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This work considers the problem of optimize the routes of the vehicles used by a real agricultural cooperative that distributes animal feed among the partners. Because solving the exact model is computationally burdensome, we propose to…

Optimization and Control · Mathematics 2016-07-11 Roque M. Guitián de Frutos , Balbina V. Casas-Méndez

For robot swarms operating on complex missions in an uncertain environment, it is important that the decision-making algorithm considers both heterogeneity and uncertainty. This paper presents a stochastic programming framework for the…

Robotics · Computer Science 2020-10-23 Bo Fu , William Smith , Denise Rizzo , Matthew Castanier , Kira Barton

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

Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…

Optimization and Control · Mathematics 2016-05-30 Genevay Aude , Marco Cuturi , Gabriel Peyré , Francis Bach

Neural routing solvers (NRSs) that leverage deep learning to tackle vehicle routing problems have demonstrated notable potential for practical applications. By learning implicit heuristic rules from data, NRSs replace the handcrafted…

Optimization and Control · Mathematics 2026-03-17 Yunpeng Ba , Xi Lin , Changliang Zhou , Ruihao Zheng , Zhenkun Wang , Xinyan Liang , Zhichao Lu , Jianyong Sun , Yuhua Qian , Qingfu Zhang

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…

Artificial Intelligence · Computer Science 2018-05-23 Mohammadreza Nazari , Afshin Oroojlooy , Lawrence V. Snyder , Martin Takáč

Recent studies in using deep learning to solve routing problems focus on construction heuristics, the solutions of which are still far from optimality. Improvement heuristics have great potential to narrow this gap by iteratively refining a…

Artificial Intelligence · Computer Science 2020-05-12 Yaoxin Wu , Wen Song , Zhiguang Cao , Jie Zhang , Andrew Lim

The availability of massive vehicle trajectory data enables the modeling of road-network constrained movement as travel-cost distributions rather than just single-valued costs, thereby capturing the inherent uncertainty of movement and…

Data Structures and Algorithms · Computer Science 2024-07-10 Chenjuan Guo , Ronghui Xu , Bin Yang , Ye Yuan , Tung Kieu , Yan Zhao , Christian S. Jensen

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…

Machine Learning · Computer Science 2022-05-06 Aigerim Bogyrbayeva , Meraryslan Meraliyev , Taukekhan Mustakhov , Bissenbay Dauletbayev

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

Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…

Numerical Analysis · Mathematics 2024-12-19 Matthias J. Ehrhardt , Zeljko Kereta , Jingwei Liang , Junqi Tang

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…

Artificial Intelligence · Computer Science 2021-05-25 Konstantin Sidorov , Alexander Morozov

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

Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to…

Data Structures and Algorithms · Computer Science 2012-07-10 Daniel Karapetyan

The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with…

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

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 address two optimisation problems arising in the context of city logistics and two-level transportation systems. The two-echelon vehicle routing problem and the two-echelon location routing problem seek to produce vehicle…

Data Structures and Algorithms · Computer Science 2016-10-05 Ulrich Breunig , Verena Schmid , Richard F. Hartl , Thibaut Vidal

Routing problems are often faced by companies who serve costumers through vehicles. Such problems have a challenging structure to optimize, despite the recent advances in combinatorial optimization. The goal of this project is to study and…

Neural and Evolutionary Computing · Computer Science 2018-09-03 Felipe F. Müller , Luis A. A. Meira

This paper deals with the Stochastic Capacitated Arc Routing Problem (SCARP), obtained by randomizing quantities on the arcs in the CARP. Optimization problems for the SCARP are characterized by decisions that are made without knowing their…

Neural and Evolutionary Computing · Computer Science 2022-11-24 Fleury Gérard , Lacomme Philippe , Christian Prins

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