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Journal ArticleDOI

Vehicle Routing Problems for Drone Delivery

01 Jan 2017-Vol. 47, Iss: 1, pp 70-85
TL;DR: In this paper, the authors propose two multi-trip vehicle routing problems (VRPs) specifically for drone delivery scenarios, one minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to budget constraint.
Abstract: 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 problems (VRPs) specifically for drone delivery scenarios. Existing VRPs are insufficient for planning drone deliveries: either multiple trips to the depot are not permitted, leading to solutions with excess drones, or the effect of battery and payload weight on energy consumption is not considered, leading to costly or infeasible routes. We propose two multitrip VRPs for drone delivery that address both issues. One minimizes costs subject to a delivery time limit, while the other minimizes the overall delivery time subject to a budget constraint. We mathematically derive and experimentally validate an energy consumption model for multirotor drones, demonstrating that energy consumption varies approximately linearly with payload and battery weight. We use this approximation to derive mixed integer linear programs for our VRPs. We propose a cost function that considers our energy consumption model and drone reuse, and apply it in a simulated annealing (SA) heuristic for finding suboptimal solutions to practical scenarios. To assist drone delivery practitioners with balancing cost and delivery time, the SA heuristic is used to show that the minimum cost has an inverse exponential relationship with the delivery time limit, and the minimum overall delivery time has an inverse exponential relationship with the budget. Numerical results confirm the importance of reusing drones and optimizing battery size in drone delivery VRPs.
Citations
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Journal ArticleDOI
01 Dec 2018-Networks
TL;DR: This article describes the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning, and provides insights into widespread and emerging modeling approaches to civil applications of UAVs.
Abstract: Unmanned aerial vehicles (UAVs), or aerial drones, are an emerging technology with significant market potential. UAVs may lead to substantial cost savings in, for instance, monitoring of difficult-to-access infrastructure, spraying fields and performing surveillance in precision agriculture, as well as in deliveries of packages. In some applications, like disaster management, transport of medical supplies, or environmental monitoring, aerial drones may even help save lives. In this article, we provide a literature survey on optimization approaches to civil applications of UAVs. Our goal is to provide a fast point of entry into the topic for interested researchers and operations planning specialists. We describe the most promising aerial drone applications and outline characteristics of aerial drones relevant to operations planning. In this review of more than 200 articles, we provide insights into widespread and emerging modeling approaches. We conclude by suggesting promising directions for future research.

576 citations

Journal ArticleDOI
TL;DR: In this article, a UAV-based mobile cloud computing system is studied in which a moving UAV is endowed with computing capabilities to offer computation offloading opportunities to MUs with limited local processing capabilities.
Abstract: Unmanned aerial vehicles (UAVs) have been recently considered as means to provide enhanced coverage or relaying services to mobile users (MUs) in wireless systems with limited or no infrastructure. In this paper, a UAV-based mobile cloud computing system is studied in which a moving UAV is endowed with computing capabilities to offer computation offloading opportunities to MUs with limited local processing capabilities. The system aims at minimizing the total mobile energy consumption while satisfying quality of service requirements of the offloaded mobile application. Offloading is enabled by uplink and downlink communications between the mobile devices and the UAV, which take place by means of frequency division duplex via orthogonal or nonorthogonal multiple access schemes. The problem of jointly optimizing the bit allocation for uplink and downlink communications as well as for computing at the UAV, along with the cloudlet's trajectory under latency and UAV's energy budget constraints is formulated and addressed by leveraging successive convex approximation strategies. Numerical results demonstrate the significant energy savings that can be accrued by means of the proposed joint optimization of bit allocation and cloudlet's trajectory as compared to local mobile execution as well as to partial optimization approaches that design only the bit allocation or the cloudlet's trajectory.

352 citations

Journal ArticleDOI
TL;DR: In this paper, a novel framework for optimizing the performance of such UAV-based wireless systems in terms of the average number of bits (data service) transmitted to users as well as the UAVs' hover duration (i.e. flight time) is proposed.
Abstract: In this paper, the effective use of flight-time constrained unmanned aerial vehicles (UAVs) as flying base stations that provide wireless service to ground users is investigated. In particular, a novel framework for optimizing the performance of such UAV-based wireless systems in terms of the average number of bits (data service) transmitted to users as well as the UAVs’ hover duration (i.e. flight time) is proposed. In the considered model, UAVs hover over a given geographical area to serve ground users that are distributed within the area based on an arbitrary spatial distribution function. In this case, two practical scenarios are considered. In the first scenario, based on the maximum possible hover times of UAVs, the average data service delivered to the users under a fair resource allocation scheme is maximized by finding the optimal cell partitions associated to the UAVs. Using the powerful mathematical framework of optimal transport theory, this cell partitioning problem is proved to be equivalent to a convex optimization problem. Subsequently, a gradient-based algorithm is proposed for optimally partitioning the geographical area based on the users’ distribution, hover times, and locations of the UAVs. In the second scenario, given the load requirements of ground users, the minimum average hover time that the UAVs need for completely servicing their ground users is derived. To this end, first, an optimal bandwidth allocation scheme for serving the users is proposed. Then, given this optimal bandwidth allocation, optimal cell partitions associated with the UAVs are derived by exploiting the optimal transport theory. Simulation results show that our proposed cell partitioning approach leads to a significantly higher fairness among the users compared with the classical weighted Voronoi diagram. Furthermore, the results demonstrate that the average hover time of the UAVs can be reduced by 64% by adopting the proposed optimal bandwidth allocation scheme as well as the optimal cell partitioning approach. In addition, our results reveal an inherent tradeoff between the hover time of UAVs and bandwidth efficiency while serving the ground users.

321 citations

Journal ArticleDOI
TL;DR: In this article, a six-layer reference model of the blockchain framework is proposed with detailed description for each of its six layers, and potential applications of blockchain and cryptocurrencies are also addressed.
Abstract: As an emerging decentralized architecture and distributed computing paradigm underlying Bitcoin and other cryptocurrencies, blockchain has attracted intensive attention in both research and applications in recent years. The key advantage of this technology lies in the fact that it enables the establishment of secured, trusted, and decentralized autonomous ecosystems for various scenarios, especially for better usage of the legacy devices, infrastructure, and resources. In this paper, we presented a systematic investigation of blockchain and cryptocurrencies. Related fundamental rationales, technical advantages, existing and potential ecosystems of Bitcoin and other cryptocurrencies are discussed, and a six-layer reference model of the blockchain framework is proposed with detailed description for each of its six layers. Potential applications of blockchain and cryptocurrencies are also addressed. Our aim here is to provide guidance and reference for future research along this promising and important direction.

310 citations

Posted Content
TL;DR: A UAV-based mobile cloud computing system is studied in which a moving UAV is endowed with computing capabilities to offer computation offloading opportunities to MUs with limited local processing capabilities, aimed at minimizing the total mobile energy consumption while satisfying quality of service requirements of the offloaded mobile application.
Abstract: Unmanned Aerial Vehicles (UAVs) have been recently considered as means to provide enhanced coverage or relaying services to mobile users (MUs) in wireless systems with limited or no infrastructure. In this paper, a UAV-based mobile cloud computing system is studied in which a moving UAV is endowed with computing capabilities to offer computation offloading opportunities to MUs with limited local processing capabilities. The system aims at minimizing the total mobile energy consumption while satisfying quality of service requirements of the offloaded mobile application. Offloading is enabled by uplink and downlink communications between the mobile devices and the UAV that take place by means of frequency division duplex (FDD) via orthogonal or non-orthogonal multiple access (NOMA) schemes. The problem of jointly optimizing the bit allocation for uplink and downlink communication as well as for computing at the UAV, along with the cloudlet's trajectory under latency and UAV's energy budget constraints is formulated and addressed by leveraging successive convex approximation (SCA) strategies. Numerical results demonstrate the significant energy savings that can be accrued by means of the proposed joint optimization of bit allocation and cloudlet's trajectory as compared to local mobile execution as well as to partial optimization approaches that design only the bit allocation or the cloudlet's trajectory.

306 citations

References
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Journal ArticleDOI
13 May 1983-Science
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Abstract: There is a deep and useful connection between statistical mechanics (the behavior of systems with many degrees of freedom in thermal equilibrium at a finite temperature) and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters). A detailed analogy with annealing in solids provides a framework for optimization of the properties of very large and complex systems. This connection to statistical mechanics exposes new information and provides an unfamiliar perspective on traditional optimization problems and methods.

41,772 citations

Journal ArticleDOI
TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.
Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.

35,161 citations

Book
01 Jan 2005
TL;DR: Algorithm Design introduces algorithms by looking at the real-world problems that motivate them and encourages an understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science.
Abstract: Algorithm Design introduces algorithms by looking at the real-world problems that motivate them. The book teaches students a range of design and analysis techniques for problems that arise in computing applications. The text encourages an understanding of the algorithm design process and an appreciation of the role of algorithms in the broader field of computer science.

1,541 citations

Journal ArticleDOI
01 May 2013
TL;DR: In this paper, Flying Ad-Hoc Networks (FANETs) are surveyed which is an ad hoc network connecting the UAVs, and the main FANET design challenges are introduced.
Abstract: One of the most important design problems for multi-UAV (Unmanned Air Vehicle) systems is the communication which is crucial for cooperation and collaboration between the UAVs. If all UAVs are directly connected to an infrastructure, such as a ground base or a satellite, the communication between UAVs can be realized through the in-frastructure. However, this infrastructure based communication architecture restricts the capabilities of the multi-UAV systems. Ad-hoc networking between UAVs can solve the problems arising from a fully infrastructure based UAV networks. In this paper, Flying Ad-Hoc Networks (FANETs) are surveyed which is an ad hoc network connecting the UAVs. The differences between FANETs, MANETs (Mobile Ad-hoc Networks) and VANETs (Vehicle Ad-Hoc Networks) are clarified first, and then the main FANET design challenges are introduced. Along with the existing FANET protocols, open research issues are also discussed.

1,072 citations

Journal ArticleDOI
TL;DR: Two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery are provided, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels.
Abstract: Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.

851 citations