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In dynamic vehicle routing problems (DVRPs), some part of the information is revealed or changed on the fly, and the decision maker has the opportunity to re-plan the vehicle routes during their execution, reflecting on the changes.…

Optimization and Control · Mathematics 2025-05-13 Markó Horváth , Tímea Tamási

Despite the extensive research efforts and the remarkable results obtained on Vehicle Routing Problems (VRP) by using algorithms proposed by the Machine Learning community that are partially or entirely based on data-driven analysis, most…

Machine Learning · Computer Science 2021-09-30 Luca Accorsi , Andrea Lodi , Daniele Vigo

In this paper, we evaluate the use of Reinforcement Learning (RL) to solve a classic combinatorial optimization problem: the Capacitated Vehicle Routing Problem (CVRP). We formalize this problem in the RL framework and compare two of the…

Artificial Intelligence · Computer Science 2022-01-17 Leo Ardon

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 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

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

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution…

Machine Learning · Computer Science 2023-06-21 Jianan Zhou , Yaoxin Wu , Wen Song , Zhiguang Cao , Jie Zhang

Route planning for a fleet of vehicles is an important task in applications such as package delivery, surveillance, or transportation, often integrated within larger Intelligent Transportation Systems (ITS). This problem is commonly…

Artificial Intelligence · Computer Science 2025-05-21 Daniel Fuertes , Carlos R. del-Blanco , Fernando Jaureguizar , Narciso García

Vehicle Routing Problems (VRPs) in real-world applications often come with various constraints, therefore bring additional computational challenges to exact solution methods or heuristic search approaches. The recent idea to learn heuristic…

Artificial Intelligence · Computer Science 2022-08-01 Qiaoyue Tang , Yangzhe Kong , Lemeng Pan , Choonmeng Lee

The Vehicle Routing Problem (VRP) is the combinatorial optimization problem of designing routes for vehicles to visit customers in such a fashion that a cost function, typically the number of vehicles, or the total travelled distance is…

Artificial Intelligence · Computer Science 2021-07-01 Sabino Francesco Roselli , Martin Fabian , Knut Åkesson

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

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem…

Discrete Mathematics · Computer Science 2020-04-07 Thibaut Vidal , Gilbert Laporte , Piotr Matl

Most neural methods for Vehicle Routing Problems (VRPs) are limited to Euclidean settings or simple graphs. In this work, we instead consider multigraphs, where parallel edges represent distinct travel options with varying trade-offs (e.g.,…

Machine Learning · Computer Science 2026-05-08 Filip Rydin , Morteza Haghir Chehreghani , Balázs Kulcsár

We consider vehicle-routing problems (VRPs) that incorporate the notion of {\em regret} of a client, which is a measure of the waiting time of a client relative to its shortest-path distance from the depot. Formally, we consider both the…

Data Structures and Algorithms · Computer Science 2013-11-26 Zachary Friggstad , Chaitanya Swamy

Recently, the applications of the methodologies of Reinforcement Learning (RL) to NP-Hard Combinatorial optimization problems have become a popular topic. This is essentially due to the nature of the traditional combinatorial algorithms,…

Optimization and Control · Mathematics 2022-08-02 Simone Foa , Corrado Coppola , Giorgio Grani , Laura Palagi

Recent advancements in deep learning have significantly enhanced the performance and efficiency of traffic classification in networking systems. However, the lack of transparency in their predictions and decision-making has made network…

Networking and Internet Architecture · Computer Science 2025-09-23 Riya Ponraj , Ram Durairajan , Yu Wang

Despite enjoying desirable efficiency and reduced reliance on domain expertise, existing neural methods for vehicle routing problems (VRPs) suffer from severe robustness issues -- their performance significantly deteriorates on clean…

Artificial Intelligence · Computer Science 2024-10-08 Jianan Zhou , Yaoxin Wu , Zhiguang Cao , Wen Song , Jie Zhang , Zhiqi Shen

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

Vehicle Routing Problems (VRPs) can model many real-world scenarios and often involve complex constraints. While recent neural methods excel in constructing solutions based on feasibility masking, they struggle with handling complex…

Artificial Intelligence · Computer Science 2024-10-29 Jieyi Bi , Yining Ma , Jianan Zhou , Wen Song , Zhiguang Cao , Yaoxin Wu , Jie Zhang

Vehicle routing problems (VRPs) are central to combinatorial optimization with significant practical implications. Recent advancements in neural combinatorial optimization (NCO) have demonstrated promising results by leveraging neural…

Machine Learning · Computer Science 2025-07-08 Han Li , Fei Liu , Zhenkun Wang , Qingfu Zhang