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Deep learning has been extensively explored to solve vehicle routing problems (VRPs), which yields a range of data-driven neural solvers with promising outcomes. However, most neural solvers are trained to tackle VRP instances in a…

Machine Learning · Computer Science 2025-08-19 Shaodi Feng , Zhuoyi Lin , Jianan Zhou , Cong Zhang , Jingwen Li , Kuan-Wen Chen , Senthilnath Jayavelu , Yew-Soon Ong

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous…

Machine Learning · Computer Science 2025-09-23 Ido Greenberg , Piotr Sielski , Hugo Linsenmaier , Rajesh Gandham , Shie Mannor , Alex Fender , Gal Chechik , Eli Meirom

The electric vehicle routing problem with time windows (EVRPTW) is a complex optimization problem in sustainable logistics, where routing decisions must minimize total travel distance, fleet size, and battery usage while satisfying strict…

Machine Learning · Computer Science 2026-01-22 Mertcan Daysalilar , Fuat Uyguroglu , Gabriel Nicolosi , Adam Meyers

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

Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…

Machine Learning · Computer Science 2020-07-21 Wenpeng Wei , Toshiko Aizono

Motivated by the promising advances of deep-reinforcement learning (DRL) applied to cooperative multi-agent systems we propose a model and learning procedure to solve the Capacitated Multi-Vehicle Routing Problem (CMVRP) with fixed fleet…

Neural and Evolutionary Computing · Computer Science 2019-12-10 Jose Manuel Vera , Andres G. Abad

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

Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve…

Artificial Intelligence · Computer Science 2019-10-01 Antoine François , Quentin Cappart , Louis-Martin Rousseau

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

A key challenge in solving a combinatorial optimization problem is how to guide the agent (i.e., solver) to efficiently explore the enormous search space. Conventional approaches often rely on enumeration (e.g., exhaustive, random, or tabu…

Artificial Intelligence · Computer Science 2020-08-11 Xingwen Zhang , Shuang Yang

Vehicle routing problems (VRPs), which can be found in numerous real-world applications, have been an important research topic for several decades. Recently, the neural combinatorial optimization (NCO) approach that leverages a…

Machine Learning · Computer Science 2024-04-15 Fei Liu , Xi Lin , Zhenkun Wang , Qingfu Zhang , Xialiang Tong , Mingxuan Yuan

This paper presents an approach to learn the local-search heuristics that iteratively improves the solution of Vehicle Routing Problem (VRP). A local-search heuristics is composed of a destroy operator that destructs a candidate solution,…

Neural and Evolutionary Computing · Computer Science 2020-02-21 Lei Gao , Mingxiang Chen , Qichang Chen , Ganzhong Luo , Nuoyi Zhu , Zhixin Liu

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

Machine learning has been adapted to help solve NP-hard combinatorial optimization problems. One prevalent way is learning to construct solutions by deep neural networks, which has been receiving more and more attention due to the high…

Machine Learning · Computer Science 2024-05-07 Chengrui Gao , Haopu Shang , Ke Xue , Dong Li , Chao Qian

Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces…

Artificial Intelligence · Computer Science 2020-06-03 Quentin Cappart , Thierry Moisan , Louis-Martin Rousseau , Isabeau Prémont-Schwarz , Andre Cire

In this work, a novel idea is presented for combinatorial optimization problems, a hybrid network, which results in a superior outcome. We applied this method to graph pointer networks [1], expanding its capabilities to a higher level. We…

Heavy goods vehicles are vital backbones of the supply chain delivery system but also contribute significantly to carbon emissions with only 60% loading efficiency in the United Kingdom. Collaborative vehicle routing has been proposed as a…

Machine Learning · Computer Science 2024-06-12 Stefan Schoepf , Stephen Mak , Julian Senoner , Liming Xu , Netland Torbjörn , Alexandra Brintrup

In this research, we propose an iterative learning hybrid optimization solver developed to strengthen the performance of metaheuristic algorithms in solving the Capacitated Vehicle Routing Problem (CVRP). The iterative hybrid mechanism…

Artificial Intelligence · Computer Science 2025-08-13 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux , Daniele Vigo

Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust…

Machine Learning · Computer Science 2022-02-16 Yuan Jiang , Yaoxin Wu , Zhiguang Cao , Jie Zhang

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or…

Artificial Intelligence · Computer Science 2023-06-12 Pierre Tassel , Martin Gebser , Konstantin Schekotihin