner, Martin S Krejca, Ralf Rothenberger, others

30. Learning To Scale Mixed-Integer Programs AAAI, 2021. paper

    Timo Berthold, Gregor Hendel

31. Learning Pseudo-Backdoors for Mixed Integer Programs AAAI, 2021. paper

    Aaron Ferber, Jialin Song, Bistra Dilkina, Yisong Yue

32. Confidence Threshold Neural Diving NeurIPS ML4CO Competition Workshop, 2021. paper

    Taehyun Yoon

33. Learning Primal Heuristics for Mixed Integer Programs IJCNN, 2021. paper

    Yunzhuang Shen, Yuan Sun, Andrew Eberhard, Xiaodong Li

34. Learning to Solve Large-scale Security-constrained Unit Commitment Problems INFORMS Journal on Computing, 2021. journal

    {'A}linson S Xavier, Feng Qiu, Shabbir Ahmed

35. Learning to Branch with Tree MDPs Arxiv, 2022. paper, code

    Lara, F. Chen, Didier Ch'etelat, Maxime Gasse, Andrea Lodi, N. Yorke-Smith Scavuzzo, Karen Aardal.

36. A Deep Reinforcement Learning Framework For Column Generation Arxiv, 2022. paper

    Cheng, Amine Mohamed Aboussalah, Elias Boutros Khalil, Juyoung Wang Chi, Zoha Sherkat-Masoumi.

37. Ranking Constraint Relaxations for Mixed Integer Programs Using a Machine Learning Approach Arxiv, 2022. journal

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

38. Learning to Accelerate Approximate Methods for Solving Integer Programming via Early Fixing Arxiv, 2022. journal, code

    Longkang Li, Baoyuan Wu.

39. Learning to Cut by Looking Ahead: Cutting Plane Selection via Imitation Learning ICML, 2022. paper

    Max B., Giulia Zarpellon, Andreas Krause, Laurent Charlin Paulus, Chris J. Maddison.

40. Lookback for Learning to Branch Arxiv, 2022. journal

    Prateek, Elias Boutros Khalil, Didier Chet'elat, Maxime Gasse, Yoshua Bengio, Andrea Lodi Gupta, M. Pawan Kumar.

41. Learning to Search in Local Branching AAAI, 2022. paper, code

    Defeng Liu, Matteo Fischetti, Andrea Lodi

42. Deep Reinforcement Learning for Exact Combinatorial Optimization: Learning to Branch Arxiv, 2022. paper

    Tianyu Zhang, Amin Banitalebi-Dehkordi, Yong Zhang

43. Learning to Branch with Tree-aware Branching Transformers Knowledge-Based Systems, 2022. journal, code

    Jiacheng Lin, Jialin Zhu, Huangang Wang, Tao Zhang

44. An Improved Reinforcement Learning Algorithm for Learning to Branch Arxiv, 2022. paper

    Qingyu Qu, Xijun Li, Yunfan Zhou, Jia Zeng, Mingxuan Yuan, Jie Wang, Jinhu Lv, Kexin Liu, Kun Mao

45. Learning to Use Local Cuts Arxiv, 2022. paper

    Timo Berthold, Matteo Francobaldi, Gregor Hendel

46. DOGE-Train: Discrete Optimization on GPU with End-to-end Training Arxiv, 2022. paper

    Ahmed Abbas, Paul Swoboda

47. Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts NeurIPS, 2022. paper

    Maria-Florina Balcan, Siddharth Prasad, Tuomas Sandholm, Ellen Vitercik

48. Constrained Discrete Black-Box Optimization using Mixed-Integer Programming ICML, 2022. paper

    Theodore, Christian Tjandraatmadja, Ross Anderson, Juan Pablo Vielma Papalexopoulos, Daving Belanger.

49. A GNN-Guided Predict-and-Search Framework for Mixed-Integer Linear Programming ICLR, 2023. paper, code

    Qingyu Han, Linxin Yang, Qian Chen, Xiang Zhou, Dong Zhang, Akang Wang, Ruoyu Sun, Xiaodong Luo

50. Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model ICLR, 2023. paper, code

    Zhihai Wang, Xijun Li, Jie Wang, Yufei Kuang, Mingxuan Yuan, Jia Zeng, Yongdong Zhang, Feng Wu

51. On Representing Mixed-Integer Linear Programs by Graph Neural Networks ICLR, 2023. paper, code

    Ziang Chen, Jialin Liu, Xinshang Wang, Wotao Yin

52. Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model ICLR, 2023. paper, code

    Zhihai Wang, Xijun Li, Jie Wang, Yufei Kuang, Mingxuan Yuan, Jia Zeng, Yongdong Zhang, Feng Wu

53. GNN-GBDT-Guided Fast Optimizing Framework for Large-scale Integer Programming ICML, 2023. paper, code

    Huigen Ye, Hua Xu, Hongyan Wang, Chengming Wang, Yu Jiang

54. Searching Large Neighborhoods for Integer Linear Programs with Contrastive Learning ICML, 2023. paper, code

    Taoan Huang, Aaron M Ferber, Yuandong Tian, Bistra Dilkina, Benoit Steiner

55. GNN&GBDT-Guided Fast Optimizing Framework for Large-scale Integer Programming ICML, 2023. paper

    Huigen, Hua-Hui Xu, Hongyan Wang, Cheng . Wang Ye, YueYen Jiang.

56. Learning to Configure Separators in Branch-and-Cut NeurIPS, 2023. paper

    Sirui Li, Wenbin Ouyang, Max B Paulus, Cathy Wu

57. Learning to Dive in Branch and Bound NeurIPS, 2023. paper

    Max B Paulus, Andreas Krause

58. A Deep Instance Generative Framework for MILP Solvers Under Limited Data Availability NeurIPS, 2023. paper, code

    Zijie Geng, Xijun Li, Jie Wang, Xiao Li, Yongdong Zhang, Feng Wu

59. Scalable Primal Heuristics Using Graph Neural Networks for Combinatorial Optimization JAIR, 2024. journal, code

    Furkan Canturk, Taha Varol, Reyhan Aydogan, Okan O Ozener

60. OptimAI: Optimization from Natural Language Using LLM-Powered AI Agents arXiv, 2025. paper

    Thind, Raghav and Sun, Youran and Liang, Ling and Yang, Haizhao

Causal Discovery

1. DAGs with NO TEARS: Continuous Optimization for Structure Learning. NeurIPS, 2018. paper

   Xun Zheng, Bryon Aragam, Pradeep Ravikumar, Eric Xing

2. Causal Discovery with Reinforcement Learning. ICLR, 2020. paper

   Shengyu Zhu, Ignavier Ng, Zhitang Chen

3. Large-Scale Differentiable Causal Discovery of Factor Graphs NeurIPS, 2022. paper, code

   Romain Lopez, Jan-Christian H{"u}tter, Jonathan K Pritchard, Aviv Regev

4. Boosting Causal Discovery via Adaptive Sample Reweighting ICLR, 2023. paper, code

   An Zhang, Fangfu Liu, Wenchang Ma, Zhibo Cai, Xiang Wang, Tat-seng Chua

5. CUTS: Neural Causal Discovery from Irregular Time-Series Data ICLR, 2023. paper, code

   Yuxiao Cheng, Runzhao Yang, Tingxiong Xiao, Zongren Li, Jinli Suo, Kunlun He, Qionghai Dai

6. Diffusion Models for Causal Discovery via Topological Ordering ICLR, 2023. paper, code

   Pedro Sanchez, Xiao Liu, Alison Q O'Neil, Sotirios A Tsaftaris

7. Nonlinear Causal Discovery with Latent Confounders ICML, 2023. paper, code

   David Kaltenpoth, Jilles Vreeken

8. BayesDAG: Gradient-Based Posterior Inference for Causal Discovery NeurIPS, 2023. paper

   Yashas Annadani, Nick Pawlowski, Joel Jennings, Stefan Bauer, Cheng Zhang, Wenbo Gong

9. Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modeling NeurIPS, 2023. paper

   Zhenyu Zhu, Francesco Locatello, Volkan Cevher

Game Theoretic Semantics

1. First-Order Problem Solving through Neural MCTS based Reinforcement Learning. Arxiv, 2021. paper

   Ruiyang Xu, Prashank Kadam, Karl Lieberherr

Differentiable Optimization

1. Differentiable Learning of Submodular Models NeurIPS, 2017. paper, code

   Josip Djolonga, Andreas Krause

2. Differentiation of Blackbox Combinatorial Solvers ICLR, 2020. paper, code

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

3. MIPaaL: Mixed Integer Program as a Layer AAAI, 2020. paper, code

   Aaron Ferber, Bryan Wilder, Bistra Dilkina, Milind Tambe

4. Differentiation of blackbox combinatorial solvers ICLR, 2020. paper, code

   Marin Vlastelica Pogani, Anselm Paulus, Vit Musil, Georg Martius, Michal Rolinek

5. SurCo: Learning Linear Surrogates For Combinatorial Nonlinear Optimization Problems ICML, 2023. paper, code

   Aaron M Ferber, Taoan Huang, Daochen Zha, Martin Schubert, Benoit Steiner, Bistra Dilkina, Yuandong Tian

6. Backpropagation through Combinatorial Algorithms: Identity with Projection Works ICLR, 2023. paper, code

   Subham Sekhar Sahoo, Anselm Paulus, Marin Vlastelica, Vít Musil, Volodymyr Kuleshov, Georg Martius

Car Dispatch

1. Dispatch of autonomous vehicles for taxi services: A deep reinforcement learning approach Transportation Research, 2020. journal

   Chao Mao, Yulin Liu, Zuo-Jun (Max) Shen

Electronic Design Automation

1. ⭐On Joint Learning for Solving Placement and Routing in Chip Design NeurIPS, 2021. paper, code

   Ruoyu Cheng, Junchi Yan

2. A graph placement methodology for fast chip design Nature, 2021. journal

   Azalia Mirhoseini, Anna Goldie, Mustafa Yazgan, Joe Wenjie Jiang, Ebrahim Songhori, Shen Wang, Young-Joon Lee, Eric Johnson, Omkar Pathak, Azade Nazi, Jiwoo Pak, Andy Tong, Kavya Srinivasa, William Hang, Emre Tuncer, Quoc V. Le, James Laudon, Richard Ho, Roger Carpenter, Jeff Dean

3. Unsupervised Learning for Combinatorial Optimization with Principled Objective Relaxation NeurIPS, 2022. paper, code

   Haoyu Peter Wang, Nan Wu, Hang Yang, Cong Hao, Pan Li

4. ⭐The Policy-gradient Placement and Generative Routing Neural Networks for Chip Design NeurIPS, 2022. paper, code

   Ruoyu Cheng, Xianglong Lyu, Yang Li, Junjie Ye, Jianye Hao, Junchi Yan

5. CktGNN: Circuit Graph Neural Network for Electronic Design Automation ICLR, 2023. paper

   Zehao Dong, Weidong Cao, Muhan Zhang, Dacheng Tao, Yixin Chen, Xuan Zhang

6. ⭐HubRouter: Learning Global Routing via Hub Generation and Pin-hub Connection NeurIPS, 2023. paper

   Xingbo Du, Chonghua Wang, Ruizhe Zhong, Junchi Yan

7. HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization ICLR, 2026. paper, code

   Hongzheng Chen, Yingheng Wang, Yaohui Cai, Hins Hu, Jiajie Li, Shirley Huang, Chenhui Deng, Rongjian Liang, Shufeng Kong, Haoxing Ren, Samitha Samaranayake, Carla P. Gomes, Zhiru Zhang

Conjunctive Query Containment

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

   Gal Yehuda, Moshe Gabel, Assaf Schuster

Virtual Network Embedding

1. Virtual Network Embedding via Monte Carlo Tree Search IEEE Trans. Cybern, 2017. journal

   Soroush Haeri, Ljiljana Trajković

2. A novel reinforcement learning algorithm for virtual network embedding Neurocomputing, 2018. journal

   Haipeng Yao, Xu Chen, Maozhen Li, Peiying Zhang, Luyao Wang

3. NeuroViNE: A Neural Preprocessor for Your Virtual Network Embedding Algorithm INFOCOM, 2018. paper

   Andreas Blenk, Patrick Kalmbach, Johannes Zerwas, Michael Jarschel, Stefan Schmid, Wolfgang Kellerer

4. A Virtual Network Embedding Algorithm Based On Double-Layer Reinforcement Learning TCJ, 2019. journal

   Meng Li, MeiLian Lu

5. NFVdeep: Adaptive Online Service Function Chain Deployment with Deep Reinforcement Learning IWQoS, 2019. paper

   Yikai Xiao, Qixia Zhang, Fangming Liu, Jia Wang, Miao Zhao, Zhongxing Zhang, Jiaxing Zhang

6. A Continuous-Decision Virtual Network Embedding Scheme Relying on Reinforcement Learning IEEE TNSM, 2020. journal

   Haipeng Yao, Sihan Ma, Jingjing Wang, Peiying Zhang, Chunxiao Jiang, Song Guo

7. Automatic Virtual Network Embedding A Deep Reinforcement Learning Approach With Graph Convolutional Networks J-SAC, 2020. journal

   Zhongxia Yan, Jingguo Ge, Yulei Wu, Liangxiong Li, Tong Li

8. A Q-learning-based approach for virtual network embedding in data center NCA, 2020. journal

   Ying Yuan, Zejie Tian, Cong Wang, Fanghui Zheng, Yanxia Lv

9. Accelerating Virtual Network Embedding with Graph Neural Networks CNSM, 2020. journal

   Farzad Habibi, Mahdi Dolati, Ahmad Khonsari, Majid Ghaderi

10. Dynamic Virtual Network Embedding Algorithm Based on Graph Convolution Neural Network and Reinforcement Learning IoT-J, 2021. journal

    Peiying Zhang, Chao Wang, Neeraj Kumar, Weishan Zhang, Lei Liu

11. Deep Reinforcement Based Optimization of Function Splitting in Virtualized Radio Access Networks ICC, 2021. paper, code

    Fahri Wisnu Murti, Samad Ali, Matti Latva-aho

12. DRL-SFCP: Adaptive Service Function Chains Placement with Deep Reinforcement Learning ICC, 2021. paper

    Tianfu Wang, Qilin Fan, Xiuhua Li, Xu Zhang, Qingyu Xiong, Shu Fu, Min Gao

13. ⭐GAL-VNE: Solving the VNE Problem with Global Reinforcement Learning and Local One-Shot Neural Prediction KDD, 2023. paper, code

    Haoyu Geng, Runzhong Wang, Fei Wu, Junchi Yan

Predict+Optimize

1. OptNet: differentiable optimization as a layer in neural networks ICML, 2017. paper, code

   Brandon Amos, J. Zico Kolter

2. Differentiable Convex Optimization Layers NeurIPS, 2019. paper, code

   Akshay Agrawal, Stephen Boyd

3. 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

4. Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization AAAI, 2019. paper

   Bryan Wilder, Bistra Dilkina, Milind Tambe

5. Automatically Learning Compact Quality-aware Surrogates for Optimization Problems NeurIPS, 2020. paper

   Kai Wang, Bryan Wilder, Andrew Perrault, Milind Tambe

6. Smart Predict-and-Optimize for Hard Combinatorial Optimization Problems AAAI, 2020. paper, code

   Jayanta Mandi, Emir Demirovic, Peter J. Stuckey, Tias Guns

7. Interior Point Solving for LP-based prediction+optimization NeurIPS, 2020. paper, code

   Jayanta Mandi, Tias Guns

8. Contrastive Losses and Solution Caching for Predict-and-Optimize IJCAI, 2021. paper, code

   Maxime Mulamba, Jayanta Mandi, Michelangelo Diligenti, Michele Lombardi, Victor Bucarey, Tias Guns

9. A Surrogate Objective Framework for Prediction+Programming with Soft Constraints NeurIPS, 2021. paper, code

   Kai Yan, Jie Yan, Chuan Luo, Liting Chen, Qingwei Lin, Dongmei Zhang

10. Implicit MLE: Backpropagating Through Discrete Exponential Family Distributions NeurIPS, 2021. paper, code

    Mathias Niepert, Pasquale Minervini, Luca Franceschi

11. COPS: Combinatorial Optimization for Panoptic Segmentation: A Fully Differentiable Approach NeurIPS, 2021. paper, code

    Ahmed Abbas, Paul Swoboda

12. End-to-End Stochastic Optimization with Energy-Based Model NeurIPS, 2022. paper, code

    Lingkai Kong, Jiaming Cui, Yuchen Zhuang, Rui Feng, B. Aditya Prakash, Chao Zhang

13. Deep Declarative Networks TPAMI, 2022. paper, code

    Stephen Gould, Richard Hartley, Dylan Campbell

14. An Exact Symbolic Reduction of Linear Smart Predict+Optimize to Mixed Integer Linear Programming ICML, 2022. paper, code

    Jihwan Jeong, Parth Jaggi, Andrew Butler, Scott Sanner

15. Two-Stage Predict+Optimize for Mixed Integer Linear Programs with Unknown Parameters in Constraints NeurIPS, 2023. paper, code

    Xinyi Hu, Jasper CH Lee, Jimmy HM Lee

16. Predict+ Optimize for packing and covering LPs with unknown parameters in constraints AAAI, 2023. paper

    Xinyi Hu, Jasper C.H. Lee, Jimmy H.M. Lee

Optimal Power Flow

1. DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow SmartGridComm, 2019. paper

   Xiang Pan, Tianyu Zhao, Minghua Chen

2. Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods AAAI, 2020. paper, code

   Ferdinando Fioretto, Terrence W.K. Mak, Pascal Van Hentenryck

3. Adversarially Robust Learning for Security-Constrained Optimal Power Flow NeurIPS, 2021. paper

   Priya Donti, Aayushya Agarwal, Neeraj Vijay Bedmutha, Larry Pileggi, J. Zico Kolter

4. Ensuring DNN Solution Feasibility for Optimization Problems with Linear Constraints ICLR, 2023. paper

   Tianyu Zhao, Xiang Pan, Minghua Chen, Steven Low

Facility Location Problem

1. Learning to Prune Instances of k-median and Related Problems. ALENEX, 2022. paper, code

   Dena Tayebi, Saurabh Ray, Deepak Ajwani

2. Solving uncapacitated P-Median problem with reinforcement learning assisted by graph attention networks Applied Intelligence, 2023. paper

   Chenguang Wang, Congying Han, Tiande Guo, Man Ding

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

Combinatorial Drug Recommendation

1. GAMENet: Graph Augmented MEmory Networks for Recommending Medication Combination AAAI, 2019. paper, code

   Junyuan Shang, Cao Xiao, Tengfei Ma, Hongyan Li, Jimeng Sun

2. SafeDrug: Dual Molecular Graph Encoders for Recommending Effective and Safe Drug Combinations IJCAI, 2021. paper, code

   Chaoqi Yang, Cao Xiao, Fenglong Ma, Lucas Glass, Jimeng Sun

3. Debiased, Longitudinal and Coordinated Drug Recommendation through Multi-Visit Clinic Recordss NeurIPS, 2022. paper, code

   Hongda Sun, Shufang Xie, Shuqi Li, Yuhan Chen, Ji-Rong Wen, Rui Yan

4. ⭐MoleRec: Combinatorial Drug Recommendation with Substructure-Aware Molecular Representation Learning WWW, 2023. paper, code

   Nianzu Yang, Kaipeng Zeng, Qitian Wu, Junchi Yan

5. Enhancing Activity Prediction Models in Drug Discovery with the Ability to Understand Human Language ICML, 2023. paper

   Philipp Seidl, Andreu Vall, Sepp Hochreiter, Gunter Klambauer

6. Learning Subpocket Prototypes for Generalizable Structure-based Drug Design ICML, 2023. paper

   Zaixin Zhang, Qi Liu

7. DECOMPDIFF: Diffusion Models with Decomposed Priors for Structure-Based Drug Design ICML, 2023. paper

   Jiaqi Guan, Xiangxin Zhou, Yuwei Yang, Yu Bao, Jian-wei Peng, Jianzhu Ma, Q. Liu, Liang Wang, Quanquan Gu

Stochastic Combinatorial Optimization

1. Learning fast optimizers for contextual stochastic integer programs UAI, 2018. paper

   V Nair, D Dvijotham, I Dunning, O Vinyals

2. USCO-Solver: Solving Undetermined Stochastic Combinatorial Optimization Problems NeurIPS, 2021. paper, code

   Guangmo Tong

3. A New Approach for Vehicle Routing with Stochastic Demand- Combining Route Assignment with Process Flexibility OR, 2022. journal

   Kirby Ledvina, Hanzhang Qin, David Simchi-Levi, Yehua Wei

4. Neur2SP- Neural Two-Stage Stochastic Programming NeurIPS, 2022. paper, code

   Rahul Mihir Patel, Justin Dumouchelle, Elias Boutros Khalil, Merve Bodur

5. Learning to Optimize with Stochastic Dominance Constraints AISTATS, 2023. paper

   Hanjun Dai, Yuan Xue, Niao He, Yixin Wang, Na Li, Dale Schuurmans, Bo Dai

6. From Sequential to Parallel: Reformulating Dynamic Programming as GPU Kernels for Large-Scale Stochastic Combinatorial Optimization ICLR, 2026. paper, code

   Jingyi Zhao, Linxin Yang, Haohua Zhang, Qile He, Tian Ding

Vertex Cover

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

   Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

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

   Jiale Ma, Wenzheng Pan, Yang Li, Junchi Yan

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

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

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

   Antonios Antoniadis, Marek Elias, Adam Polak, Moritz Venzin

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

   Ziao Guo, Yang Li, Shiyue Wang, Junchi Yan