Neural Combinatorial Optimization

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Overview

Neural combinatorial optimization studies how learned models can construct, improve, or guide solutions to problems with many discrete choices and hard constraints, including vehicle routing, scheduling, packing, and graph optimization. Common approaches include graph neural networks and Transformers trained with supervised examples from solvers, reinforcement learning, self-supervised objectives, and newer diffusion or preference-based methods. Many systems combine learned policies with classical search, local improvement, or exact optimization to improve feasibility and solution quality. A central challenge is whether they generalize to larger or unfamiliar instances and offer a practical advantage over strong classical heuristics when training and inference costs are counted.

Latest papers

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137 papers17 papers in the last four weeks, up 113% on the four weeks before. 0.1% of all new papers.

  1. Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solver

    May 11, 2026Canhong Yu, Changliang Zhou, Rongsheng Chen +2Neural Network OptimizationCombinatorial Optimization

    College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China · School of Automation and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, China · Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China +1

  2. Neural Cluster First, Route Second: Capacitated Vehicle Routing via Differentiable Optimal Transport

    May 10, 2026Samuel J. K. Chin, Maximilian SchifferVehicle RoutingNeural Combinatorial Optimization

    MIT · TUM

  3. LINC: Decoupling Local Consequence Scoring from Hidden Matching in Constructive Neural Routing

    May 7, 2026Shaofeng Qin, Li WangVehicle RoutingNeural Combinatorial Optimization

    Beijing University of Posts and Telecommunications

  4. Two-Stage Learned Decomposition for Scalable Routing on Multigraphs

    May 6, 2026Filip Rydin, Morteza Haghir Chehreghani, Balázs KulcsárVehicle RoutingNeural Combinatorial Optimization

    Chalmers University of Technology · University of Gothenburg

  5. ARMATA: Auto-Regressive Multi-Agent Task Assignment

    May 5, 2026Yazan Youssef, Aboelmagd Noureldin, Sidney GivigiMulti-Agent System OptimizationMulti-Robot Task Allocation

    Department of Electrical and Computer Engineering, Queen’s University, Kingston, ON, Canada · Department of Electrical and Computer Engineering at the Royal Military College of Canada, and the Department of Electrical and Computer Engineering at Queen’s University, both in Kingston, Canada · School of Computing, Queen’s University, Kingston, ON, Canada

  6. FiLMMeD: Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing

    Apr 30, 2026Arthur Corrêa, Paulo Nascimento, Samuel MonizMulti-Task LearningVehicle Routing

    University of Coimbra, CEMMPRE, ARISE, Department of Mechanical Engineering, Coimbra, 3030-788, Portugal

  7. Crystal structure prediction using graph neural combinatorial optimization

    Apr 27, 2026Stavros Gerolymatos, J. Kyle Brubaker, Martin J. A. Schuetz +1Graph Neural NetworksCrystal Structure Prediction

    School of Computer Science and Informatics, University of Liverpool, Liverpool, England, UK · Amazon Advanced Solutions Lab, Seattle, Washington 98170, USA · Arm Inc., San Jose, California 95134

  8. ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs

    Apr 24, 2026Weimin Huang, Natalie M. Isenberg, Ján Drgoňa +2Combinatorial OptimizationMixed-Integer QP

    University of Southern California, USA · Pacific Northwest National Laboratory, USA · Johns Hopkins University, USA

  9. Learning to Solve the Quadratic Assignment Problem with Warm-Started MCMC Finetuning

    Apr 22, 2026Yicheng Pan, Ruisong Zhou, Haijun Zou +2Markov Chain Monte CarloCombinatorial Optimization

    School of Mathematical Science, Peking University, Beijing 100871, China · State Key Laboratory of Mathematical Sciences, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China · Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China

  10. NCO4CVRP: Neural Combinatorial Optimization for the Capacitated Vehicle Routing Problem

    Apr 17, 2026Mahir Labib Dihan, Md. Ashrafur Rahman Khan, Wasif Jalal +2Inference-Time SearchMetaheuristic Optimization

    Department of Computer Science and Engineering Bangladesh University of Engineering and Technology

  11. Generating Hadamard matrices with transformers

    Apr 13, 2026Geordie Williamson, Oded Yacobi, Paul Zinn-JustinCombinatorial OptimizationNeural Combinatorial Optimization

  12. Enhancing Cross-Problem Vehicle Routing via Federated Learning

    Apr 12, 2026Xiangchi Meng, Jianan Zhou, Jie Gao +4Vehicle RoutingNeural Combinatorial Optimization

    Dalian University of Technology · Nanyang Technological University · Delft University of Technology +1

  13. A First Guess is Rarely the Final Answer: Learning to Search in the Traveling Salesperson Problem

    Apr 8, 2026Andoni Irazusta GarmendiaTraveling Salesperson ProblemNeural Combinatorial Optimization

    University of the Basque Country (UPV/EHU)

  14. Neural Network Pruning via QUBO Optimization

    Apr 7, 2026Osama Orabi, Artur Zagitov, Hadi Salloum +3Neural Network PruningQuadratic Unconstrained Binary Optimization

    Department of Computer Science and Engineering, Innopolis University, 420500 Innopolis, Russia · Q Deep, Laboratory of Quantum Computing, 420502 Innopolis, Russia · Research Center of the Artificial Intelligence Institute, Innopolis University, 420500 Innopolis, Russia +2

  15. Vehicle-as-Prompt: A Unified Deep Reinforcement Learning Framework for Heterogeneous Fleet Vehicle Routing Problem

    Apr 6, 2026Shihong Huang, Shengjie Wang, Lei Gao +4Vehicle RoutingRL for Combinatorial Optimization

    Polytechnic Institute, Zhejiang University, 310015, Hangzhou, China · S.F. Technology Co., Ltd., 518054, Shenzhen, China · School of Management, Zhejiang University, 310058, Hangzhou, China

  16. Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization

    Mar 28, 2026Shaodi Feng, Zhuoyi Lin, Yaoxin Wu +4Combinatorial OptimizationNeural Combinatorial Optimization

    National Yang Ming Chiao Tung University · Institute for Infocomm Research (I2R), A*STAR · Eindhoven University of Technology Eindhoven +3

  17. Offline Decision Transformers for Neural Combinatorial Optimization: Surpassing Heuristics on the Traveling Salesman Problem

    Mar 26, 2026Hironori Ohigashi, Shinichiro HamadaPointer NetworksNeural Combinatorial Optimization

    Panasonic Connect Co., Ltd., Japan

  18. A Deep Reinforcement Learning (DRL)-Based Transformer Method for Solving the Open Shop Scheduling Problem

    Mar 25, 2026Faezeh Ardali, Mwembezi A. Nyelele, Gerald M. KnappCombinatorial OptimizationNeural Combinatorial Optimization

    Louisiana State University, Baton Rouge, LA, USA · University of Minnesota Duluth, Duluth, MN, USA

  19. A Learning Method with Gap-Aware Generation for Heterogeneous DAG Scheduling

    Mar 24, 2026Ruisong Zhou, Haijun Zou, Li Zhou +2Neural Combinatorial OptimizationRL for Combinatorial Optimization

    School of Mathematical Science, Peking University, Beijing 100871, China · State Key Laboratory of Mathematical Sciences, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China · Theory Lab, Central Research Institute, 2012 Labs, Huawei Technologies Co., Ltd, China +1

  20. CAMO: A Conditional Neural Solver for the Multi-objective Multiple Traveling Salesman Problem

    Mar 19, 2026Fengxiaoxiao Li, Xiao Mao, Mingfeng Fan +4Neural Combinatorial OptimizationMulti-Objective Optimization

    National University of Singapore, Singapore. · China Unicom Shenzhen Branch, Shenzhen, China. · Central South University, Changsha, China.

  21. Towards Solving Polynomial-Objective Integer Programming with Hypergraph Neural Networks

    Mar 16, 2026Minshuo Li, Yaoxin Wu, Pavel Troubil +2Combinatorial OptimizationNeural Combinatorial Optimization

    Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, the Netherlands · Eindhoven Artificial Intelligence Systems Institute, Eindhoven University of Technology, Eindhoven, the Netherlands · Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, Eindhoven, the Netherlands +1

  22. UniHetCO: A Unified Heterogeneous Representation for Multi-Problem Learning in Unsupervised Neural Combinatorial Optimization

    Mar 12, 2026Kien X. Nguyen, Ilya SafroCombinatorial OptimizationNeural Combinatorial Optimization

    Department of Computer and Information Sciences, University of Delaware, Newark DE 19716, USA

  23. Cluster-Aware Attention-Based Deep Reinforcement Learning for Pickup and Delivery Problems

    Mar 9, 2026Wentao Wang, Lifeng Han, Guangyu ZouVehicle RoutingRL for Combinatorial Optimization

    Leicester International Institute, Dalian University of Technology, Panjin, 124221, Liaoning, China. · Department of Electronic and Information Technology, Dalian University of Technology, Panjin, 124221, Liaoning, China.

  24. Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems

    Mar 8, 2026Zhenwei Wang, Tiehua Zhang, Ning Xue +3Vehicle RoutingNeural Combinatorial Optimization

    School of Computer Science, University of Nottingham Ningbo China, Ningbo, 315100, China · School of Computer Science and Technology, Tongji University, Shanghai, 200092, China · Computational Optimisation and Learning Lab, School of Computer Science, University of Nottingham, NG8 1BB Nottingham, U.K. +1

  25. Learning to Solve Orienteering Problem with Time Windows and Variable Profits

    Mar 6, 2026Songqun Gao, Zanxi Ruan, Patrick Floor +3Learning to OptimizeCombinatorial Optimization

    Department of Industrial Engineering, Università di Trento, Trento, Italy · Interdepartmental Robotics Labs (IDRA), Trento, Italy · Department of Engineering for Innovation Medicine, Università di Verona, Verona, Italy +2

  26. RADAR: Learning to Route with Asymmetry-aware DistAnce Representations

    Mar 3, 2026Hang Yi, Ziwei Huang, Yining Ma +1Vehicle RoutingNeural Combinatorial Optimization

    Singapore Management University · Massachusetts Institute of Technology

  27. Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?

    Mar 2, 2026Semih Cantürk, Thomas Sabourin, Frederik Wenkel +2Neural Combinatorial OptimizationTransfer Learning

    Dept. of Computer Science and Operations Research, Université de Montréal · Mila – Quebec AI Institute · Dept. of Mathematics & Statistics, Université de Montréal +2

  28. Efficient Decoder Scaling Strategy for Neural Routing Solvers

    Feb 28, 2026Qing Luo, Fu Luo, Ke Li +1Neural Combinatorial OptimizationNeural Scaling Laws

    Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, School of Automation and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, China. · Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China.

  29. Survey on Neural Routing Solvers

    Feb 25, 2026Yunpeng Ba, Xi Lin, Changliang Zhou +7Neural Combinatorial OptimizationVehicle Routing

    Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, School of Automation and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, China. · the School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China. · the Institute of Big Data Science and Industry, Shanxi University, Taiyuan, China. +1

  30. Mamba Meets Scheduling: Learning to Solve Flexible Job Shop Scheduling with Efficient Sequence Modeling

    Feb 25, 2026Zhi Cao, Cong Zhang, Yaoxin Wu +2Flexible Job Shop SchedulingJob Shop Scheduling

    Dalian University of Technology, Dalian, China · Nanyang Technological University, Singapore · Eindhoven University of Technology, Eindhoven, the Netherlands