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The capacitated vehicle routing problem (CVRP) involves distributing (identical) items from a depot to a set of demand locations, using a single capacitated vehicle. We study a generalization of this problem to the setting of multiple…

数据结构与算法 · 计算机科学 2010-12-09 Inge Li Gortz , Marco Molinaro , Viswanath Nagarajan , R. Ravi

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…

机器学习 · 计算机科学 2024-11-08 Elija Deineko , Carina Kehrt

Vehicle routing problems (VRPs) form a class of combinatorial problems with wide practical applications. While previous heuristic or learning-based works achieve decent solutions on small problem instances of up to 100 cities, their…

机器学习 · 计算机科学 2021-10-29 Sirui Li , Zhongxia Yan , Cathy Wu

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…

机器学习 · 计算机科学 2022-02-22 Bingjie Li , Guohua Wu , Yongming He , Mingfeng Fan , Witold Pedrycz

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…

数据结构与算法 · 计算机科学 2026-01-30 Jingyang Zhao , Mingyu Xiao

The Vehicle Fleet Sizing, Positioning and Routing Problem with Stochastic Customers (VFSPRP-SC) consists on pairing strategic decisions of depot positioning and fleet sizing with operational vehicle routing decisions while taking into…

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…

人工智能 · 计算机科学 2025-08-11 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

In this paper we consider a 2-vehicle routing problem which can be viewed as a building block for the varieties of the vehicle routing problems (VRPs). To approach this problem, we suggest a framework based on the Held and Karp dynamic…

数据结构与算法 · 计算机科学 2016-10-07 Vladimir Deineko

We consider a 2-vehicle routing problem (2VRP) which can be viewed as a building block for the variety of vehicle routing problems (VRP). As a simplified version of the 2VRP, we consider a 2-period balanced travelling salesman problem…

最优化与控制 · 数学 2018-02-23 Vladimir Deineko , Bettina Klinz

This paper deals with generating of an optimized route for multiple Vehicle routing Problems (mVRP). We used a methodology of clustering the given cities depending upon the number of vehicles and each cluster is allotted to a vehicle. k-…

分布式、并行与集群计算 · 计算机科学 2010-01-26 R. Nallusamy , K. Duraiswamy , R. Dhanalaksmi , P. Parthiban

We present a two-level decomposition strategy for solving the Vehicle Routing Problem (VRP) using the Quantum Approximate Optimization Algorithm. A Problem-Level Decomposition partitions a 13-node (156-qubit) VRP into smaller Traveling…

量子物理 · 物理学 2025-07-09 Andrew Maciejunes , John Stenger , Dan Gunlycke , Nikos Chrisochoides

We introduce the multimodal car- and ride-sharing problem (MMCRP), in which a pool of cars is used to cover a set of ride requests while uncovered requests are assigned to other modes of transport (MOT). A car's route consists of one or…

人工智能 · 计算机科学 2022-09-29 Miriam Enzi , Sophie N. Parragh , David Pisinger , Matthias Prandtstetter

In this paper, we develop a profit-sharing-based optimal routing mechanism to incentivize horizontal collaboration among urban goods distributors. This paper investigates a collaborative routing problem for urban logistics, in which the…

最优化与控制 · 数学 2025-07-02 Fangting Zhou , Ala Arvidsson , Jiaming Wu , Balazs Kulcsar

We propose a new model for formalizing reward collection problems on graphs with dynamically generated rewards which may appear and disappear based on a stochastic model. The *robot routing problem* is modeled as a graph whose nodes are…

系统与控制 · 计算机科学 2017-07-18 Rayna Dimitrova , Ivan Gavran , Rupak Majumdar , Vinayak S. Prabhu , Sadegh Esmaeil Zadeh Soudjani

Combinatorial optimization (CO) problems are traditionally addressed using Operations Research (OR) methods, including metaheuristics. In this study, we introduce a demand selection problem for the Vehicle Routing Problem (VRP) with an…

数据结构与算法 · 计算机科学 2025-05-27 Farid Najar , Dominique Barth , Yann Strozecki

Min-max routing problems aim to minimize the maximum tour length among multiple agents by having agents conduct tasks in a cooperative manner. These problems include impactful real-world applications but are known as NP-hard. Existing…

机器学习 · 计算机科学 2024-02-06 Jiwoo Son , Minsu Kim , Sanghyeok Choi , Hyeonah Kim , Jinkyoo Park

Collaborative Vehicle Routing is where delivery companies cooperate by sharing their delivery information and performing delivery requests on behalf of each other. This achieves economies of scale and thus reduces cost, greenhouse gas…

机器学习 · 计算机科学 2023-10-27 Stephen Mak , Liming Xu , Tim Pearce , Michael Ostroumov , Alexandra Brintrup

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…

量子物理 · 物理学 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

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…

神经与进化计算 · 计算机科学 2022-01-13 Veronika Lesch , Maximilian König , Samuel Kounev , Anthony Stein , Christian Krupitzer

Collaborative vehicle routing occurs when carriers collaborate through sharing their transportation requests and performing transportation requests on behalf of each other. This achieves economies of scale, thus reducing cost, greenhouse…

机器学习 · 计算机科学 2023-10-27 Stephen Mak , Liming Xu , Tim Pearce , Michael Ostroumov , Alexandra Brintrup