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Multi-depot vehicle routing problems (MDVRPs) are prevalent in a variety of practical applications. However, they are computationally challenging to solve due to their inherent complexity. This paper proposes an effective hybrid algorithm…

Robotics · Computer Science 2026-05-08 Zhenyu Lei , Jin-Kao Hao

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

Existing deep reinforcement learning (DRL) based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence,…

Machine Learning · Computer Science 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

For NP-hard combinatorial optimization problems, it is usually difficult to find high-quality solutions in polynomial time. The design of either an exact algorithm or an approximate algorithm for these problems often requires significantly…

Machine Learning · Computer Science 2021-05-07 Kun Lei , Peng Guo , Yi Wang , Xiao Wu , Wenchao Zhao

We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration…

Optimization and Control · Mathematics 2018-03-07 Puca Huachi Vaz Penna , Anand Subramanian , Luiz Satoru Ochi , Thibaut Vidal , Christian Prins

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 rapid growth of pharmaceutical refrigerated logistics poses sustainability challenges, including elevated costs, energy consumption, and resource inefficiency. Collaborating multiple depots can enhance logistics efficiency when…

Applications · Statistics 2023-11-09 Tingting Chen , Feng Chu , Jiantong Zhang , Jiaqing Sun

The rapid growth of online retail and e-commerce has made effective and efficient Vehicle Routing Problem (VRP) solutions essential. To meet rising demand, companies are adding more depots, which changes the VRP problem to a complex…

Databases · Computer Science 2025-08-11 Saeed Nasehi , Farhana Choudhury , Egemen Tanin , Majid Sarvi

Machine learning has been adapted to help solve NP-hard combinatorial optimization problems. One prevalent way is learning to construct solutions by deep neural networks, which has been receiving more and more attention due to the high…

Machine Learning · Computer Science 2024-05-07 Chengrui Gao , Haopu Shang , Ke Xue , Dong Li , Chao Qian

This paper introduces TuneNSearch, a hybrid transfer learning and local search approach for addressing diverse variants of the vehicle routing problem (VRP). Our method uses reinforcement learning to generate high-quality solutions, which…

Machine Learning · Computer Science 2026-02-19 Arthur Corrêa , Cristóvão Silva , Liming Xu , Alexandra Brintrup , Samuel Moniz

The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making…

Machine Learning · Computer Science 2025-03-14 Zhenwei Wang , Ruibin Bai , Tiehua Zhang

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

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

Transportation occupies one-third of the amount in the logistics costs, and accordingly transportation systems largely influence the performance of the logistics system. This work presents an adaptive data-driven innovative modular approach…

Artificial Intelligence · Computer Science 2020-01-08 Emir Zunic , Dzenana Donko , Emir Buza

Over the past decade, neural network solvers powered by generative artificial intelligence have garnered significant attention in the domain of vehicle routing problems (VRPs), owing to their exceptional computational efficiency and…

Machine Learning · Computer Science 2026-03-10 Zhenwei Wang , Tiehua Zhang , Ning Xue , Ender Ozcan , Ling Wang , Ruibin Bai

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

Generative Flow Networks (GFlowNets), a new family of probabilistic samplers, have demonstrated remarkable capabilities to generate diverse sets of high-reward candidates, in contrast to standard return maximization approaches (e.g.,…

Machine Learning · Computer Science 2025-02-25 Haoran He , Can Chang , Huazhe Xu , Ling Pan

Solving practical multi-depot vehicle routing problems (MDVRP) is a challenging optimization task central to modern logistics, increasingly driven by e-commerce. To address the MDVRP's computational complexity, neural-based combinatorial…

Machine Learning · Computer Science 2026-05-01 Arthur Corrêa , Paulo Nascimento , Samuel Moniz

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…

Travelling Salesperson Problems (TSPs) and Vehicle Routing Problems (VRPs) have achieved reasonable improvement in accuracy and computation time with the adaptation of Machine Learning (ML) methods. However, none of the previous works…

Machine Learning · Computer Science 2023-11-21 Cong Dao Tran , Thong Bach , Truong Son Hy
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