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Existing neural methods for the Travelling Salesman Problem (TSP) mostly aim at finding a single optimal solution. To discover diverse yet high-quality solutions for Multi-Solution TSP (MSTSP), we propose a novel deep reinforcement learning…

机器学习 · 计算机科学 2025-01-03 Qi Li , Zhiguang Cao , Yining Ma , Yaoxin Wu , Yue-Jiao Gong

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…

机器学习 · 计算机科学 2022-04-08 Zeyang Zhang , Ziwei Zhang , Xin Wang , Wenwu Zhu

There has been a growing number of machine learning methods for approximately solving the travelling salesman problem. However, these methods often require solved instances for training or use complex reinforcement learning approaches that…

机器学习 · 计算机科学 2022-07-28 Elīza Gaile , Andis Draguns , Emīls Ozoliņš , Kārlis Freivalds

The traveling salesman problem is a fundamental combinatorial optimization problem with strong exact algorithms. However, as problems scale up, these exact algorithms fail to provide a solution in a reasonable time. To resolve this, current…

机器学习 · 计算机科学 2025-01-09 Yong Liang Goh , Wee Sun Lee , Xavier Bresson , Thomas Laurent , Nicholas Lim

This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city…

人工智能 · 计算机科学 2017-01-16 Irwan Bello , Hieu Pham , Quoc V. Le , Mohammad Norouzi , Samy Bengio

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,…

机器学习 · 计算机科学 2022-10-13 Pingbang Hu

The Traveling Salesman Problem (TSP) is the most popular and most studied combinatorial problem, starting with von Neumann in 1951. It has driven the discovery of several optimization techniques such as cutting planes, branch-and-bound,…

机器学习 · 计算机科学 2021-03-05 Xavier Bresson , Thomas Laurent

The Traveling Salesman Problem (TSP) is a well-known NP-hard combinatorial optimization problem with wide-ranging applications in logistics, routing, and intelligent systems. Due to its factorial complexity, solving large-scale instances…

分布式、并行与集群计算 · 计算机科学 2025-05-27 Rabab Alkhalifa , Fatima Alkhomayes , Boushra Almazroua , Dana Alhaidan , Maryam Alothman , Jumana Almuhaidib

The Travelling Salesman Problem (TSP) is a classical combinatorial optimisation problem. Deep learning has been successfully extended to meta-learning, where previous solving efforts assist in learning how to optimise future optimisation…

机器学习 · 计算机科学 2020-11-04 Nasrin Sultana , Jeffrey Chan , A. K. Qin , Tabinda Sarwar

The Traveling Salesman Problem (TSP) is a classic NP-hard combinatorial optimization task with numerous practical applications. Classic heuristic solvers can attain near-optimal performance for small problem instances, but become…

机器学习 · 计算机科学 2025-08-13 Michael Li , Eric Bae , Christopher Haberland , Natasha Jaques

Neural solvers have shown significant potential in solving the Traveling Salesman Problem (TSP), yet current approaches face significant challenges. Supervised learning (SL)-based solvers require large amounts of high-quality labeled data,…

机器学习 · 计算机科学 2025-09-18 Junrui Wen , Yifei Li , Bart Selman , Kun He

In the new wave of artificial intelligence, deep learning is impacting various industries. As a closely related area, optimization algorithms greatly contribute to the development of deep learning. But the reverse applications are still…

机器学习 · 计算机科学 2019-11-06 Zhengxuan Ling , Xinyu Tao , Yu Zhang , Xi Chen

Most neural solvers for the Traveling Salesperson Problem (TSP) are trained to output a single solution, even though practitioners rarely stop there: at test time, they routinely spend extra compute on sampling or post-hoc search. This…

机器学习 · 计算机科学 2026-05-04 Andoni Irazusta Garmendia

The Traveling Salesman Problem (often called TSP) is a classic algorithmic problem in the field of computer science and operations research. It is an NP-Hard problem focused on optimization. TSP has several applications even in its purest…

数据结构与算法 · 计算机科学 2022-05-31 Amey Gohil , Manan Tayal , Tezan Sahu , Vyankatesh Sawalpurkar

End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with…

机器学习 · 计算机科学 2022-05-26 Chaitanya K. Joshi , Quentin Cappart , Louis-Martin Rousseau , Thomas Laurent

In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input,…

机器学习 · 计算机科学 2019-11-13 Qiang Ma , Suwen Ge , Danyang He , Darshan Thaker , Iddo Drori

This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in…

机器学习 · 计算机科学 2019-10-15 Chaitanya K. Joshi , Thomas Laurent , Xavier Bresson

This paper gives a detailed review of reinforcement learning (RL) in combinatorial optimization, introduces the history of combinatorial optimization starting in the 1950s, and compares it with the RL algorithms of recent years. This paper…

机器学习 · 计算机科学 2023-10-04 Yunhao Yang , Andrew Whinston

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…

人工智能 · 计算机科学 2020-07-10 Amal Nammouchi , Hakim Ghazzai , Yehia Massoud

We propose UTSP, an unsupervised learning (UL) framework for solving the Travelling Salesman Problem (TSP). We train a Graph Neural Network (GNN) using a surrogate loss. The GNN outputs a heat map representing the probability for each edge…

人工智能 · 计算机科学 2024-04-11 Yimeng Min , Yiwei Bai , Carla P. Gomes
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