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Vehicle routing problem (VRP) is a typical discrete combinatorial optimization problem, and many models and algorithms have been proposed to solve the VRP and its variants. Although existing approaches have contributed a lot to the…

Machine Learning · Computer Science 2022-02-22 Bingjie Li , Guohua Wu , Yongming He , Mingfeng Fan , Witold Pedrycz

Existing neural heuristics often train a deep architecture from scratch for each specific vehicle routing problem (VRP), ignoring the transferable knowledge across different VRP variants. This paper proposes the cross-problem learning to…

Artificial Intelligence · Computer Science 2024-06-19 Zhuoyi Lin , Yaoxin Wu , Bangjian Zhou , Zhiguang Cao , Wen Song , Yingqian Zhang , Senthilnath Jayavelu

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

Recently, the applications of the methodologies of Reinforcement Learning (RL) to NP-Hard Combinatorial optimization problems have become a popular topic. This is essentially due to the nature of the traditional combinatorial algorithms,…

Optimization and Control · Mathematics 2022-08-02 Simone Foa , Corrado Coppola , Giorgio Grani , Laura Palagi

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these…

Machine Learning · Computer Science 2024-12-31 Joshua Levin , Randall Correll , Takanori Ide , Takafumi Suzuki , Saito Takaho , Alan Arai

Learning to solve combinatorial optimization problems, such as the vehicle routing problem, offers great computational advantages over classical operations research solvers and heuristics. The recently developed deep reinforcement learning…

Machine Learning · Computer Science 2022-01-06 Daniela Thyssens , Jonas Falkner , Lars Schmidt-Thieme

Many real-world vehicle routing problems involve rich sets of constraints with respect to the capacities of the vehicles, time windows for customers etc. While in recent years first machine learning models have been developed to solve basic…

Machine Learning · Computer Science 2020-06-17 Jonas K. Falkner , Lars Schmidt-Thieme

Learning to solve vehicle routing problems (VRPs) has garnered much attention. However, most neural solvers are only structured and trained independently on a specific problem, making them less generic and practical. In this paper, we aim…

Artificial Intelligence · Computer Science 2024-05-07 Jianan Zhou , Zhiguang Cao , Yaoxin Wu , Wen Song , Yining Ma , Jie Zhang , Chi Xu

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 min-max vehicle routing problem (min-max VRP) traverses all given customers by assigning several routes and aims to minimize the length of the longest route. Recently, reinforcement learning (RL)-based sequential planning methods have…

Machine Learning · Computer Science 2024-06-07 Zhi Zheng , Shunyu Yao , Zhenkun Wang , Xialiang Tong , Mingxuan Yuan , Ke Tang

The Vehicle Routing Problem with Route Balancing (VRPRB) is a biobjective version of the original Vehicle Routing Problem (VRP) in which, besides minimizing the total distance traveled by the vehicles involved, the balance among route loads…

Optimization and Control · Mathematics 2017-02-21 Jairo Lozano , Luis C. González-Gurrola , Eduardo Rodríguez-Tello , Philippe Lacomme

Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in…

Artificial Intelligence · Computer Science 2020-12-01 André Hottung , Kevin Tierney

Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when…

Artificial Intelligence · Computer Science 2026-05-26 Rongsheng Chen , Changliang Zhou , Canhong Yu , Yuanyao Chen , Yu Zhou , Zhuo Chen , Zhenkun Wang

The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…

Data Structures and Algorithms · Computer Science 2026-04-07 Yongyu Chen

In recent years, deep reinforcement learning (DRL) has gained traction for solving the NP-hard traveling salesman problem (TSP). However, limited attention has been given to the close-enough TSP (CETSP), primarily due to the challenge…

Machine Learning · Computer Science 2025-10-06 Mingfeng Fan , Jiaqi Cheng , Yaoxin Wu , Yifeng Zhang , Yibin Yang , Guohua Wu , Guillaume Sartoretti

We consider a Persistent Intelligence, Surveillance and Reconnaissance (PISR) routing problem, which includes collecting data from a set of specified task locations and delivering that data to a control station. Each task is assigned a…

Optimization and Control · Mathematics 2017-03-01 Satyanarayana G. Manyam , Steven Rasmussen , David W. Casbeer , Krishnamoorthy Kalyanam , Suresh Manickam

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…

Machine Learning · Computer Science 2021-12-06 Wouter Kool , Herke van Hoof , Joaquim Gromicho , Max Welling

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

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…

Machine Learning · Computer Science 2025-11-24 Yuanyao Chen , Rongsheng Chen , Fu Luo , Zhenkun Wang

Deep reinforcement learning (RL) has been shown to be effective in producing approximate solutions to some vehicle routing problems (VRPs), especially when using policies generated by encoder-decoder attention mechanisms. While these…

Machine Learning · Computer Science 2024-12-19 Joshua Levin , Randall Correll , Takanori Ide , Takafumi Suzuki , Takaho Saito , Alan Arai