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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 a fixed number of customers with optimal…

Quantum Physics · Physics 2022-01-14 Nishikanta Mohanty , Bikash K. Behera

We investigate the problem of coordinating multiple automated vehicles (AVs) in confined areas. This problem can be formulated as an optimal control problem (OCP) where the motion of the AVs is optimized such that collisions are avoided in…

Optimization and Control · Mathematics 2022-10-28 Stefan Kojchev , Robert Hult , Jonas Fredriksson

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

This paper deals with the Pollution-Routing Problem (PRP), a Vehicle Routing Problem (VRP) with environmental considerations, recently introduced in the literature by [Bektas and Laporte (2011), Transport. Res. B-Meth. 45 (8), 1232-1250].…

Data Structures and Algorithms · Computer Science 2014-04-22 Raphael Kramer , Anand Subramanian , Thibaut Vidal , Lucídio dos Anjos Formiga Cabral

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

We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates…

Optimization and Control · Mathematics 2017-06-13 Teobaldo Bulhões , Minh Hoàng Hà , Rafael Martinelli , Thibaut Vidal

Finding a feasible and prompt solution to the Vehicle Routing Problem (VRP) is a prerequisite for efficient freight transportation, seamless logistics, and sustainable mobility. Traditional optimization methods reach their limits when…

Machine Learning · Computer Science 2024-11-08 Elija Deineko , Carina Kehrt

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

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

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

In the Cumulative Vehicle Routing Problem (Cu-VRP), we need to find a feasible itinerary for a capacitated vehicle located at the depot to satisfy customers' demand, as in the well-known Vehicle Routing Problem (VRP), but the goal is to…

Data Structures and Algorithms · Computer Science 2025-07-14 Jingyang Zhao , Mingyu Xiao

The Vehicle Routing Problem (VRP) has been widely studied throughout its history as a way of optimizing routes by minimizing distances, and the issue of risk in VRP has been received less attention, which is essential to increase transport…

Optimization and Control · Mathematics 2022-08-23 Gabriel Adam Bilato , Cleber Damião Rocco , Anibal Tavares de Azevedo

We propose a hierarchical quantum approximate optimization framework for solving large-scale Vehicle Routing Problems (VRP) using Quantum Approximate Optimization Algorithm (QAOA). The method decomposes a VRP instance into balanced clusters…

Quantum Physics · Physics 2026-05-12 Shreetam Dash , Shreya Banerjee , Prasanta K. Panigrahi

We study the load balanced capacitated vehicle routing problem (LBCVRP): the problem is to design a collection of tours for a fixed fleet of vehicles with capacity Q to distribute a supply from a single depot between a number of predefined…

Data Structures and Algorithms · Computer Science 2020-07-28 Haniyeh Fallah , Farzad Didehvar , Farhad Rahmati

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 abundance of materials and the development of the economy have led to the flourishing of the logistics industry, but have also caused certain pollution. The research on GVRP (Green vehicle routing problem) for planning vehicle routes…

Neural and Evolutionary Computing · Computer Science 2024-10-22 YY. Feng

This paper addresses the problem of planning time-optimal trajectories for multiple cooperative agents along specified paths through a static road network. Vehicle interactions at intersections create non-trivial decisions, with complex…

Robotics · Computer Science 2018-10-08 Philip Gun , Andrew Hill , Robin Vujanic

The Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In…

Data Structures and Algorithms · Computer Science 2025-07-08 Jingyang Zhao , Mingyu Xiao

In this short paper, we study the capacity-constrained vehicle routing problem (CVRP) and its solution by randomized Monte Carlo methods. For solving CVRP we use some pseudorandom number generators commonly used in practice. We use linear,…

Optimization and Control · Mathematics 2020-05-13 İbrahim Ethem Demirci , Şaziye Ece Özdemir , Oğuz Yayla

In this paper, we are concerned with the automated exchange of orders between logistics companies in a marketplace platform to optimize total revenues. We introduce a novel multi-agent approach to this problem, focusing on the Collaborative…

Multiagent Systems · Computer Science 2023-09-01 Paul Mingzheng Tang , Ba Phong Tran , Hoong Chuin Lau