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Learning to solve combinatorial optimization problems, such as the vehicle routing problem, offers great computational advantages over classical operations research solvers and heuristics. The recently developed deep reinforcement learning…

Machine Learning · Computer Science 2022-01-06 Daniela Thyssens , Jonas Falkner , Lars Schmidt-Thieme

We study a stochastic variant of the vehicle routing problem arising in the context of domestic donor collection services. The problem we consider combines the following attributes. Customers requesting services are variable, in the sense…

Optimization and Control · Mathematics 2022-07-15 Mohsen Dastpak , Fausto Errico , Ola Jabali

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

Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in…

Artificial Intelligence · Computer Science 2020-12-01 André Hottung , Kevin Tierney

The Capacitated Vehicle Routing Problem (CVRP) is a core NP-hard problem in the field of combinatorial optimization. It aims to plan optimal routes for a fleet of vehicles with uniform capacity, serving a set of customers with specific…

Data Structures and Algorithms · Computer Science 2026-04-07 Yongyu Chen

We investigate a structural decomposition for the capacitated vehicle routing problem (CVRP) based on vehicle-to-customer "assignment" and visits "sequencing" decision variables. We show that an heuristic search focused on assignment…

Optimization and Control · Mathematics 2018-03-19 Túlio A. M. Toffolo , Thibaut Vidal , Tony Wauters

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

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

This paper introduces a new set of large-scale benchmark instances for the Capacitated Vehicle Routing Problem (CVRP). The proposed XL set extends existing benchmarks by covering instances with 1,000 to 10,000 customers and a wide range of…

Optimization and Control · Mathematics 2026-01-19 Eduardo Queiroga , Rafael Martinelli , Anand Subramanian , Eduardo Uchoa , Thibaut Vidal

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

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

The Vehicle Routing Problem with Route Balancing (VRPRB) is a biobjective version of the original Vehicle Routing Problem (VRP) in which, besides minimizing the total distance traveled by the vehicles involved, the balance among route loads…

Optimization and Control · Mathematics 2017-02-21 Jairo Lozano , Luis C. González-Gurrola , Eduardo Rodríguez-Tello , Philippe Lacomme

This paper presents a model for a vehicle routing problem in which customer demands are stochastic and vehicles are divided into compartments. The problem is motivated by the needs of certain agricultural cooperatives that produce various…

Optimization and Control · Mathematics 2024-10-24 Juan Carlos Gonçalves-Dosantos , Laura Davila-Pena , Balbina Casas-Méndez

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

Designing high-performing metaheuristics for NP-hard combinatorial optimization problems, such as the Vehicle Routing Problem (VRP), remains a significant challenge, often requiring extensive domain expertise and manual tuning. Recent…

Neural and Evolutionary Computing · Computer Science 2026-04-10 Manuj Malik , Jianan Zhou , Shashank Reddy Chirra , Zhiguang Cao

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

Real-world Vehicle Routing Problems (VRPs) are characterized by a variety of practical constraints, making manual solver design both knowledge-intensive and time-consuming. Although there is increasing interest in automating the design of…

Artificial Intelligence · Computer Science 2025-05-20 Kai Li , Fei Liu , Zhenkun Wang , Xialiang Tong , Xiongwei Han , Mingxuan Yuan , Qingfu 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

The worldwide growth of e-commerce has created new challenges for logistics companies, one of which is being able to deliver products quickly and at low cost, which reflects directly in the way of sorting packages, needing to eliminate…

Surveillance applications require a collection of heterogeneous vehicles to visit a set of targets. In this article, we consider a fundamental routing problem that arises in these applications involving two vehicles. Specifically, we…

Discrete Mathematics · Computer Science 2015-03-19 Jungyun Bae , Sivakumar Rathinam