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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

The Dynamic Pickup and Delivery Problem (DPDP) is aimed at dynamically scheduling vehicles among multiple sites in order to minimize the cost when delivery orders are not known a priori. Although DPDP plays an important role in modern…

Artificial Intelligence · Computer Science 2021-05-28 Xijun Li , Weilin Luo , Mingxuan Yuan , Jun Wang , Jiawen Lu , Jie Wang , Jinhu Lu , Jia Zeng

The use of drones in logistics is gaining more and more interest, and drones are becoming a more viable and common way of distributing parcels in an urban environment. As a consequence, there is a flourishing production of articles in the…

Discrete Mathematics · Computer Science 2021-07-29 Mauro Dell'Amico , Roberto Montemanni , Stefano Novellani

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…

Artificial Intelligence · Computer Science 2025-08-11 Bachtiar Herdianto , Romain Billot , Flavien Lucas , Marc Sevaux

Many transit agencies operating paratransit and microtransit services have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid…

Recent studies and industry advancements indicate that modular vehicles (MVs) have the potential to enhance transportation systems through their ability to dock and split during a trip. Although various applications of MVs have been…

Optimization and Control · Mathematics 2025-03-17 Hang Zhou , Yang Li , Chengyuan Ma , Keke Long , Xiaopeng Li

Unmanned Aerial Vehicles (UAVs) or drones are increasingly used for urban applications like traffic monitoring and construction surveys. Autonomous navigation allows drones to visit waypoints and accomplish activities as part of their…

Robotics · Computer Science 2021-02-18 Aakash Khochare , Yogesh Simmhan , Francesco Betti Sorbelli , Sajal K. Das

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…

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…

Aerial drones offer a distinct potential to reduce the delivery time and energy consumption for the delivery of time-sensitive and small products. However, there is still a need in the relevant industry to understand the performance of…

Optimization and Control · Mathematics 2022-09-12 Tanveer Hossain Bhuiyan , Mohammad Roni , Victor Walker

The Vehicle Routing Problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most…

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

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

This paper presents a new approach for formulating the delivery problem by drones with general energy consumption models where the drones visit a set of places to deliver parcels to customers. Drones can perform multiple trips that start…

Optimization and Control · Mathematics 2022-11-03 Amir Ahmadi-Javid , Mahla Meskar

The paper explores the Biased Random-Key Genetic Algorithm (BRKGA) in the domain of logistics and vehicle routing. Specifically, the application of the algorithm is contextualized within the framework of the Vehicle Routing Problem with…

Neural and Evolutionary Computing · Computer Science 2024-05-02 Paola Festa , Francesca Guerriero , Mauricio G. C. Resende , Edoardo Scalzo

In this study, we develop an innovative data-driven optimization approach to solve the drone delivery service planning problem with online demand. Drone-based logistics are expected to improve operations by enhancing flexibility and…

Optimization and Control · Mathematics 2024-04-04 Aditya Paul , Michael W. Levin , S. Travis Waller , David Rey

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

Drones have recently emerged as a faster, safer, and cost-efficient way for last-mile deliveries of parcels, particularly for urgent medical deliveries highlighted during the pandemic. This paper addresses a new challenge of multi-parcel…

Robotics · Computer Science 2025-09-22 Chuhao Qin , Arun Narayanan , Evangelos Pournaras

Unmanned Aerial Vehicles (UAVs), commonly known as drones, have experienced expanding use in urban environments in recent years. However, the growing density of drones raises significant challenges, such as avoiding collisions and managing…

Networking and Internet Architecture · Computer Science 2025-09-30 Zhouyu Qu , Andreas Willig , Xiaobing Wu

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

Traditional vehicle routing algorithms do not consider the changing nature of traffic. While implementations of Dijkstra's algorithm with varying weights exist, the weights are often changed after the outcome of algorithm is executed, which…

Optimization and Control · Mathematics 2022-05-31 Piyush Udhan , Akhilesh Ganeshkar , Poobigan Murugesan , Abhishek Raj Permani , Sameep Sanjeeva , Parth Deshpande