A Branch-and-Bound Algorithm for the Close-Enough Traveling Salesman Problem

Coutinho, Walton Pereira; Nascimento, Roberto Quirino do; Pessoa, Artur Alves; Subramanian, Anand

doi:10.1287/ijoc.2016.0711

Cited by 56 publications

(25 citation statements)

References 14 publications

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“…The authors of Reference [31] proposed an exact algorithm, based on Branch-and-Bound and Second-Order Cone Programming (SOCP) to solve the CETSP. They studied the feasibility of embedding path algorithm in a UAV in order to compute a trajectory that visits all points with the highest resolution of images.…”

Section: Monitoring Tracking Filmingmentioning

confidence: 99%

A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles

Khoufi

Laouiti

Adjih

2019

Drones

125

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The use of Unmanned Aerial Vehicles (UAVs) is rapidly growing in popularity. Initially introduced for military purposes, over the past few years, UAVs and related technologies have successfully transitioned to a whole new range of civilian applications such as delivery, logistics, surveillance, entertainment, and so forth. They have opened new possibilities such as allowing operation in otherwise difficult or hazardous areas, for instance. For all applications, one foremost concern is the selection of the paths and trajectories of UAVs, and at the same time, UAVs control comes with many challenges, as they have limited energy, limited load capacity and are vulnerable to difficult weather conditions. Generally, efficiently operating a drone can be mathematically formalized as a path optimization problem under some constraints. This shares some commonalities with similar problems that have been extensively studied in the context of urban vehicles and it is only natural that the recent literature has extended the latter to fit aerial vehicle constraints. The knowledge of such problems, their formulation, the resolution methods proposed—through the variants induced specifically by UAVs features—are of interest for practitioners for any UAV application. Hence, in this study, we propose a review of existing literature devoted to such UAV path optimization problems, focusing specifically on the sub-class of problems that consider the mobility on a macroscopic scale. These are related to the two existing general classic ones—the Traveling Salesman Problem and the Vehicle Routing Problem. We analyze the recent literature that adapted the problems to the UAV context, provide an extensive classification and taxonomy of their problems and their formulation and also give a synthetic overview of the resolution techniques, performance metrics and obtained numerical results.

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Section: Monitoring Tracking Filmingmentioning

confidence: 99%

A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles

Khoufi

Laouiti

Adjih

2019

Drones

125

View full text Add to dashboard Cite

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“…We believe that a number of computational heuristics and benchmark instances could now be developed to find VRPD solutions as close to optimal as possible for practical values of α . Using solution methods for

{CEVRP}^{*}

(such as in ), modifying them to maintain VRPD feasibility, and then applying some local optimization procedures is one new idea for obtaining computational solutions to VRPD. An alternative idea is starting with a

{VRP}^{*}

solution and inserting drone deliveries in a smart way.…”

Section: Discussionmentioning

confidence: 99%

The vehicle routing problem with drones: Extended models and connections

2017

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The vehicle routing problem with drones (VRPD) is inspired by the increasing interest in commercial drone delivery by companies such as Amazon, Google, DHL, and Walmart. In our model, a fleet of m homogeneous trucks each carries k drones with a speed of α times that of the truck. Each drone may dispatch from the top of the truck and carry a package to a customer location. The drone then returns to the top of its truck to recharge or swap batteries (we assume instantaneously). The truck itself is allowed to move and deliver packages, but must be stationary at a delivery location or the depot when launching or retrieving drones. The goal is to minimize the completion time to deliver all packages and return all vehicles back to the central depot. In this article, we review and extend several worst‐case results from an earlier paper and we make connections with another practical variant of the vehicle routing problem and with Amdahl's Law. We find that the VRPD model offers some important practical advantages. The drones allow the truck to parallelize tasks and they are able to take advantage of crow‐fly distances. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 34–43 2017

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“…These algorithms are generally divided into two groups; exact and approximate algorithms. The branch-and-bound [8] and cutting planes [9] are the two examples of exact algorithms which are excessively time consuming especially in large scale problems. Approximate algorithms are further classified into heuristic and meta-heuristic algorithms.…”

Section: Related Workmentioning

confidence: 99%

Development a New Crossover Scheme for Traveling Salesman Problem by aid of Genetic Algorithm

Ehtasham-ul-Haq¹,

Hussain²,

Ahmad³

2019

IJISA

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─This research work provides a detailed working principle and analysis technique of multioffspring crossover operator. The proposed approach is an extension of the basic partially-mapped crossover (PMX) based upon survival of the fittest theory. It improves the performance of the genetic algorithm (GA) for solving the well-known combinatorial optimization problem, the traveling salesman problem (TSP). This study is based on numerical experiments of the proposed with other traditional crossover operators for eighteen benchmarks TSPLIB instances. The simulation results show a considerable improvement because the proposed operator enhances the opportunity of having better offspring. Moreover, the t-test also establishes the improved significance of the proposed operator. Its preferable results not only confirm the advantages over others, but also show the long run survival of a generation having a number of offspring more than the number of parents with the help of mathematical ecology theory.

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A Branch-and-Bound Algorithm for the Close-Enough Traveling Salesman Problem

Cited by 56 publications

References 14 publications

A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles

A Survey of Recent Extended Variants of the Traveling Salesman and Vehicle Routing Problems for Unmanned Aerial Vehicles

The vehicle routing problem with drones: Extended models and connections

Development a New Crossover Scheme for Traveling Salesman Problem by aid of Genetic Algorithm

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