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Electric Vehicles (EVs) are becoming increasingly prevalent nowadays, with studies highlighting their potential as mobile energy storage systems to provide grid support. Realising this potential requires effective charging coordination,…

Systems and Control · Electrical Eng. & Systems 2025-07-22 Jun Kang Yap , Vishnu Monn Baskaran , Wen Shan Tan , Ze Yang Ding , Hao Wang , David L. Dowe

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 Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until…

Artificial Intelligence · Computer Science 2014-04-29 Thibaut Vidal , Maria Battarra , Anand Subramanian , Güneş Erdoǧan

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

The Vehicle Routing Problem (VRP) is one of the most intensively studied combinatorial optimisation problems for which numerous models and algorithms have been proposed. To tackle the complexities, uncertainties and dynamics involved in…

This paper introduces a reinforcement learning approach to optimize the Stochastic Vehicle Routing Problem with Time Windows (SVRP), focusing on reducing travel costs in goods delivery. We develop a novel SVRP formulation that accounts for…

Artificial Intelligence · Computer Science 2024-02-16 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac

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

The Capacitated Vehicle Routing Problem is a well-known NP-hard problem that poses the challenge of finding the optimal route of a vehicle delivering products to multiple locations. Recently, new efforts have emerged to create constructive…

Neural Combinatorial Optimization (NCO) has emerged as a promising learning-based paradigm for addressing Vehicle Routing Problems (VRPs) by minimizing the need for extensive manual engineering. While existing NCO methods, trained on…

Machine Learning · Computer Science 2025-11-24 Yuanyao Chen , Rongsheng Chen , Fu Luo , Zhenkun Wang

Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…

Machine Learning · Computer Science 2023-05-22 Jonas K. Falkner , Lars Schmidt-Thieme

The profiled vehicle routing problem (PVRP) is a generalization of the heterogeneous capacitated vehicle routing problem (HCVRP) in which the objective is to optimize the routes of vehicles to serve client demands subject to different…

Multiagent Systems · Computer Science 2025-02-05 Chuanbo Hua , Federico Berto , Jiwoo Son , Seunghyun Kang , Changhyun Kwon , Jinkyoo Park

The Fleet Size and Mix Vehicle Routing Problem (FSMVRP) is a prominent variant of the Vehicle Routing Problem (VRP), extensively studied in operations research and computational science. FSMVRP requires simultaneous decisions on fleet…

Artificial Intelligence · Computer Science 2026-01-01 Pengfu Wan , Jiawei Chen , Gangyan Xu

Metaheuristics are widely employed to solve hard optimization problems, like vehicle routing problems (VRP), for which exact solution methods are impractical. In particular, local search-based metaheuristics have been successfully applied…

Optimization and Control · Mathematics 2022-04-12 Vinícius R. Máximo , Mariá C. V. Nascimento

This paper presents an approach to learn the local-search heuristics that iteratively improves the solution of Vehicle Routing Problem (VRP). A local-search heuristics is composed of a destroy operator that destructs a candidate solution,…

Neural and Evolutionary Computing · Computer Science 2020-02-21 Lei Gao , Mingxiang Chen , Qichang Chen , Ganzhong Luo , Nuoyi Zhu , Zhixin Liu

In this letter, we consider the Multi-Robot Efficient Search Path Planning (MESPP) problem, where a team of robots is deployed in a graph-represented environment to capture a moving target within a given deadline. We prove this problem to…

Robotics · Computer Science 2021-01-14 Beatriz A. Asfora , Jacopo Banfi , Mark Campbell

The vehicle routing problem with two-dimensional loading constraints (2L-CVRP) and the last-in-first-out (LIFO) rule presents significant practical and algorithmic challenges. While numerous heuristic approaches have been proposed to…

Artificial Intelligence · Computer Science 2024-06-19 Yifan Xia , Xiangyi Zhang

The Capacitated Vehicle Routing Problem (CVRP), a fundamental combinatorial optimization challenge, focuses on optimizing fleet operations under vehicle capacity constraints. While extensively studied in operational research, the NP-hard…

Artificial Intelligence · Computer Science 2026-02-27 Zhuoliang Xie , Fei Liu , Zhenkun Wang , Qingfu Zhang

This study addresses a gap in the utilization of Reinforcement Learning (RL) and Machine Learning (ML) techniques in solving the Stochastic Vehicle Routing Problem (SVRP) that involves the challenging task of optimizing vehicle routes under…

Artificial Intelligence · Computer Science 2023-11-15 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac

In this paper, we present the Foundation Model for the Montreal Capacitated Vehicle Routing Problem (FM-MCVRP), a novel Deep Learning (DL) model that approximates high-quality solutions to a variant of the Capacitated Vehicle Routing…

Machine Learning · Computer Science 2024-03-04 Samuel J. K. Chin , Matthias Winkenbach , Akash Srivastava

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…

Data Structures and Algorithms · Computer Science 2010-12-09 Inge Li Gortz , Marco Molinaro , Viswanath Nagarajan , R. Ravi