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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

We study the problem of routing vehicles with energy constraints through a network where there are at least some charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations by determining routes as…

Optimization and Control · Mathematics 2014-01-28 Tao Wang , Christos G. Cassandras , Sepideh Pourazarm

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed…

Optimization and Control · Mathematics 2014-04-25 Sepideh Pourazarm , Christos G. Cassandras

The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is a fundamental NP-hard optimization problem in logistics. Solving large-scale instances remains computationally challenging for exact solvers. This paper introduces a…

Artificial Intelligence · Computer Science 2026-04-14 Mustafa Mert Özyılmaz

The Capacitated Vehicle Routing Problem (CVRP) is an NP-optimization problem (NPO) that arises in various fields including transportation and logistics. The CVRP extends from the Vehicle Routing Problem (VRP), aiming to determine the most…

Quantum Physics · Physics 2024-04-23 Ningyi Xie , Xinwei Lee , Dongsheng Cai , Yoshiyuki Saito , Nobuyoshi Asai , Hoong Chuin Lau

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

This study presents an in-depth computational analysis of four well-known Capacitated Vehicle Routing Problem (CVRP) formulations with polynomial number of subtour elimination constraints: a node-based formulation and three arc-based…

Optimization and Control · Mathematics 2018-10-02 Deniz Aksen , Temel Oncan , Mir Ehsan Hesam Sadati

We explore the near-term intersection of quantum computing with the transport sector. To support near-term integration, we introduce a framework for assessing the suitability of transport optimization problems for obtaining potential…

In the last decades, the classical Vehicle Routing Problem (VRP), i.e., assigning a set of orders to vehicles and planning their routes has been intensively researched. As only the assignment of order to vehicles and their routes is already…

Neural and Evolutionary Computing · Computer Science 2022-01-13 Veronika Lesch , Maximilian König , Samuel Kounev , Anthony Stein , Christian Krupitzer

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

The goal of this paper is to propose and test a new memetic algorithm for the capacitated vehicle routing problem in parallel computing environment. In this paper we consider simple variation of vehicle routing problem in which the only…

Distributed, Parallel, and Cluster Computing · Computer Science 2017-03-07 Michał Karpiński , Maciej Pacut

Recent neural combinatorial optimization (NCO) methods have shown promising problem-solving ability without requiring domain-specific expertise. Most existing NCO methods use training and testing data with a fixed constraint value and lack…

Machine Learning · Computer Science 2025-10-31 Fu Luo , Yaoxin Wu , Zhi Zheng , Zhenkun Wang

The energy transition in transportation benefits from demand-based models to determine the optimal placement of refueling stations for alternative fuel vehicles such as battery electric trucks. A formulation known as the refueling station…

Optimization and Control · Mathematics 2023-10-10 Nicholas Nordlund , Leandros Tassiulas , Jan-Hendrik Lange

The Vehicle Routing Problem is about optimizing the routes of vehicles to meet the needs of customers at specific locations. The route graph consists of depots on several levels and customer positions. Several optimization methods have been…

Artificial Intelligence · Computer Science 2024-09-18 László Kovács , Ali Jlidi

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed…

Data Structures and Algorithms · Computer Science 2012-03-02 Inge Li Goertz , Viswanath Nagarajan , Rishi Saket

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

SNCF, the French public train company, is experimenting to develop new types of transportation services by tackling vehicle routing problems. While many deep learning models have been used to tackle efficiently vehicle routing problems, it…

Artificial Intelligence · Computer Science 2023-01-11 Baptiste Rabecq , Rémy Chevrier

We study the vehicle routing problem with stochastic demands (VRPSD), an important variant of the classical capacitated vehicle routing problem in which customer demands are modeled as random variables. We develop the first algorithm for…

Optimization and Control · Mathematics 2026-04-15 Matheus J. Ota , Ricardo Fukasawa

This paper considers the problem of routing and rebalancing a shared fleet of autonomous (i.e., self-driving) vehicles providing on-demand mobility within a capacitated transportation network, where congestion might disrupt throughput. We…

Multiagent Systems · Computer Science 2017-08-15 Rick Zhang , Federico Rossi , Marco Pavone

The Capacitated Arc Routing Problem (CARP) occurs in applications like urban waste collection or winter gritting. It is usually defined in literature on an undirected graph , with a set of nodes and a set of edges. A fleet of identical…

Optimization and Control · Mathematics 2022-11-15 Fleury Gérard , Lacomme Philippe , Prins Christian , Sevaux Marc