The Clustered Traveling Salesman Problem (CTSP) is a variant of the popular Traveling Salesman Problem (TSP) arising from a number of real-life applications. In this work, we explore a transformation approach that solves the CTSP by converting it to the well-studied TSP. For this purpose, we first investigate a technique to convert a CTSP instance to a TSP and then apply powerful TSP solvers (including exact and heuristic solvers) to solve the resulting TSP instance. We want to answer the following questions: How do state-of-the-art TSP solvers perform on clustered instances converted from the CTSP? Do state-of-the-art TSP solvers compete well with the best performing methods specifically designed for the CTSP? For this purpose, we present intensive computational experiments on various benchmark instances to draw conclusions.
The Travelling Salesman Problem (TSP) is a challenging graph task in combinatorial optimization that requires reasoning about both local node neighborhoods and global graph structure. In this paper, we propose to use the novel Graph Learning Network (GLN), a generative approach, to approximately solve the TSP. GLN model learns directly the pattern of TSP instances as training dataset, encodes the graph properties, and merge the different node embeddings to output node-to-node an optimal tour directly or via graph search technique that validates the final tour. The preliminary results of the pr…
H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problem
School of Computer Science, Huazhong University of Science and Technology（华中科技大学计算机科学与学院）；University of Science and Technology of China（中国科学技术大学）；Microsoft Research Asia（微软亚洲研究院）
本文提出分层强化学习框架 H-TSP，通过上下层策略协同从零构造大规模 TSP 解，无需搜索即可扩展至 10000 节点，并在质量接近 SOTA 的同时大幅缩短求解时间。
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）
A Hybrid Genetic Algorithm for the Traveling Salesman Problem with Drone
Université Catholique de Louvain（鲁汶大学）；Hanoi University of Technology（河内理工大学）；University of Engineering and Technology, Vietnam National University（越南国立大学工程技术大学）
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）
School of Computer Science, Huazhong University of Science and Technology（华中科技大学计算机科学与技术学院）；Institute of Artificial Intelligence, Huazhong University of Science and Technology（华中科技大学人工智能研究院）；MIS, University of Picardie Jules Verne（皮卡第儒勒-凡尔纳大学MIS实验室）
We address the Traveling Salesman Problem (TSP), a famous NP-hard combinatorial optimization problem. And we propose a variable strategy reinforced approach, denoted as VSR-LKH, which combines three reinforcement learning methods (Q-learning, Sarsa and Monte Carlo) with the well-known TSP algorithm, called Lin-Kernighan-Helsgaun (LKH). VSR-LKH replaces the inflexible traversal operation in LKH, and lets the program learn to make choice at each search step by reinforcement learning. Experimental results on 111 TSP benchmarks from the TSPLIB with up to 85,900 cities demonstrate the excellent per…
Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are independent and identically distributed. However, the existing literature fails to solve TSP instances when training and testing data have different distributions. Concretely, we find that different training and testing distribution will result in more difficult TSP instances, i.e., the solution obtained by the model has a large gap from the optimal solution…
Solving the clustered traveling salesman problem with d-relaxed priority rule
University of Technology and Engineering, Vietnam National University（越南国立大学工程技术大学）；Interuniversitary Research Centre on Entreprise Networks, Logistics and Transportation (CIRRELT)（企业网络、物流与运输校际研究中心（CIRRELT））；Polytechnique Montréal（蒙特利尔理工学院）
Huazhong University of Science and Technology（华中科技大学）；University of Picardie Jules Verne（皮卡第儒勒·凡尔纳大学）
TSP is a classical NP-hard combinatorial optimization problem with many practical variants. LKH is one of the state-of-the-art local search algorithms for the TSP. LKH-3 is a powerful extension of LKH that can solve many TSP variants. Both LKH and LKH-3 associate a candidate set to each city to improve the efficiency, and have two different methods, $α$-measure and POPMUSIC, to decide the candidate sets. In this work, we first propose a Variable Strategy Reinforced LKH (VSR-LKH) algorithm, which incorporates three reinforcement learning methods (Q-learning, Sarsa, Monte Carlo) with LKH, for th…
Suleyman Demirel University（苏莱曼·德米雷尔大学）；UNIST（蔚山科学技术院）；Korea University（高丽大学）；Amazon（亚马逊）；University of South Florida（南佛罗里达大学）
Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems, including the Traveling Salesman Problem (TSP). Unfortunately, they perform poorly for the TSP with Drone (TSP-D), requiring routing a heterogeneous fleet of vehicles in coordination -- a truck and a drone. In TSP-D, the two vehicles are moving in tandem and may need to wait at a node for the other vehicle to join. State-less attention-based decoder fails to mak…
Huazhong University of Science and Technology（华中科技大学）
In this paper, we propose a new method called the Reinforced Hybrid Genetic Algorithm (RHGA) for solving the famous NP-hard Traveling Salesman Problem (TSP). Specifically, we combine reinforcement learning with the well-known Edge Assembly Crossover genetic algorithm (EAX-GA) and the Lin-Kernighan-Helsgaun (LKH) local search heuristic. In the hybrid algorithm, LKH can help EAX-GA improve the population by its effective local search, and EAX-GA can help LKH escape from local optima by providing high-quality and diverse initial solutions. We restrict that there is only one special individual amo…
In this paper, we provide a novel strategy for solving Traveling Salesman Problem, which is a famous combinatorial optimization problem studied intensely in the TCS community. In particular, we consider the imitation learning framework, which helps a deterministic algorithm making good choices whenever it needs to, resulting in a speed up while maintaining the exactness of the solution without suffering from the unpredictability and a potential large deviation. Furthermore, we demonstrate a strong generalization ability of a graph neural network trained under the imitation learning framework. …
Eyeballing Combinatorial Problems: A Case Study of Using Multimodal Large Language Models to Solve Traveling Salesman Problems
Queensland University of Technology（昆士兰科技大学）；Minia University（明亚大学）；Al-Ahliyya Amman University（安曼阿赫利亚大学）；Arab American University（阿拉伯美国大学）；Columbia University（哥伦比亚大学）
An End-to-End Deep Reinforcement Learning Approach for Solving the Traveling Salesman Problem with Drones
School of Management Science and Real Estate, Chongqing University（重庆大学管理科学与房地产学院）；School of Management, Guizhou University（贵州大学管理学院）；Chongqing Changan Minsheng APLL Logistics Co., Ltd.（重庆长安民生APLL物流有限公司）；State Grid Chongqing Electric Power Company Material Branch（国网重庆市电力公司物资分公司）
Recent works using deep learning to solve the Traveling Salesman Problem (TSP) have focused on learning construction heuristics. Such approaches find TSP solutions of good quality but require additional procedures such as beam search and sampling to improve solutions and achieve state-of-the-art performance. However, few studies have focused on improvement heuristics, where a given solution is improved until reaching a near-optimal one. In this work, we propose to learn a local search heuristic based on 2-opt operators via deep reinforcement learning. We propose a policy gradient algorithm to …
