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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,…

Optimization and Control · Mathematics 2022-12-06 Aigerim Bogyrbayeva , Taehyun Yoon , Hanbum Ko , Sungbin Lim , Hyokun Yun , Changhyun Kwon

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…

Machine Learning · Computer Science 2025-01-09 Yong Liang Goh , Wee Sun Lee , Xavier Bresson , Thomas Laurent , Nicholas Lim

This paper presents a novel and efficient heuristic framework for approximating the solutions to the multiple traveling salesmen problem (m-TSP) and other variants on the TSP. The approach adopted in this paper is an extension of the…

Optimization and Control · Mathematics 2016-04-15 Mayank Baranwal , Brian Roehl , Srinivasa M. Salapaka

Routing problems are optimization problems that consider a set of goals in a graph to be visited by a vehicle (or a fleet of them) in an optimal way, while numerous constraints have to be satisfied. We present a solution based on…

Robotics · Computer Science 2017-08-01 Miroslav Kulich , Roman Sushkov , Libor Přeučil

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…

Machine Learning · Computer Science 2020-11-04 Nasrin Sultana , Jeffrey Chan , A. K. Qin , Tabinda Sarwar

The traveling purchaser problem (TPP) is an important combinatorial optimization problem with broad applications. Due to the coupling between routing and purchasing, existing works on TPPs commonly address route construction and purchase…

Optimization and Control · Mathematics 2025-07-03 Haofeng Yuan , Rongping Zhu , Wanlu Yang , Shiji Song , Keyou You , Wei Fan , C. L. Philip Chen

Traveling Salesman Problem (TSP), as a classic routing optimization problem originally arising in the domain of transportation and logistics, has become a critical task in broader domains, such as manufacturing and biology. Recently, Deep…

Artificial Intelligence · Computer Science 2023-04-20 Yan Jin , Yuandong Ding , Xuanhao Pan , Kun He , Li Zhao , Tao Qin , Lei Song , Jiang Bian

The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the…

Robotics · Computer Science 2026-03-24 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

This paper develops an inherently parallelised, fast, approximate learning-based solution to the generic class of Capacitated Vehicle Routing Problems with Time Windows and Dynamic Routing (CVRP-TWDR). Considering vehicles in a fleet as…

Artificial Intelligence · Computer Science 2021-04-15 Nazneen N Sultana , Vinita Baniwal , Ansuma Basumatary , Piyush Mittal , Supratim Ghosh , Harshad Khadilkar

The Travelling Salesman Problem (TSP) is a classical NP-hard problem and has broad applications in many disciplines and industries. In a large scale location-based services system, users issue TSP queries concurrently, where a TSP query is…

Artificial Intelligence · Computer Science 2021-04-15 Kangfei Zhao , Shengcai Liu , Yu Rong , Jeffrey Xu Yu

Recent work applying deep reinforcement learning (DRL) to solve traveling salesman problems (TSP) has shown that DRL-based solvers can be fast and competitive with TSP heuristics for small instances, but do not generalize well to larger…

Machine Learning · Computer Science 2021-10-07 Wenbin Ouyang , Yisen Wang , Shaochen Han , Zhejian Jin , Paul Weng

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

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

Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a…

Artificial Intelligence · Computer Science 2020-05-12 Yaoxin Wu , Wen Song , Zhiguang Cao , Jie Zhang , Andrew Lim

The past decade has seen a rapid penetration of electric vehicles (EV) in the market, more and more logistics and transportation companies start to deploy EVs for service provision. In order to model the operations of a commercial EV fleet,…

Machine Learning · Computer Science 2021-08-24 Bo Lin , Bissan Ghaddar , Jatin Nathwani

This study addresses the Min-Max Multiple Traveling Salesmen Problem ($m^3$-TSP), which aims to coordinate tours for multiple salesmen such that the length of the longest tour is minimized. Due to its NP-hard nature, exact solvers become…

Artificial Intelligence · Computer Science 2025-08-26 Wen Wang , Xiangchen Wu , Liang Wang , Hao Hu , Xianping Tao , Linghao Zhang

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,…

Machine Learning · Computer Science 2019-11-13 Qiang Ma , Suwen Ge , Danyang He , Darshan Thaker , Iddo Drori

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

The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits…

Robotics · Computer Science 2024-10-28 Anoop Bhat , Geordan Gutow , Bhaskar Vundurthy , Zhongqiang Ren , Sivakumar Rathinam , Howie Choset

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