Existing neural constructive solvers for routing problems have predominantly employed transformer architectures, conceptualizing the route construction as a set-to-sequence learning task. However, their efficacy has primarily been demonstrated on entirely random problem instances that inadequately capture real-world scenarios. In this paper, we introduce realistic Traveling Salesman Problem (TSP) scenarios relevant to industrial settings and derive the following insights: (1) The optimal next node (or city) to visit often lies within proximity to the current node, suggesting the potential benefits of biasing choices based on current locations. (2) Effectively solving the TSP requires robust tracking of unvisited nodes and warrants succinct grouping strategies. Building upon these insights, we propose integrating a learnable choice layer inspired by Hypernetworks to prioritize choices based on the current location, and a learnable approximate clustering algorithm inspired by the Expectation-Maximization algorithm to facilitate grouping the unvisited cities. Together, these two contributions form a hierarchical approach towards solving the realistic TSP by considering both immediate local neighbourhoods and learning an intermediate set of node representations. Our hierarchical approach yields superior performance compared to both classical and recent transformer models, showcasing the efficacy of the key designs.
LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solvers
School of Computer Science, Huazhong University of Science and Technology, China（华中科技大学计算机学院）；Department of Computer Science, Cornell University, United States（康奈尔大学计算机系）
Learning-Based TSP-Solvers Tend to Be Overly Greedy
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematics Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）
A New Constructive Heuristic driven by Machine Learning for the Traveling Salesman Problem
Dalle Molle Institute for Artificial Intelligence（达尔莫尔人工智能研究所）；Università della Svizzera Italiana（提契诺大学）；University of Modena and Reggio Emilia（摩德纳和雷焦艾米利亚大学）
Reinforcement Learning-based Non-Autoregressive Solver for Traveling Salesman Problems
College of Computer Science and Technology, Jilin University（吉林大学计算机科学与技术学院）；Nanyang Technological University（南洋理工大学）；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）；School of Computer Science, University of Science & Technology of China（中国科学技术大学计算机学院）；School of Mathematical and Computer Sciences, Heriot-Watt University（赫瑞瓦特大学数学与计算机科学学院）；College of Computer, National University of Defense Technology（国防科技大学计算机学院）
GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scales
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, Nanyang Technological University（老年人积极生活卓越研究中 心（NTU-UBC合作）、南洋理工大学）；College of Computing and Data Science, Nanyang Technological University（计算与数据科学学院、南洋理工大学）
DualOpt: A Dual Divide-and-Optimize Algorithm for the Large-scale Traveling Salesman Problem
School of Computer Science, Huazhong University of Science and Technology（华中科技大学计算机学院）；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）
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）
A Game-Theoretic Approach for Improving Generalization Ability of TSP Solvers
University of Chinese Academy of Sciences（中国科学院大学）；King’s College London（伦敦国王学院）；University College London（伦敦大学学院）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
在本文中，我们在可训练的\emph{Solver}和\emph{Data Generator}之间引入了一个两人零和框架，以提高基于深度学习的TSP求解器的泛化能力。基于\textsl{Policy Space Response Oracle}（PSRO）方法，我们的两人框架输出了一个最佳响应的求解器群体，我们可以混合并输出一个组合模型，该模型实现了对生成器的最小可利用性，从而在不同的TSP任务上实现了最具普遍性的性能。我们对不同类型和大小的TSP实例进行了实验。结果表明，我们的求解器即使在求解器从未遇到的任务上也能实现最先进的性能，而其他基于深度学习的求解器的性能由于过度拟合而急剧下降。为了证明我们的框架的原理，我们研究了所提出的两人游戏的学习结果，并证明了在训练过程中求解器种群的可利用性降低，并且它最终与生成器一起接近纳什均衡。
Mechanistic Interpretability for Neural TSP Solvers
University of Washington, Michael G. Foster School of Business（华盛顿大学，迈克尔·G·福斯特商学院）；University of Washington, Paul G. Allen School of Computer Science & Engineering（华盛顿大学，保罗·G·阿伦计算机科学与工程学院）
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）
Diversity Optimization for Travelling Salesman Problem via Deep Reinforcement Learning
South China University of Technology（华南理工大学）；Singapore Management University（新加坡管理大学）；Massachusetts Institute of Technology（麻省理工学院）；Eindhoven University of Technology（埃因霍温理工大学）
Geometric Self-Supervised Pre-training for Neural Combinatorial Optimization
Universidad Politécnica de Madrid（马德里理工大学）；Information Processing and Telecomunications Center（信息处理与通信中心）；ETSI Telecomunicación（电信高等技术工程学院）；Grupo de Tratamiento de Imágenes（图像处理组）
University of Latvia（拉脱维亚大学）；Institute of Mathematics and Computer Science at University of Latvia（拉脱维亚大学数学与计算机科学研究所）；Institute of Electronics and Computer Science（电子与计算机科学研究所）
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））
Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers
School of Data Science, The Chinese University of Hong Kong, Shenzhen, China（数据科学学院，香港中文大学（深圳））；Shenzhen Research Institute of Big Data, Shenzhen, China（深圳大数据研究院）
