Drone Routing Research Articles

Delivery optimization for collaborative truck–drone routing problem considering vehicle obstacle avoidance

Drone participating in logistics delivery has gained much concern due to its potential superiority of operational efficiency and service costs. How to optimize the hybrid vehicle delivery trip is still a crucial issue. Besides, complex urban environment and regulatory no-through zones bring more rigorous challenges. The aim is to develop an efficient routing solution that considers obstacles encountered by the truck and drone, ensuring the timely delivery. This paper proposes an efficient deep reinforcement learning to optimize the collaborative truck–drone routing problem (C-TDRP) under vehicle obstacle avoidance trail. Specifically, the trucks deploy a fleet of drones to serve the random distributed consumers subject to minimum delivery cost. Homogeneous drones serve multiple demand nodes per trip with limited energy carrying capacity. We design the C-TDRP formulation with studying the feasibility of obstacle avoidance routing. Owing to the computational complexity of the proposed mathematical model, an intelligent optimization algorithm based on deep reinforcement learning is developed, named pointer network (Ptr-Net), which can capture the position weights associated with network sequence automatically. Through rigorous experimental validations, the results demonstrate that the vehicle energy consumption of final trajectory reduces by more than 42%, even for large-scale delivery scenarios. Our proposed method not only enhances the optimization performance but also lays the foundation for more intelligent and adaptable logistics delivery in complex urban environments.

Energy-Saving Multi-Agent Deep Reinforcement Learning Algorithm for Drone Routing Problem.

With the rapid advancement of drone technology, the efficient distribution of drones has garnered significant attention. Central to this discourse is the energy consumption of drones, a critical metric for assessing energy-efficient distribution strategies. Accordingly, this study delves into the energy consumption factors affecting drone distribution. A primary challenge in drone distribution lies in devising optimal, energy-efficient routes for drones. However, traditional routing algorithms, predominantly heuristic-based, exhibit certain limitations. These algorithms often rely on heuristic rules and expert knowledge, which can constrain their ability to escape local optima. Motivated by these shortcomings, we propose a novel multi-agent deep reinforcement learning algorithm that integrates a drone energy consumption model, namely EMADRL. The EMADRL algorithm first formulates the drone routing problem within a multi-agent reinforcement learning framework. It subsequently designs a strategy network model comprising multiple agent networks, tailored to address the node adjacency and masking complexities typical of multi-depot vehicle routing problem. Training utilizes strategy gradient algorithms and attention mechanisms. Furthermore, local and sampling search strategies are introduced to enhance solution quality. Extensive experimentation demonstrates that EMADRL consistently achieves high-quality solutions swiftly. A comparative analysis against contemporary algorithms reveals EMADRL's superior energy efficiency, with average energy savings of 5.96% and maximum savings reaching 12.45%. Thus, this approach offers a promising new avenue for optimizing energy consumption in last-mile distribution scenarios.

Dynamic collaborative truck-drone delivery with en-route synchronization and random requests

Coordinated truck and drone delivery is gaining popularity in logistics as it can greatly reduce operation costs. However, existing studies on related operations management problems typically ignore the following important features: (i) the random appearance of requests, which require operators to dynamically respond to the requests; and (ii) the decisions of optimal launch and retrieval locations for trucks and drones instead of fixed to customer locations, which can significantly impact the overall time costs. To tackle these challenges, this study investigates the dynamic collaborative truck-drone routing problem with randomly arriving requests and synchronization on routes. We model the problem as a Markov Decision Process (MDP) and solve the MDP via a reinforcement learning (RL) approach. The proposed RL approach determines: (i) whether each request should be serviced upon arrival, (ii) which truck or drone should be assigned for the request, and (iii) the optimal en-route take-off and landing positions for paired trucks and drones. We further employ a framework of decentralized learning and centralized dispatching in RL to increase performance. Numerical experiments are conducted to assess the proposed solution approach on instances generated based on both the Solomon dataset and real-world operational data of a logistics operator in Singapore over several benchmark algorithms under various battery endurance levels of drones and distinct transportation scenarios including node-based dynamic collaborative truck-drone routing problem, dynamic non-collaborative truck and drone routing problem, and dynamic vehicle routing problem. The results show that our RL solution outperforms the benchmark algorithm in total profit by an average of 28.03 %, and our en-route takeoff and landing scenario outperforms the benchmark scenarios in total profit by an average of 8.43 % in multi-day instances. Additionally, compared to the traditional node-based landing scenario, employing our en-route takeoff and landing strategy can save 0.9 h/(drone*day) of waiting time on average.

About the Problem of Drone Routing

Introduction. Unmanned aerial vehicles (UAVs) are attracting considerable interest in a variety of areas, such as logistics, defence, search and rescue, agriculture, manufacturing and environmental monitoring. The effective use of these flexible resources requires the development of models and methods that ensure the creation of safe and efficient flight routes for UAVs. The purpose of the paper is to study the current state of UAV routing problems, including an analysis of existing research in this field and systematization of scientific approaches and algorithms as well as the formalization of some practically important problems. Results. A classification of UAV routing problems has been proposed based on various criteria, including the number of UAVs, the number of base locations, UAV recharging constraints, additional conditions, evaluation criteria, and the constancy of conditions. An analysis and classification of UAV routing problems are presented, highlighting the significance of these problems in various fields such as logistics, defense, agriculture, and others. Meaningful formulations of several interrelated practical UAV routing problems have been proposed, and their formalization has been carried out in the form of specific mathematical models. Conclusions. The development of unmanned aerial vehicles (UAVs) is a dynamic and relevant area with a wide range of applications. The paper systemises scientific approaches and algorithms for optimising UAV routes, analyses and classifies routing problems according to various criteria. The proposed classification allows for a better understanding of the structure of the problems and the selection of appropriate methods for solving them. The main result is the formalisation of a number of practical UAV routing problems in the form of mathematical models, which allows developing effective algorithms for solving these problems, increasing the efficiency of UAVs in various fields, such as logistics, defence and agriculture. Keywords: route optimization, unmanned aerial vehicle, drone, mathematical model, flight resource, combinatorial optimization, monitoring, logistics.

End-to-end drone route planning in flexible airspace design

Drone traffic, consisting of anything from small quadcopters for video and photography to large eVTOL transporting people, is expected to grow rapidly as soon as the challenges currently barring urban flights can be solved. One of the main challenges is how to automate authorization while both keeping full control over where and how drones fly over specific areas, and at the same time allowing the operators the freedom they require to successfully provide their services. While restrictions are necessary, being overly restrictive on plans has a negative impact on capacity, safety and efficiency. In this article we propose the combination of no-fly zones and flight grids into design elements for airspace design, to be used only where and when necessary. City planners can use these design elements to make both strategic decisions and real-time updates, and thereby set the rules for an automated system for planning and authorization. We describe the design elements, how to automatically find the optimal end-to-end route between or through these elements, a set of modifications or extension to improve flexibility even more, and demonstrate the efficacy of the approach through example airspace design patterns and by showing the resulting traffic in a drone traffic simulator.

Matheuristic approaches for multi-visit drone routing problem to prevent forest fires

Forest fires draw more attention as the impact of elements that threaten nature increases, such as the thinning of the ozone layer, and global warming. The prevention of forest fires is extremely important for the protection of natural life, and the provision of a healthy world to future generations. Some of the methods used for the prevention of forest fires are observation towers, unmanned aerial vehicles, images taken from satellites, and detectors. Noticing the fire as soon as it starts and intervening in the fire prevents the fire from spreading and causing major and negative consequences. The degree of fire sensitivity of forest areas may vary depending on factors such as the climate of the region, topographic structure, humidity ratio, vegetation, tree species, and density. Observing regions with high fire sensitivity more frequently than regions with low fire sensitivity will prevent the spread of fires faster by detecting them. Different from the literature, in this study, the degree of sensitivity of fire-sensitive areas are taken into account. Visit frequency is determined according to the degree of fire sensitivity. Due to the complexity of the constraints, the mathematical model can not reach the optimal solution in a short time. To solve larger problem decomposition based matheuristic approaches are proposed. Matheuristic algorithms are compared using different parameters for samples of different sizes.

An Energy-Efficient Logistic Drone Routing Method Considering Dynamic Drone Speed and Payload

Unmanned aerial vehicles (UAVs), or drones, are recognized for their potential to improve efficiency in last-mile delivery. Unlike the vehicle routing problem, drone route design is challenging due to several operational signatures, such as speed optimization, multi-trip operation, and energy consumption estimation. Drone energy consumption is a nonlinear function of both speed and payload. Moreover, the high speed of drones can significantly curtail the drone range, thereby limiting the efficiency of drone delivery systems. This paper addresses the trade-off between speed and flight range in a multi-trip drone routing problem with variable flight speeds (DRP–VFS). We propose a new model to specifically consider energy constraints using a nonlinear energy consumption model and treat drone speeds as decision variables. The DRP–VFS is initially formulated using mixed-integer linear programming (MILP) to minimize energy consumption. To solve large-scale instances, we propose a three-phase adaptive large neighborhood search (ALNS) algorithm and compare its performance with a commercial MIP solver. The experimental results demonstrate that the proposed method is capable of effectively identifying suboptimal solutions in practical scenarios. Furthermore, results indicate that operating drones at variable speeds leads to about 21% energy savings compared to fixed speeds, with advantages in cost savings and range extension.

Integrated truck drone delivery services with an optimal charging stations

Battery-powered drones, or unmanned aerial vehicles (UAVs), present significant market potential for faster, economical, and eco-friendly urban delivery solutions. Many firms are investing in drone logistics ventures to capitalize on their capabilities. However, the limited range of drone deliveries, dictated by battery capacity, poses a significant challenge. Hybrid delivery systems combining trucks and drones have gained attention to overcome this challenge. Traditional models assume trucks park at customer sites while drones handle additional deliveries, yet this approach may hinder drone efficiency due to constraints in parking availability. Alternative approaches like battery swapping and mobile charging stations on trucks have been explored but exhibit limitations such as blind spots and substantial battery reserves. We propose establishing dedicated drone charging stations and optimizing drone routing for efficient deliveries to address these issues We present a MINLP (Mixed Integer Non-Linear Programming) model aimed at identifying the most cost-effective solution that optimizes both transportation efficiency and charging infrastructure investment. Quantitative experiments demonstrate the efficacy of this approach, alongside sensitivity analysis aiding economic decision-making across various operational scenarios. Notably, our experiments show a 15% reduction in total costs when extending the operational lifespan of charging stations from 2 to 4 years.

Aerial drone fleet deployment optimization with endogenous battery replacements for direct delivery of time-sensitive products

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 drone-based delivery under different business needs and drone operating conditions. We studied a drone deployment optimization problem for direct delivery of time-sensitive products with release dates to customers maintaining a specified time window. This paper presents a new mixed-integer programming model, new valid inequalities, a new greedy heuristic algorithm, and a Genetic algorithm to help business owners optimally schedule and route their drone fleet minimizing the required fleet size, the required number of additional batteries, and total energy consumption. A realistic feature of the optimization method is that instead of replacing the drone battery after each return to the depot, it keeps track of the remaining energy in the drone battery and decides on battery replacements accounting for the drone routing and the user-specified minimum required battery energy. Numerical results based on real data from drone flight tests and prepared food delivery industry provide insights into the effect of different practical drone operating parameters on the required fleet size, the required number of battery replacements, and energy consumption. Results demonstrate that the proposed heuristic algorithm substantially outperforms the accelerated CPLEX in runtime while sacrificing the solution quality by a small amount. Additionally, results show that using a mixed fleet of hexacopter and quadcopter drones reduces the total energy consumption by 48.52% compared to using a homogeneous fleet of only hexacopters.

Minimizing the total travel distance for the locker-based drone delivery: A branch-and-cut-based method

This article investigates the problem of minimizing the total travel distance in locker-based drone delivery, where the roofs of lockers are reused as parking platforms for drones. It is a drone routing and parking hybrid problem with modeling challenges. We find the sufficient and necessary conditions for feasible solutions and transform the original problem into a scale-tractable one. Subsequently, we propose a compact lower-bound formulation for the transformed problem and prove the total unimodality of the coefficient matrix. Furthermore, we develop a two-stage method in which a branch and cut algorithm solves the transformed problem and a heuristic constructs practical schedules for the original problem. Simulated tests demonstrate that the method can solve each simulated instance within one second. Random tests reveal that the method can efficiently solve instances with 1000 sites and 1500 tasks within an acceptable CPU time. A sensitivity analysis indicates that the complexity arising from routing flexibility is greater than that arising from parking flexibility.

The multidepot drone general routing problem with duration and capacity constraints

AbstractThis paper studies the multidepot drone general routing problem with duration and capacity constraints (MDdGRP), an extension of the classical general routing problem with several depots. A fleet of drones with limited flight time and payload, each one located in a different depot, must jointly perform the service. In this continuous optimization problem, a set of lines of a network has to be serviced and a set of nodes has to be visited to deliver a given commodity. The aim is to find a set of drone routes performing the complete service with the shortest total duration. Aerial drones can enter a line at any point, service a portion of that line, and exit through another point, without following the lines of the network. While this flexibility allows for potentially better solutions, it also adds complexity to the problem. To deal with this, we digitize the MDdGRP instances by approximating each line with a polygonal chain containing a finite number of points that can be used to enter and exit each line. Thus, an instance of a discrete multidepot general routing problem (MDGRP) is obtained. This paper proposes an integer formulation for the MDGRP, some families of valid inequalities, and a branch‐and‐cut algorithm based on the strengthened formulation. Two matheuristic algorithms are presented, focused on sequentially selecting (and adding) some promising intermediate points to enter and exit a line. Instances involving up to six depots, 22 delivery points, and 88 original lines have been generated to test the performance of the methods proposed.

Locating charging stations and routing drones for efficient automated stocktaking

Drones have received growing attention in logistics recently. One possible application is deploying drones for auditing inventory in warehouses. With the use of drones, warehouses are able to increase inventory record accuracy and decrease labor costs. In this research, we introduce the stocktaking drone routing problem (STDRP), which consists of routing a fleet of drones through a warehouse for stocktaking purposes as well as deciding on the location of charging stations on the warehouse floor, which is necessary due to the limited battery capacity of the drones. Subsequently, we develop an adaptive large neighborhood search-based heuristic (ALNS) with novel solution encoding and decoding approaches to solve the STDRP. In a numerical study, we show that ALNS can solve realistic instances in reasonable time. We also derive recommendations regarding the ideal size of the drone fleet, the charging infrastructure, and battery capacity. Finally, we investigate the interplay between the storage assignment policy (such as the popular ABC rule) and stocktaking efficiency using drones.

Optimization of trucks and drones in tandem delivery network with drone trajectory planning

Drones are widely recognized as an efficient method for delivering small and lightweight parcels, such as medicines, to customers who are difficult to reach by logistic vehicles. Various studies and projects have been conducted to integrate drones into the traditional logistic service. In this approach, drones stay on trucks, take off from trucks at specific locations to make deliveries to customers, and return to the trucks to replenish and recharge. However, drone trajectories could overlap when multiple drones are used for delivery, which can lead to the risk of collisions. Consequently, the need to address the trajectory planning of drones becomes essential. This work introduces a novel truck-drone routing problem. The novelty presented by this problem lies in the integration of drone trajectory planning problems into the truck-drone routing to generate collision-free routes for drones. This concept has not been previously explored in the existing body of literature. The problem is formulated as a mixed-integer programming problem, and a matheuristic is proposed to solve it. Computational experiments show that the proposed matheuristic outperforms the commercial solver and genetic algorithm in terms of solution quality and search efficiency. Results demonstrate that the integrated truck-drone delivery mode has a lower operating cost than the mere truck mode, and including trajectory planning can prevent potential collisions.

Solving the probabilistic drone routing problem: Searching for victims in the aftermath of disasters

AbstractSeveral major industrial disasters happen each year around the world. They usually involve limited accessibility, poor ground conditions, and toxic wastes. As a consequence, this reduces the efficiency of humanitarian operations. In such a context, flying drones may be a viable alternative: faster, no dependency on ground conditions, and larger areas scanned. They are also better suited for following the population and the crisis dynamic. For such a purpose, various issues have to be addressed such as defining and optimizing the drone's routes, their energy consumption, choosing the relay points for recharging equipment, among others. In this study, several additional features from existing works are considered: first, a probability of identifying individuals is defined. Thus, each node can be scanned several times in order to improve the observation. In addition, the nodes are prioritized according to a given heatmap. The probabilistic drone routing problem (PDRP) consists of finding a route, that is, a sequence of trips, for each drone such that the sum of the expected number of identified individuals on all routes is maximized. Constraints on energy consumption, collision avoidance and drone‐base assignment are considered. We propose a heuristic and metaheuristics based on the adaptive large neighborhood search for the PDRP. The methods are tested on theoretical instances, as well as on a case study of the Beirut Port explosion on August 4, 2020, in order to analyze the performance of the proposed methods.

A predictive multistage postdisaster damage assessment framework for drone routing

AbstractThis study focuses on postdisaster damage assessment operations supported by a set of drones. We propose a multistage framework, consisting of two phases applied iteratively to rapidly gather damage information within an assessment period. In the initial phase, the problem involves determining areas to be scanned by each drone and the optimal sequence for visiting these selected areas. We have adapted an electric vehicle routing formulation and devised a variable neighborhood descent heuristic for this phase. In the second phase, information collected from the scanned areas is employed to predict the damage status of the unscanned areas. We have introduced a novel, fast, and easily implementable imputation policy for this purpose. To evaluate the performance of our approach in real‐life disasters, we develop a case study for the expected 7.5 magnitude earthquake in Istanbul, Turkey. Our numerical study demonstrates a significant improvement in response time and priority‐based metrics.

Cooperated delivery of drones and truck for “last 100 metres” in rural areas

This paper focuses on addressing the “last 100 metres” home delivery in rural areas, using a cooperated delivery method of drones and truck. Considering the constraints of drone load, drone energy consumption and customer time window, a mixed integer linear programming model is established to minimize the delivery cost. Owing to the computational complexity of this problem, a double ant colony optimization with neighbourhood search is proposed. First, the raw data are sorted and encoded. Second, the ant colony optimization with search operators is used to solve drone routes and truck route. Finally, the local search algorithm with search operators is used to solve the connection point between the drones and truck to obtain the cooperated delivery routes. Extensive experiments are conducted on the instances randomly generated in the Solomon dataset, and results demonstrate the proposed algorithm effectively solves problems within reasonable runtimes. Sensitivity analysis is conducted on factors that may affect the delivery cost of the solution and provide insights about drones participating in the “last hundred metres” home delivery service.

Blockchain-Enabled Infection Sample Collection System Using Two-Echelon Drone-Assisted Mechanism

The collection and transportation of samples are crucial steps in stopping the initial spread of infectious diseases. This process demands high levels of safety and timeliness. The rapid advancement of technologies such as the Internet of Things (IoT) and blockchain offers a viable solution to this challenge. To this end, we propose a Blockchain-enabled Infection Sample Collection system (BISC) consisting of a two-echelon drone-assisted mechanism. The system utilizes collector drones to gather samples from user points and transport them to designated transit points, while deliverer drones convey the packaged samples from transit points to testing centers. We formulate the described problem as a Two-Echelon Heterogeneous Drone Routing Problem with Transit point Synchronization (2E-HDRP-TS). To obtain near-optimal solutions to 2E-HDRP-TS, we introduce a multi-objective Adaptive Large Neighborhood Search algorithm for Drone Routing (ALNS-RD). The algorithm’s multi-objective functions are designed to minimize the total collection time of infection samples and the exposure index. In addition to traditional search operators, ALNS-RD incorporates two new search operators based on flight distance and exposure index to enhance solution efficiency and safety. Through a comparison with benchmark algorithms such as NSGA-II and MOLNS, the effectiveness and efficiency of the proposed ALNS-RD algorithm are validated, demonstrating its superior performance across all five instances with diverse complexity levels.

Urban wind field prediction based on sparse sensors and physics‐informed graph‐assisted auto‐encoder

AbstractThe urban flow wind field is a critical element for downstream research, such as mitigation of urban wind disasters, assessment of urban wind environment, and urban drone route planning. However, it is impractical to arrange a large number of sensors to monitor an urban wind flow field. Hence, acquiring the entire urban wind flow field via sparse sensors would be highly valuable. To date, no scheme including deep learning (DL) model has been specifically designed for this purpose. This study presents an innovative approach to reconstruct complex high‐resolution urban wind fields based on sparse sensors, using a physics‐informed graph neural network (GNN)‐assisted auto‐encoder. The proposed method leverages the relationship between sensors and their surrounding environment enabled by deep mining capabilities of GNNs. As a result, the utilization and emphasis on sparse sensors data are significantly enhanced. The continuity equation of fluid flow is incorporated into the loss function of the convolution neural network to improve the stability and performance of the model. The findings suggest that, in contrast to prevalent generative DL models, the proposed model yields an approximate 50% reduction in root mean square error for reconstructing high‐resolution urban wind fields for multiple wind attack angles.

Offshore Oilfield Inspection Planning With Drone Routing Optimization

Offshore Oilfield Inspection Planning With Drone Routing Optimization

3D Hover Location and Drone Routing Optimization for One-to-Many Continuous Wireless Charging Problem

3D Hover Location and Drone Routing Optimization for One-to-Many Continuous Wireless Charging Problem