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This paper addresses the Capacitated Vehicle Routing Problem (CVRP) by comparing classical and quantum Reinforcement Learning (RL) approaches. An Advantage Actor-Critic (A2C) agent is implemented in classical, full quantum, and hybrid…

Artificial Intelligence · Computer Science 2026-02-06 Eva Andrés

The Multiple Travelling Salesman Problem (MTSP) is among the most interesting combinatorial optimization problems because it is widely adopted in real-life applications, including robotics, transportation, networking, etc. Although the…

Computational Complexity · Computer Science 2021-02-26 Omar Cheikhrouhou , Ines Khoufi

In recent years, reinforcement learning (RL) methods have emerged as a promising approach for solving combinatorial problems. Among RL-based models, POMO has demonstrated strong performance on a variety of tasks, including variants of the…

Artificial Intelligence · Computer Science 2025-08-13 Szymon Jakubicz , Karol Kuźniak , Jan Wawszczak , Paweł Gora

This paper presents a new branch-and-cut algorithm based on infeasible path elimination for the three-dimensional loading capacitated vehicle routing problem (3L-CVRP) with different loading problem variants. We show that a previously…

Optimization and Control · Mathematics 2024-02-26 Felix Tamke , Florian Linß , Leopold Kuttner , Udo Buscher

The traditional Capacitated Vehicle Routing Problem (CVRP) minimizes the total distance of the routes under the capacity constraints of the vehicles. But more often, the objective involves multiple criteria including not only the total…

Machine Learning · Computer Science 2021-08-31 Jayanta Mandi , Rocsildes Canoy , Víctor Bucarey , Tias Guns

This thesis introduces stochastic generalized routing problem model and proposes exact and heuristic algorithms to solve it efficiently, in a wide range of problem sizes. At first, the classic routing problem with its common variations in…

Optimization and Control · Mathematics 2019-03-08 Faraz Dadgostari

Existing deep reinforcement learning (DRL) based methods for solving the capacitated vehicle routing problem (CVRP) intrinsically cope with homogeneous vehicle fleet, in which the fleet is assumed as repetitions of a single vehicle. Hence,…

Machine Learning · Computer Science 2022-03-08 Jingwen Li , Yining Ma , Ruize Gao , Zhiguang Cao , Andrew Lim , Wen Song , Jie Zhang

Vehicle Routing Problems (VRP) are widely studied issues that play important roles in many production scenarios. We have noticed that in some practical scenarios of VRP, the size of cities and their entrances can significantly influence the…

Robotics · Computer Science 2025-02-27 Haotian Xu , Xiaohui Fan , Jialin Zhu , Qing Zhuo , Tao Zhang

Electric vehicles (EVs) have been highly favoured as a future transportation mode in the transportation section in recent years. EVs have many advantages compared to traditional transportation, especially the environmental aspect. However,…

Optimization and Control · Mathematics 2022-04-26 Jaehee Jeong , Bissan Ghaddar , Nicolas Zufferey , Jatin Nathwani

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

The Profiled Vehicle Routing Problem (PVRP) extends the classical VRP by incorporating vehicle-client-specific preferences and constraints, reflecting real-world requirements such as zone restrictions and service-level preferences. While…

Machine Learning · Computer Science 2025-08-26 Chuanbo Hua , Federico Berto , Zhikai Zhao , Jiwoo Son , Changhyun Kwon , Jinkyoo Park

The Conflict-Free Electric Vehicle Routing Problem (CF-EVRP) is an extension of the Vehicle Routing Problem (VRP), a combinatorial optimization problem of designing routes for vehicles to visit customers such that a cost function, typically…

Systems and Control · Electrical Eng. & Systems 2022-03-15 Sabino Francesco Roselli , Per-Lage Götvall , Martin Fabian , Knut Åkesson

Public transport is vital for meeting people's mobility needs. Providers need to plan their services well to offer high quality and low cost. Optimized planning can benefit providers, customers, and municipalities. The planning process for…

Optimization and Control · Mathematics 2023-10-23 Lucas Mertens , Lena-Antonia Wolbeck , David Rößler , Lin Xie , Natalia Kliewer

Unmanned aerial vehicles, or drones, have the potential to significantly reduce the cost and time of making last-mile deliveries and responding to emergencies. Despite this potential, little work has gone into developing vehicle routing…

Optimization and Control · Mathematics 2016-08-09 Kevin Dorling , Jordan Heinrichs , Geoffrey G. Messier , Sebastian Magierowski

In this paper we consider a 2-vehicle routing problem which can be viewed as a building block for the varieties of the vehicle routing problems (VRPs). To approach this problem, we suggest a framework based on the Held and Karp dynamic…

Data Structures and Algorithms · Computer Science 2016-10-07 Vladimir Deineko

Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed…

Optimization and Control · Mathematics 2022-08-16 Jian Zhang , Kelin Luo , Alexandre M. Florio , Tom Van Woensel

Dynamic Vehicle Routing Problem (DVRP), is an extension of the classic Vehicle Routing Problem (VRP), which is a fundamental problem in logistics and transportation. Typically, DVRPs involve two stakeholders: service providers that deliver…

Artificial Intelligence · Computer Science 2024-05-30 Yufan Kang , Rongsheng Zhang , Wei Shao , Flora D. Salim , Jeffrey Chan

One of the most well-known problems in transportation and logistics is the Capacitated Vehicle Routing Problem (CVRP). It involves optimizing a set of truck routes to service a set of customers, subject to limits on truck capacity, to…

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…

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed…

Data Structures and Algorithms · Computer Science 2012-03-02 Inge Li Goertz , Viswanath Nagarajan , Rishi Saket