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A new variant of the classic capacitated facility location problem, which considers incompatibilities between customers, has recently been introduced in the literature. This problem captures the situation where given pairs of customers…

Artificial Intelligence · Computer Science 2026-05-28 Ida Gjergji , Lucas Kletzander , Nysret Musliu , Andrea Schaerf

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

Vehicle routing problems (VRPs) constitute a core optimization challenge in modern logistics and supply chain management. The recent neural combinatorial optimization (NCO) has demonstrated superior efficiency over some traditional…

Artificial Intelligence · Computer Science 2026-04-14 Xiangchi Meng , Jianan Zhou , Jie Gao , Yifan Lu , Yaoxin Wu , Gonglin Yuan , Yaqing Hou

This paper introduces a new set of large-scale benchmark instances for the Capacitated Vehicle Routing Problem (CVRP). The proposed XL set extends existing benchmarks by covering instances with 1,000 to 10,000 customers and a wide range of…

Optimization and Control · Mathematics 2026-01-19 Eduardo Queiroga , Rafael Martinelli , Anand Subramanian , Eduardo Uchoa , Thibaut Vidal

The paper presents an approach to solving the Robust Energy Capacitated Vehicle Routing Problem (RECVRP), focusing on electric vehicles and their limited battery capacity. A finite number of customers, each with their own demand, have to be…

Systems and Control · Electrical Eng. & Systems 2024-03-22 Mark Pustilnik , Francesco Borrelli

This paper addresses the Capacitated Vehicle Routing Problem (CVRP) by comparing classical and quantum Reinforcement Learning (RL) approaches. An Advantage Actor-Critic (A2C) agent is implemented in classical, full quantum, and hybrid…

Artificial Intelligence · Computer Science 2026-02-06 Eva Andrés

The cutting plane method is a key technique for successful branch-and-cut and branch-price-and-cut algorithms that find the exact optimal solutions for various vehicle routing problems (VRPs). Among various cuts, the rounded capacity…

Artificial Intelligence · Computer Science 2023-10-31 Hyeonah Kim , Jinkyoo Park , Changhyun Kwon

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

Existing GFlowNet-based methods for vehicle routing problems (VRPs) typically employ Trajectory Balance (TB) to achieve global optimization but often neglect important aspects of local optimization. While Detailed Balance (DB) addresses…

Artificial Intelligence · Computer Science 2025-10-07 Ni Zhang , Zhiguang Cao

One of the most well-known problems in transportation and logistics is the Capacitated Vehicle Routing Problem (CVRP). It involves optimizing a set of truck routes to service a set of customers, subject to limits on truck capacity, to…

In recent years new deep learning approaches to solve combinatorial optimization problems, in particular NP-hard Vehicle Routing Problems (VRP), have been proposed. The most impactful of these methods are sequential neural construction…

Machine Learning · Computer Science 2023-10-02 Jonas K. Falkner , Lars Schmidt-Thieme

This paper attempts to solve the famous Vehicle Routing Problem by considering multiple constraints including capacitated vehicles, single depot, and distance using two approaches namely, cluster first and route the second algorithm and…

Data Structures and Algorithms · Computer Science 2022-08-02 Apurv Choudhari , Ameya Ekbote , Prerona Chaudhuri

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…

Machine Learning · Computer Science 2021-10-29 Sirui Li , Zhongxia Yan , Cathy Wu

Large Neighborhood Search (LNS) is a universal approach that is broadly applicable and has proven to be highly efficient in practice for solving optimization problems. We propose to integrate machine learning (ML) into LNS to assist in…

Machine Learning · Computer Science 2024-03-15 Willem Feijen , Guido Schäfer , Koen Dekker , Seppo Pieterse

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

The increasing use of electric vehicles (EVs) requires efficient route planning solutions that take into account the limited range of EVs and the associated charging times, as well as the different types of charging stations. In this work,…

Systems and Control · Electrical Eng. & Systems 2025-12-29 Dominik Köster , Florian Porkert , Klaus Volbert

Heavy goods vehicles are vital backbones of the supply chain delivery system but also contribute significantly to carbon emissions with only 60% loading efficiency in the United Kingdom. Collaborative vehicle routing has been proposed as a…

Machine Learning · Computer Science 2024-06-12 Stefan Schoepf , Stephen Mak , Julian Senoner , Liming Xu , Netland Torbjörn , Alexandra Brintrup

The Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem in logistics. Augmented Lagrangian Methods (ALM) for solving CVRP performance depends heavily on well-tuned penalty parameters. In this paper, we propose a…

Physics and Society · Physics 2025-09-22 Monit Sharma , Hoong Chuin Lau

The growing aging population has significantly increased demand for efficient home health care (HHC) services. This study introduces a Vehicle Routing and Appointment Scheduling Problem (VRASP) to simultaneously optimize caregiver routes…

Optimization and Control · Mathematics 2025-05-28 Yi Zhang , Zhenzhen Zhang

Solving large-scale capacitated vehicle routing problems (CVRP) is hindered by the high complexity of heuristics and the limited generalization of neural solvers on massive graphs. We propose OD-DEAL, an adversarial learning framework that…

Machine Learning · Computer Science 2026-02-04 Dongbin Jiao , Zisheng Chen , Xianyi Wang , Jintao Shi , Shengcai Liu , Shi Yan