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The Orienteering Problem with Time Windows (OPTW) is a combinatorial optimization problem where the goal is to maximize the total score collected from different visited locations. The application of neural network models to combinatorial…

Machine Learning · Computer Science 2021-07-01 Ricardo Gama , Hugo L. Fernandes

Travelling Salesperson Problems (TSPs) and Vehicle Routing Problems (VRPs) have achieved reasonable improvement in accuracy and computation time with the adaptation of Machine Learning (ML) methods. However, none of the previous works…

Machine Learning · Computer Science 2023-11-21 Cong Dao Tran , Thong Bach , Truong Son Hy

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…

Machine Learning · Computer Science 2025-08-13 Michael Li , Eric Bae , Christopher Haberland , Natasha Jaques

In order to deal with the high development time of exact and approximation algorithms for NP-hard combinatorial optimisation problems and the high running time of exact solvers, deep learning techniques have been used in recent years as an…

Machine Learning · Computer Science 2021-04-20 James Fitzpatrick , Deepak Ajwani , Paula Carroll

In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points…

Robotics · Computer Science 2007-05-23 Ketan Savla , Francesco Bullo , Emilio Frazzoli

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem…

Data Structures and Algorithms · Computer Science 2012-08-14 Olaf Mersmann , Bernd Bischl , Heike Trautmann , Markus Wagner , Frank Neumann

Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and…

Quantum Physics · Physics 2025-09-30 Hikaru Wakaura

The travelling salesperson problem (TSP) is a classic resource allocation problem used to find an optimal order of doing a set of tasks while minimizing (or maximizing) an associated objective function. It is widely used in robotics for…

Robotics · Computer Science 2022-07-19 Ishaan Mehta , Sharareh Taghipour , Sajad Saeedi

The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of…

Artificial Intelligence · Computer Science 2025-07-31 Yiya Diao , Changhe Li , Sanyou Zeng , Xinye Cai , Wenjian Luo , Shengxiang Yang , Carlos A. Coello Coello

Most of the recent studies tackling routing problems like the Traveling Salesman Problem (TSP) with machine learning use a transformer or Graph Neural Network (GNN) based encoder architecture. However, many of them apply these encoders…

Machine Learning · Computer Science 2024-03-28 Attila Lischka , Jiaming Wu , Rafael Basso , Morteza Haghir Chehreghani , Balázs Kulcsár

This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…

Quantum Physics · Physics 2026-05-18 Alejandro Mata Ali , Iñigo Perez Delgado , Aitor Moreno Fdez. de Leceta

The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge with widespread applications in logistics, operations research, and network design. While classical algorithms effectively solve small to medium-sized…

Quantum Physics · Physics 2025-03-04 Christos Lytrosyngounis , Ioannis Lytrosyngounis

The Traveling Salesperson Problem (TSP), a quintessential NP-hard combinatorial optimisation challenge, is vital for logistics and network design but limited by exponential complexity in large instances. We propose a hybrid…

Quantum Physics · Physics 2025-10-01 Christos Lytrosyngounis , Ioannis Lytrosyngounis

Combinatorial optimization problems like the Traveling Salesman Problem are critical in industry yet NP-hard. Neural Combinatorial Optimization has shown promise, but its reliance on online reinforcement learning (RL) hampers deployment and…

Machine Learning · Computer Science 2026-03-27 Hironori Ohigashi , Shinichiro Hamada

We demonstrate that a single training trajectory can transform a graph neural network into an unsupervised heuristic for combinatorial optimization. Focusing on the Travelling Salesman Problem, we show that encoding global structural…

Artificial Intelligence · Computer Science 2026-02-03 Yimeng Min , Carla P. Gomes

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…

Machine Learning · Computer Science 2022-04-08 Zeyang Zhang , Ziwei Zhang , Xin Wang , Wenwu Zhu

In this paper, the problem of joint communication and sensing is studied in the context of terahertz (THz) vehicular networks. In the studied model, a set of service provider vehicles (SPVs) provide either communication service or sensing…

Networking and Internet Architecture · Computer Science 2023-02-07 Xuefei Li , Mingzhe Chen , Yuchen Liu , Zhilong Zhang , Danpu Liu , Shiwen Mao

This paper introduces a new deep learning approach to approximately solve the Covering Salesman Problem (CSP). In this approach, given the city locations of a CSP as input, a deep neural network model is designed to directly output the…

Neural and Evolutionary Computing · Computer Science 2021-09-15 Kaiwen Li , Tao Zhang , Rui Wang Yuheng Wang , Yi Han

The travelling salesman problem (TSP) of space trajectory design is complicated by its complex structure design space. The graph based tree search and stochastic seeding combinatorial approaches are commonly employed to tackle the…

Optimization and Control · Mathematics 2021-09-07 Liqiang Hou , Shufan Wu , Zhongcheng Mu , Meilin Liu

Using an enhanced Self-Organizing Map method, we provided suboptimal solutions to the Traveling Salesman Problem. Besides, we employed hyperparameter tuning to identify the most critical features in the algorithm. All improvements in the…

Neural and Evolutionary Computing · Computer Science 2022-01-20 Joao P. A. Dantas , Andre N. Costa , Marcos R. O. A. Maximo , Takashi Yoneyama