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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-…

Distributed, Parallel, and Cluster Computing · Computer Science 2010-01-26 R. Nallusamy , K. Duraiswamy , R. Dhanalaksmi , P. Parthiban

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

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

The recent end-to-end neural solvers have shown promise for small-scale routing problems but suffered from limited real-time scaling-up performance. This paper proposes GLOP (Global and Local Optimization Policies), a unified hierarchical…

Artificial Intelligence · Computer Science 2024-07-23 Haoran Ye , Jiarui Wang , Helan Liang , Zhiguang Cao , Yong Li , Fanzhang Li

When vehicle routing decisions are intertwined with higher-level decisions, the resulting optimization problems pose significant challenges for computation. Examples are the multi-depot vehicle routing problem (MDVRP), where customers are…

Neural and Evolutionary Computing · Computer Science 2024-09-10 Abhay Sobhanan , Junyoung Park , Jinkyoo Park , Changhyun Kwon

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

Several metaheuristics use decomposition and pruning strategies to solve large-scale instances of the vehicle routing problem (VRP). Those complexity reduction techniques often rely on simple, problem-specific rules. However, the growth in…

Artificial Intelligence · Computer Science 2025-09-18 Christoph Kerscher , Stefan Minner

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

In the last years, there has been a great interest in machine-learning-based heuristics for solving NP-hard combinatorial optimization problems. The developed methods have shown potential on many optimization problems. In this paper, we…

Optimization and Control · Mathematics 2022-12-19 Mouad Morabit , Guy Desaulniers , Andrea Lodi

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…

Optimization and Control · Mathematics 2018-02-23 Vladimir Deineko , Bettina Klinz

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

The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of…

Machine Learning · Statistics 2019-02-08 Wouter Kool , Herke van Hoof , Max Welling

Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed…

Optimization and Control · Mathematics 2022-08-16 Jian Zhang , Kelin Luo , Alexandre M. Florio , Tom Van Woensel

This research proposes a hybrid Machine Learning and metaheuristic mechanism that is designed to solve Vehicle Routing Problems (VRPs). The main of our method is an edge solution selector model, which classifies solution edges to identify…

Machine Learning · Computer Science 2025-08-21 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux , Daniele Vigo

Light decoder-based solvers have gained popularity for solving vehicle routing problems (VRPs) due to their efficiency and ease of integration with reinforcement learning algorithms. However, they often struggle with generalization to…

Artificial Intelligence · Computer Science 2025-03-04 Ziwei Huang , Jianan Zhou , Zhiguang Cao , Yixin Xu

Managing disruptions in railway traffic management is a major challenge. Rising traffic density and infrastructure limits increase complexity, making the Vehicle Routing and Scheduling Problem (VRSP) difficult to solve reliably and in real…

Artificial Intelligence · Computer Science 2026-05-12 Alberto Castagna , Stefan Zahlner , Adrian Egli , Christian Eichenberger , Daniel Boos , Manuel Meyer , Anton Fuxjager

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 min-max vehicle routing problem (min-max VRP) traverses all given customers by assigning several routes and aims to minimize the length of the longest route. Recently, reinforcement learning (RL)-based sequential planning methods have…

Machine Learning · Computer Science 2024-06-07 Zhi Zheng , Shunyu Yao , Zhenkun Wang , Xialiang Tong , Mingxuan Yuan , Ke Tang

This paper studies robust variants of an extended model of the classical Heterogeneous Vehicle Routing Problem (HVRP), where a mixed fleet of vehicles with different capacities, availabilities, fixed costs and routing costs is used to serve…

Optimization and Control · Mathematics 2018-10-19 Anirudh Subramanyam , Panagiotis P. Repoussis , Chrysanthos E. Gounaris

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
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