# Facility Location Problem Approach for Distributed Drones

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation for Distributed Drone Ports

#### 1.2. Related Work

#### 1.3. Challenges

#### 1.4. Facility Location Problem

#### 1.5. K-Means Clustering Algorithms

## 2. Materials and Methods

#### 2.1. Central Controller

#### 2.2. Drone Port

#### 2.3. Objective

#### 2.4. Tasks

#### 2.5. Energy Consumption

#### 2.6. Facility Location Problem

#### 2.7. Capital Expenditure

#### 2.8. Operational Expenditure

#### 2.9. Drone Port Placement Algorithm

Algorithm 1 Facility Location Problem for Drones |

procedure Drone Port Placement and Shortest Route |

$i\leftarrow \mathrm{max}\phantom{\rule{4.pt}{0ex}}\mathrm{number}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{droneports}$ |

$T\leftarrow \mathrm{Task}\phantom{\rule{4.pt}{0ex}}\mathrm{Locations}\phantom{\rule{4.pt}{0ex}}\mathrm{array}$ |

$P\leftarrow \mathrm{Set}\phantom{\rule{4.pt}{0ex}}\mathrm{of}\phantom{\rule{4.pt}{0ex}}\mathrm{drone}\phantom{\rule{4.pt}{0ex}}\mathrm{ports}\phantom{\rule{4.pt}{0ex}}\mathrm{array}$ |

${P}_{max}\leftarrow \mathit{\text{max number of droneports}}$ |

$p\leftarrow \mathit{\text{Initial number of droneports}}$ |

while $p\le {P}_{max}$ do |

$clusters\leftarrow GenerateCluster(Tasks,p)$ |

$shortestroute\leftarrow TSP(tasks,droneport)$ |

$e\leftarrow f({d}_{i}j)$ |

if $e\ge \theta $ then |

Break |

else |

$p\leftarrow p+1$ |

return Drone Port location |

return Shortest Routes |

#### 2.10. Traveling Salesman Problem

## 3. Performance Evaluation

#### 3.1. Coverage Size effect on the Combinatorial Search Space

#### 3.2. Average Round Trip Distance

#### 3.3. Infrastructure and Energy Cost

#### 3.4. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Notation | Explanation |

${e}_{c}$ | Set of drone ports |

${t}_{p}$ | Set of drones |

${d}_{i}$ | Drone i |

$v\ast $ | Vector |

$\gamma $ | Drone energy level |

${d}_{ij}$ | Distance between task j and drone port i |

${c}_{i}$ | Cost to build drone port |

${z}_{i}$ | Decision variable to build drone port |

${x}_{j}$ | Decision variable for drone i to complete task j |

${y}_{ij}$ | Task completion state $\{0,1\}$ |

${x}_{0}$ | Drone initial position |

${x}_{0}$ | Drone final position |

${\tau}_{j}$ | Calculated task completion delay |

$\widehat{{\tau}_{j}}$ | Earliest deadline first constraint |

$f\left({d}_{ij}\right)$ | Power Function |

${\tau}_{complete}$ | Drone energy function |

${\tau}_{arrival}$ | Minimum drone energy |

$\eta $ | Task’s drone energy consumption |

$\eta $ | Task’s drone energy consumption |

## References

- FAA. Unmanned Aircraft System. FAA Aerosp. Forecast.
**2018**. Available online: https://www.faa.gov/data_research/aviation/aerospace_forecasts/media/Unmanned_Aircraft_Systems.pdf (accessed on 12 November 2018). - Kanellakis, C.; Nikolakopoulos, G. Survey on Computer Vision for UAVs: Current Developments and Trends. J. Intell. Robot. Syst.
**2017**, 87, 141–168. [Google Scholar] [CrossRef] [Green Version] - Purwanda, I.G.; Adiono, T.; Situmorang, S.; Dawani, F.; Samhany, H.A.; Fuada, S. Prototyping design of a low-cost bike sharing system for smart city application. In Proceedings of the 2017 International Conference on ICT For Smart Society (ICISS), Tangerang, Indonesia, 18–19 September 2017; pp. 1–6. [Google Scholar] [CrossRef]
- Puiatti, A. Dronesense: Drone Charging Pad. 2014. Available online: https://www.skysense.co/ (accessed on 3 April 2018).
- Sharafeddine, S.; Islambouli, R. On-Demand Deployment of Multiple Aerial Base Stations for Traffic Offloading and Network Recovery. arXiv, 2018; arXiv:1807.02009. [Google Scholar]
- Chen, M.; Mozaffari, M.; Saad, W.; Yin, C.; Debbah, M.; Hong, C.S. Caching in the sky: Proactive deployment of cache-enabled unmanned aerial vehicles for optimized quality-of-experience. IEEE J. Sel. Areas Commun.
**2017**, 35, 1046–1061. [Google Scholar] [CrossRef] - Floreano, D.; Wood, R.J. Science, technology and the future of small autonomous drones. Nature
**2015**, 521, 460. [Google Scholar] [CrossRef] [PubMed] - Cesetti, A.; Frontoni, E.; Mancini, A.; Zingaretti, P.; Longhi, S. A Vision-Based Guidance System for UAV Navigation and Safe Landing Using Natural Landmarks. J. Intell. Robot. Syst.
**2010**, 57, 233–257. [Google Scholar] [CrossRef] - Ahmadian, S.; Swamy, C. Improved approximation guarantees for lower-bounded facility location. In Proceedings of the International Workshop on Approximation and Online Algorithms, Ljubljana, Slovenia, 13–14 September 2012; pp. 257–271. [Google Scholar]
- Desrochers, M.; Marcotte, P.; Stan, M. The congested facility location problem. Locat. Sci.
**1995**, 3, 9–23. [Google Scholar] [CrossRef] [Green Version] - Iellamo, S.; Lehtomaki, J.J.; Khan, Z. Placement of 5G Drone Base Stations by Data Field Clustering. In Proceedings of the 2017 IEEE 85th Vehicular Technology Conference (VTC Spring), Sydney, Australia, 4–7 June 2017; pp. 1–5. [Google Scholar] [CrossRef]
- Tang, C.; Monteleoni, C. Convergence rate of stochastic k-means. arXiv, 2016; arXiv:1610.04900. [Google Scholar]
- Geng, Q.; Zhao, Z. A kind of route planning method for UAV based on improved PSO algorithm. In Proceedings of the 2013 25th Chinese Control and Decision Conference (CCDC), Guiyang, China, 25–27 May 2013; pp. 2328–2331. [Google Scholar] [CrossRef]
- Croes, G.A. A method for solving traveling-salesman problems. Oper. Res.
**1958**, 6, 791–812. [Google Scholar] [CrossRef] - Mitchell, M. An Introduction to Genetic Algorithms; MIT Press: Cambridge, MA, USA, 1998. [Google Scholar]
- Dorigo, M.; Birattari, M.; Blum, C.; Clerc, M.; Stützle, T.; Winfield, A. Ant Colony Optimization and Swarm Intelligence, Proceedings of the 6th International Conference, ANTS 2008, Brussels, Belgium, 22–24 September 2008; Springer: Berlin/Heidelberg, Germany, 2008; Volume 5217. [Google Scholar]
- Kanungo, T.; Mount, D.M.; Netanyahu, N.S.; Piatko, C.D.; Silverman, R.; Wu, A.Y. An efficient k-means clustering algorithm: Analysis and implementation. IEEE Trans. Pattern Anal. Mach. Intell.
**2002**, 27, 881–892. [Google Scholar] [CrossRef] - Arthur, D.; Vassilvitskii, S. k-means++: The advantages of careful seeding. In Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 7–9 January 2007; pp. 1027–1035. [Google Scholar]
- Gonzalez, G. Autonomous Vehicles, Drones Offer New Insurer Risks and Opportunities. Available online: https://www.businessinsurance.com/article/20171207/NEWS06/912317799/Autonomous-vehicles,-drones-offer-new-insurer-risks-and-opportunities (accessed on 12 June 2018).

**Figure 4.**Average round trip for drones based on k-means clustering and Traveling Salesman Approximation.

Category Name | Mass [kg] | Range [km] | Flight Altitude [m] | Endurance [Hours] |
---|---|---|---|---|

Micro | <5 | <10 | 250 | 1 |

Mini | <20/30/150 | <10 | 150/250/300 | <2 |

Close Range | 25–150 | 10–30 | 3000 | 2–4 |

Medium Range | 50–250 | 30–70 | 3000 | 3–6 |

High Alt. Long Endurance | >250 | >70 | >3000 | >6 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lynskey, J.; Thar, K.; Oo, T.Z.; Hong, C.S.
Facility Location Problem Approach for Distributed Drones. *Symmetry* **2019**, *11*, 118.
https://doi.org/10.3390/sym11010118

**AMA Style**

Lynskey J, Thar K, Oo TZ, Hong CS.
Facility Location Problem Approach for Distributed Drones. *Symmetry*. 2019; 11(1):118.
https://doi.org/10.3390/sym11010118

**Chicago/Turabian Style**

Lynskey, Jared, Kyi Thar, Thant Zin Oo, and Choong Seon Hong.
2019. "Facility Location Problem Approach for Distributed Drones" *Symmetry* 11, no. 1: 118.
https://doi.org/10.3390/sym11010118