Neural routing solvers (NRSs) that leverage deep learning to tackle vehicle routing problems have demonstrated notable potential for practical applications. By learning implicit heuristic rules from data, NRSs replace the handcrafted counterparts in classic heuristic frameworks, thereby reducing reliance on costly manual design and trial-and-error adjustments. This survey makes two main contributions: (1) The heuristic nature of NRSs is highlighted, and existing NRSs are reviewed from the perspective of heuristics. A hierarchical taxonomy based on heuristic principles is further introduced. (2) A generalization-focused evaluation pipeline is proposed to address limitations of the conventional pipeline. Comparative benchmarking of representative NRSs across both pipelines uncovers a series of previously unreported gaps in current research.
Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solver
College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机科学与软件工程学院）；School of Automation and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学自动化与智能制造学院）；Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology（广东省全驱动系统控制理论与技术重点实验室，南方科技大学）；Pengcheng Laboratory（鹏城实验室）
Learning to Reduce Search Space for Generalizable Neural Routing Solver
School of Automation and Intelligent Manufacturing（自动化与智能制造学院）；Southern University of Science and Technology（南方科技大学）；School of Mathematics and Statistics（数学与统计学学院）；Xi'an Jiaotong University（西安交通大学）；Department of Computer Science（计算机科学系）；City University of Hong Kong（香港城市大学）
SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver
School of Automation and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, China（自动化与智能制造学院，南方科技大学，深圳，中国）；Pengcheng Laboratory, Shenzhen, China（鹏城实验室，深圳，中国）；Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China（广东省全驱动系统控制理论与技术重点实验室，南方科技大学，深圳，中国）；College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China（计算机科学与软件工程学院，深圳大学，深圳，中国）
Rethinking Light Decoder-based Solvers for Vehicle Routing Problems
School of Computing and Information Systems, Singapore Management University（新加坡管理大学计算与信息系统学院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
Lifelong Learner: Discovering Versatile Neural Solvers for Vehicle Routing Problems
department of Computer Science at National Yang Ming Chiao Tung University（国立阳明交通大学计算机科学系）；Institute for Infocomm Research, Agency for Science, Technology and Research (A*STAR)（资讯通信研究院，科技研究局（A*STAR））；College of Computing and Data Science at Nanyang Technological University（南洋理工大学计算与数据科学学院）；School of Computer Science, Sichuan Normal University（四川师范大学计算机科学学院）；School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）；Center for Frontier AI Research, Agency for Science, Technology and Research (A*STAR)（前沿人工智能研究中心，科技研究局（A*STAR））
LoRe: Adaptive Interaction-Evaluation Routing with Per-Step Interaction Budgets for Iterative Graph Solvers
Beijing Key Laboratory of Fault-Tolerant Quantum Computing, Beijing Academy of Quantum Information Sciences, Beijing, China（北京容错量子计算重点实验室，量子信息科学北京市院，北京，中国）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, CAS, Beijing, China（北京凝聚态物理国家实验室，物理研究所，中国科学院，北京，中国）；Beijing Key Laboratory of Advanced Quantum Technology, Beijing, China（北京先进量子技术重点实验室，北京，中国）；Hefei National Laboratory, Hefei, China（合肥国家实验室，合肥，中国）
Learning to Insert for Constructive Neural Vehicle Routing Solver
School of Automation and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, China（自动化与智能制造学院，南方科技大学，深圳，中国）；Guangdong Provincial Key Laboratory of Fully Actuated System Control Theory and Technology, Southern University of Science and Technology, Shenzhen, China（广东省全驱动系统控制理论与技术重点实验室，南方科技大学，深圳，中国）；Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China（计算机科学系，香港城市大学，香港特别行政区，中国）；School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China（数学与统计学学院，西安交通大学，西安，中国）
Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives
Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, College of Computer Science and Technology, Jilin university（教育部符号计算与知识工程重点实验室、计算机科学与技术学院、吉林大学）；Joint NTU-UBC Research Centre of Excellence in Active Living for the Elderly（卓越老龄化主动生活联合研究中心）；School of Software, Tsinghua University（软件学院、清华大学）；College of Computing and Data Science, Nanyang Technological University（计算与数据科学学院、南洋理工大学）
Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Tasks
Center of Data Science and Artificial Intelligence & School of Engineering and Computer Science（数据科学与人工智能中心及工程与计算机科学学院）；Victoria University of Wellington（怀特维尔大学）；School of Data Science（数据科学学院）
本文提出了一种应对持续漂移任务的终身学习方法，通过Dual Replay with Experience Enhancement框架提升学习效率并缓解灾难性遗忘。
Improving Generalization of Neural Vehicle Routing Problem Solvers Through the Lens of Model Architecture
Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of Education, College of Computer Science and Technology, Jilin University（吉林大学计算机科学与技术学院、教育部符号计算与知识工程重点实验室）；Joint NTU-UBC Research Centre of Excellence in Active Living for the Elderly, Nanyang Technological University（南洋理工大学、新加坡国立大学-不列颠哥伦比亚大学老年人积极生活联合卓越研究中心）；WeBank-NTU Joint Research Institute on Fintech, Nanyang Technological University（南洋理工大学微众银行金融科技联合研究院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
Adversarial Generative Flow Network for Solving Vehicle Routing Problems
Singapore Management University（新加坡管理大学）；Singapore Institute of Manufacturing Technology (SIMTech), Agency of Science, Technology and Research (A*STAR)（新加坡制造技术研究院（新加坡科技研究局下属机构））
Learning Large Neighborhood Search for Vehicle Routing in Airport Ground Handling
Nanyang Technological University（南洋理工大学）；Eindhoven University of Technology（埃因霍温理工大学）；Singapore Management University（新加坡管理大学）；Shandong University（山东大学）；Agency for Science Technology and Research (A*STAR)（新加坡科技研究局）
Towards Efficient Constraint Handling in Neural Solvers for Routing Problems
Nanyang Technological University（南洋理工大学）；Singapore Management University（新加坡管理学院）；Shandong University（山东大学）；Eindhoven University of Technology（埃因霍温理工大学）；MIT（麻省理工学院）
KAYROS: An Anytime and Exact Open-Source Solver for Duration-Minimization Time-Dependent Vehicle Routing. A Technical Report and a Case Study in Human-AI Engineering
