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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…

We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given…

人工智能 · 计算机科学 2018-05-23 Mohammadreza Nazari , Afshin Oroojlooy , Lawrence V. Snyder , Martin Takáč

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…

机器学习 · 计算机科学 2022-02-22 Bingjie Li , Guohua Wu , Yongming He , Mingfeng Fan , Witold Pedrycz

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,…

计算工程、金融与科学 · 计算机科学 2025-07-01 Souad Abdoune , Menouar Boulif

The Vehicle Routing Problem (VRP) is a complex optimization problem with numerous real-world applications, mostly solved using metaheuristic algorithms due to its $\mathcal{NP}$-Hard nature. Traditionally, these metaheuristics rely on…

人工智能 · 计算机科学 2025-08-11 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

Due to the practical importance of vehicle routing problems (VRP), there exists an ever-growing body of research in algorithms and (meta)heuristics for solving such problems. However, the diversity of VRP domains creates the separate…

人工智能 · 计算机科学 2021-05-25 Konstantin Sidorov , Alexander Morozov

Recent neural heuristics for the Vehicle Routing Problem (VRP) primarily rely on node coordinates as input, which may be less effective in practical scenarios where real cost metrics-such as edge-based distances-are more relevant. To…

机器学习 · 计算机科学 2025-06-23 Dian Meng , Zhiguang Cao , Yaoxin Wu , Yaqing Hou , Hongwei Ge , Qiang 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…

机器学习 · 计算机科学 2021-05-07 Kun Lei , Peng Guo , Yi Wang , Xiao Wu , Wenchao Zhao

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…

Deep learning has been extensively explored to solve vehicle routing problems (VRPs), which yields a range of data-driven neural solvers with promising outcomes. However, most neural solvers are trained to tackle VRP instances in a…

机器学习 · 计算机科学 2025-08-19 Shaodi Feng , Zhuoyi Lin , Jianan Zhou , Cong Zhang , Jingwen Li , Kuan-Wen Chen , Senthilnath Jayavelu , Yew-Soon Ong

This research proposes a hybrid Machine Learning and metaheuristic mechanism that is designed to solve Vehicle Routing Problems (VRPs). The main of our method is an edge solution selector model, which classifies solution edges to identify…

机器学习 · 计算机科学 2025-08-21 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux , Daniele Vigo

This paper provides a systematic overview of machine learning methods applied to solve NP-hard Vehicle Routing Problems (VRPs). Recently, there has been a great interest from both machine learning and operations research communities to…

机器学习 · 计算机科学 2022-05-06 Aigerim Bogyrbayeva , Meraryslan Meraliyev , Taukekhan Mustakhov , Bissenbay Dauletbayev

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…

机器学习 · 计算机科学 2021-10-29 Sirui Li , Zhongxia Yan , Cathy Wu

The Capacitated Vehicle Routing Problem (CVRP) is a fundamental NP-hard problem with broad applications in logistics and transportation. Real-world CVRPs often involve diverse objectives and complex constraints, such as time windows or…

人工智能 · 计算机科学 2026-05-15 Wen Wang , Xiangchen Wu , Liang Wang , Hao Hu , Xianping Tao

Complex vehicle routing problems (VRPs) remain a fundamental challenge, demanding substantial expert effort for intent interpretation and algorithm design. While large language models (LLMs) offer a promising path toward automation, current…

人工智能 · 计算机科学 2026-02-17 Ni Zhang , Zhiguang Cao , Jianan Zhou , Cong Zhang , Yew-Soon Ong

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…

Existing neural heuristics often train a deep architecture from scratch for each specific vehicle routing problem (VRP), ignoring the transferable knowledge across different VRP variants. This paper proposes the cross-problem learning to…

人工智能 · 计算机科学 2024-06-19 Zhuoyi Lin , Yaoxin Wu , Bangjian Zhou , Zhiguang Cao , Wen Song , Yingqian Zhang , Senthilnath Jayavelu

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…

机器学习 · 计算机科学 2025-09-23 Ido Greenberg , Piotr Sielski , Hugo Linsenmaier , Rajesh Gandham , Shie Mannor , Alex Fender , Gal Chechik , Eli Meirom

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…

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…

人工智能 · 计算机科学 2023-11-15 Zangir Iklassov , Ikboljon Sobirov , Ruben Solozabal , Martin Takac
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