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The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in…

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

Due to the practical importance of vehicle routing problems (VRP), there exists an ever-growing body of research in algorithms and (meta)heuristics for solving such problems. However, the diversity of VRP domains creates the separate…

Artificial Intelligence · Computer Science 2021-05-25 Konstantin Sidorov , Alexander Morozov

The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its $\mathcal{NP}$-Hard nature. Traditionally, these metaheuristics rely on…

Artificial Intelligence · Computer Science 2025-08-11 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

Routing problems are often faced by companies who serve costumers through vehicles. Such problems have a challenging structure to optimize, despite the recent advances in combinatorial optimization. The goal of this project is to study and…

Neural and Evolutionary Computing · Computer Science 2018-09-03 Felipe F. Müller , Luis A. A. Meira

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

The Vehicle Routing Problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most…

Quantum Physics · Physics 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

Transportation occupies one-third of the amount in the logistics costs, and accordingly transportation systems largely influence the performance of the logistics system. This work presents an adaptive data-driven innovative modular approach…

Artificial Intelligence · Computer Science 2020-01-08 Emir Zunic , Dzenana Donko , Emir Buza

We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given…

Artificial Intelligence · Computer Science 2018-05-23 Mohammadreza Nazari , Afshin Oroojlooy , Lawrence V. Snyder , Martin Takáč

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem…

Discrete Mathematics · Computer Science 2020-04-07 Thibaut Vidal , Gilbert Laporte , Piotr Matl

The Vehicle Routing Problem (VRP) has been widely studied throughout its history as a way of optimizing routes by minimizing distances, and the issue of risk in VRP has been received less attention, which is essential to increase transport…

Optimization and Control · Mathematics 2022-08-23 Gabriel Adam Bilato , Cleber Damião Rocco , Anibal Tavares de Azevedo

Vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver a fixed number of customers with optimal…

Quantum Physics · Physics 2022-01-14 Nishikanta Mohanty , Bikash K. Behera

Green vehicle routing problem (GVRP) aims to consider greenhouse gas emissions reduction, while routing the vehicles. It can be either through adopting Alternative Fuel Vehicles (AFVs) or with existing conventional fossil fuel vehicles in…

Optimization and Control · Mathematics 2023-01-20 Saba Sabet , Bilal Farooq

The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with…

Quantum Physics · Physics 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

Finding a feasible and prompt solution to the Vehicle Routing Problem (VRP) is a prerequisite for efficient freight transportation, seamless logistics, and sustainable mobility. Traditional optimization methods reach their limits when…

Machine Learning · Computer Science 2024-11-08 Elija Deineko , Carina Kehrt

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

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing…

Artificial Intelligence · Computer Science 2025-10-09 Fangting Zhou , Attila Lischka , Balazs Kulcsar , Jiaming Wu , Morteza Haghir Chehreghani , Gilbert Laporte

In the classic Vehicle Routing Problem (VRP) a fleet of of vehicles has to visit a set of customers while minimising the operations' costs. We study a rich variant of the VRP featuring split deliveries, an heterogeneous fleet, and…

Artificial Intelligence · Computer Science 2016-12-07 Arthur Mahéo , Tommaso Urli , Philip Kilby

The Vehicle Routing Problem (VRP) is the combinatorial optimization problem of designing routes for vehicles to visit customers in such a fashion that a cost function, typically the number of vehicles, or the total travelled distance is…

Artificial Intelligence · Computer Science 2021-07-01 Sabino Francesco Roselli , Martin Fabian , Knut Åkesson

Despite the extensive research efforts and the remarkable results obtained on Vehicle Routing Problems (VRP) by using algorithms proposed by the Machine Learning community that are partially or entirely based on data-driven analysis, most…

Machine Learning · Computer Science 2021-09-30 Luca Accorsi , Andrea Lodi , Daniele Vigo
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