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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

This paper reviews the current progress in applying machine learning (ML) tools to solve NP-hard combinatorial optimization problems, with a focus on routing problems such as the traveling salesman problem (TSP) and the vehicle routing…

Artificial Intelligence · Computer Science 2025-10-09 Fangting Zhou , Attila Lischka , Balazs Kulcsar , Jiaming Wu , Morteza Haghir Chehreghani , Gilbert Laporte

The number of optimization techniques in the combinatorial domain is large and diversified. Nevertheless, real-world based benchmarks for testing algorithms are few. This work creates an extensible real-world mail delivery benchmark to the…

Artificial Intelligence · Computer Science 2018-01-03 Luis A. A. Meira , Paulo S. Martins , Mauro Menzori , Guilherme A. Zeni

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

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

Local search plays a central role in many effective heuristic algorithms for the vehicle routing problem (VRP) and its variants. However, neighborhood exploration is known to be computationally expensive and time consuming, especially for…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-01-30 Zhenyu Lei , Jin-Kao Hao , Qinghua Wu

Neural solvers based on the divide-and-conquer approach for Vehicle Routing Problems (VRPs) in general, and capacitated VRP (CVRP) in particular, integrates the global partition of an instance with local constructions for each subproblem to…

Machine Learning · Computer Science 2025-02-13 Yuxin Pan , Ruohong Liu , Yize Chen , Zhiguang Cao , Fangzhen Lin

Deep reinforcement learning (DRL) has been used to learn effective heuristics for solving complex combinatorial optimisation problem via policy networks and have demonstrated promising performance. Existing works have focused on solving…

Machine Learning · Computer Science 2020-12-25 Nasrin Sultana , Jeffrey Chan , A. K. Qin , Tabinda Sarwar

This paper introduces RouteFinder, a comprehensive foundation model framework to tackle different Vehicle Routing Problem (VRP) variants. Our core idea is that a foundation model for VRPs should be able to represent variants by treating…

Artificial Intelligence · Computer Science 2025-09-16 Federico Berto , Chuanbo Hua , Nayeli Gast Zepeda , André Hottung , Niels Wouda , Leon Lan , Junyoung Park , Kevin Tierney , Jinkyoo Park

Recently, there is an emerging trend to apply deep reinforcement learning to solve the vehicle routing problem (VRP), where a learnt policy governs the selection of next node for visiting. However, existing methods could not handle well the…

Machine Learning · Computer Science 2021-10-07 Jingwen Li , Liang Xin , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

Vehicle Routing Problems (VRP) are an extension of the Traveling Salesperson Problem and are a fundamental NP-hard challenge in combinatorial optimization. Solving VRP in real-time at large scale has become critical in numerous…

Machine Learning · Computer Science 2025-09-23 Ido Greenberg , Piotr Sielski , Hugo Linsenmaier , Rajesh Gandham , Shie Mannor , Alex Fender , Gal Chechik , Eli Meirom

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

We consider several Vehicle Routing Problems (VRP) with profits, which seek to select a subset of customers, each one being associated with a profit, and to design service itineraries. When the sum of profits is maximized under distance…

Data Structures and Algorithms · Computer Science 2014-07-29 Thibaut Vidal , Nelson Maculan , Puca Huachi Vaz Penna , Luis Satoru Ochi

The Vehicle Routing Problem (VRP) is a fundamental challenge in logistics management research, given its substantial influence on transportation efficiency, cost minimization, and service quality. As a combinatorial optimization problem,…

Computational Engineering, Finance, and Science · Computer Science 2025-07-01 Souad Abdoune , Menouar Boulif

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…

Routing problems are a class of combinatorial problems with many practical applications. Recently, end-to-end deep learning methods have been proposed to learn approximate solution heuristics for such problems. In contrast, classical…

Machine Learning · Computer Science 2021-12-06 Wouter Kool , Herke van Hoof , Joaquim Gromicho , Max Welling

Designing high-performing heuristics for vehicle routing problems (VRPs) is a complex task that requires both intuition and deep domain knowledge. Large language model (LLM)-based code generation has recently shown promise across many…

The Vehicle Routing Problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most…

Quantum Physics · Physics 2025-05-08 Nishikanta Mohanty , Bikash K. Behera , Christopher Ferrie

VRP (Vehicle Routing Problem) is an NP hard problem, and it has attracted a lot of research interest. In contexts where vehicles have limited carrying capacity, such as volume and weight but needed to deliver items at various locations.…

Optimization and Control · Mathematics 2020-10-22 Muhammad Wildan Abdul Hakim , Syarifah Rosita Dewi , Yurio Windiatmoko , Umar Abdul Aziz

Collaborative Vehicle Routing is where delivery companies cooperate by sharing their delivery information and performing delivery requests on behalf of each other. This achieves economies of scale and thus reduces cost, greenhouse gas…

Machine Learning · Computer Science 2023-10-27 Stephen Mak , Liming Xu , Tim Pearce , Michael Ostroumov , Alexandra Brintrup