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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 Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In…

Data Structures and Algorithms · Computer Science 2025-07-08 Jingyang Zhao , Mingyu Xiao

Existing deep reinforcement learning (DRL) based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence,…

Machine Learning · Computer Science 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

The Multidepot Capacitated Vehicle Routing Problem (MCVRP) is a well-known variant of the classic Capacitated Vehicle Routing Problem (CVRP), where we need to route capacitated vehicles located in multiple depots to serve customers' demand…

Data Structures and Algorithms · Computer Science 2024-04-18 Jingyang Zhao , Mingyu Xiao

The capacitated vehicle routing problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. In this problem, we are given a depot and a set of customers, each with a demand, embedded in a metric space. The…

Data Structures and Algorithms · Computer Science 2026-01-30 Jingyang Zhao , Mingyu Xiao

In this paper, we present Approximation Schemes for Capacitated Vehicle Routing Problem (CVRP) on several classes of graphs. In CVRP, introduced by Dantzig and Ramser (1959), we are given a graph $G=(V,E)$ with metric edges costs, a depot…

Data Structures and Algorithms · Computer Science 2021-06-30 Aditya Jayaprakash , Mohammad R. Salavatipour

Efficiently solving a vehicle routing problem (VRP) in a practical runtime is a critical challenge for delivery management companies. This paper explores both a theoretical and experimental connection between the Capacitated Vehicle Routing…

Optimization and Control · Mathematics 2024-03-22 Abdelhakim Abdellaoui , Loubna Benabbou , Issmail El Hallaoui

In this paper, we present improved approximation algorithms for the (unsplittable) Capacitated Vehicle Routing Problem (CVRP) in general metrics. In CVRP, introduced by Dantzig and Ramser (1959), we are given a set of points (clients) $V$…

Data Structures and Algorithms · Computer Science 2021-11-17 Zachary Friggstad , Ramin Mousavi , Mirmahdi Rahgoshay , Mohammad R. Salavatipour

Capacitated vehicle routing problem (CVRP) is being one of the most common optimization problems in our days, considering the wide usage of routing algorithms in multiple fields such as transportation domain, food delivery, network routing,…

Artificial Intelligence · Computer Science 2021-12-28 Hassan Moussa

We investigate a structural decomposition for the capacitated vehicle routing problem (CVRP) based on vehicle-to-customer "assignment" and visits "sequencing" decision variables. We show that an heuristic search focused on assignment…

Optimization and Control · Mathematics 2018-03-19 Túlio A. M. Toffolo , Thibaut Vidal , Tony Wauters

We study the load balanced capacitated vehicle routing problem (LBCVRP): the problem is to design a collection of tours for a fixed fleet of vehicles with capacity Q to distribute a supply from a single depot between a number of predefined…

Data Structures and Algorithms · Computer Science 2020-07-28 Haniyeh Fallah , Farzad Didehvar , Farhad Rahmati

We study the capacitated vehicle routing problem in graphic metrics (graphic CVRP). Our main contribution is a new lower bound on the cost of an optimal solution. For graphic metrics, this lower bound is tight and significantly stronger…

Data Structures and Algorithms · Computer Science 2022-10-19 Tobias Mömke , Hang Zhou

We investigate the capacitated vehicle routing problem (CVRP) under a robotics context, where a vehicle with limited payload must complete delivery (or pickup) tasks to serve a set of geographically distributed customers with varying…

Robotics · Computer Science 2021-07-27 Kai Gao , Jingjin Yu

VRP (Vehicle Routing Problem) is an NP hard problem, and it has attracted a lot of research interest. In contexts where vehicles have limited carrying capacity, such as volume and weight but needed to deliver items at various locations.…

Optimization and Control · Mathematics 2020-10-22 Muhammad Wildan Abdul Hakim , Syarifah Rosita Dewi , Yurio Windiatmoko , Umar Abdul Aziz

The Vehicle Routing Problem (VRP) is a popular generalization of the Traveling Salesperson Problem. Instead of one salesperson traversing the entire weighted, undirected graph $G$, there are $k$ vehicles available to jointly cover the set…

Computational Complexity · Computer Science 2026-05-01 Michelle Döring , Jan Fehse , Tobias Friedrich , Paula Marten , Niklas Mohrin , Kirill Simonov , Farehe Soheil , Jakob Timm , Shaily Verma

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

We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each…

Data Structures and Algorithms · Computer Science 2011-03-08 Inge Li Goertz , Viswanath Nagarajan

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

Unlike traditional homogeneous routing problems, the Heterogeneous Fleet Vehicle Routing Problem (HFVRP) involves heterogeneous fixed costs, variable travel costs, and capacity constraints, rendering solution quality highly sensitive to…

Machine Learning · Computer Science 2026-04-08 Shihong Huang , Shengjie Wang , Lei Gao , Hong Ma , Zhanluo Zhang , Feng Zhang , Weihua Zhou

The Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem with broad applications in logistics and transportation. Real-world CVRPs often involve diverse objectives and complex constraints, such as time windows or…

Artificial Intelligence · Computer Science 2026-05-15 Wen Wang , Xiangchen Wu , Liang Wang , Hao Hu , Xianping Tao
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