# Overlay Optimization Algorithm for Directed Sensor Networks with Virtual Force and Particle Swarm Optimization Synergy

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## Abstract

**:**

## 1. Introduction

## 2. Perception Model and Problem Description

#### 2.1. Problem Hypothesis

#### 2.2. Direction Perception Model

#### 2.3. Direction Perception Model

## 3. Segment Virtual Negative Centroid Coverage Algorithm for Directed Sensor Networks

#### 3.1. Split Virtual Negative Centroid Model

#### 3.2. Force Analysis

## 4. Coverage Enhancement Algorithm for Directed Sensor Networks under the Synergy of Virtual Force and Particle Swarm Optimization

#### 4.1. Coverage of Directed Sensor Networks Based on Particle Swarm Optimization Algorithm

#### 4.2. Coverage Optimization Algorithm for Directed Sensor Networks under the Synergy of Virtual Force and Particle Swarm Optimization

## 5. Algorithm Simulation and Result Analysis

#### 5.1. Experimental Results and Analysis

#### 5.1.1. Experimental Environment and Parameter Setting

#### 5.1.2. Diagram of Experimental Results and Comparative Analysis

- Coverage algorithm for directional sensor networks with segmented virtual negative centroid.

^{2}, the coverage value obtained from this algorithm exceeded that of the VF algorithm by 5.11%. Moreover, when r = 60, α = 45, and S = 500 × 500 m

^{2}, three distinct initialization scenarios with identical parameters were considered, and the directional sensor was subjected to multi-initialization. According to Table 4, when the number of directional sensors equaled or exceeded five, the optimal coverage ratio reached 80%.

- 2.
- Coverage algorithm of directional sensor networks under the synergistic effect of virtual force and particle swarm optimization.

#### 5.2. Comparison between Our Algorithm and Other Similar Algorithms

#### 5.2.1. Experimental Parameter Settings

#### 5.2.2. Analysis of Experimental Results

#### 5.3. Influence of Different Parameters on Coverage Rate

#### 5.4. The Universality Analysis of This Model

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Guvensan, M.A.; Yavuz, A.G. On coverage issues in directional sensor networks: A survey. Ad Hoc Netw.
**2011**, 9, 1238–1255. [Google Scholar] [CrossRef] - Tian, X.; He, J.; Guo, M.; Liu, G.; Zhu, Y. Mobile charging and data collection strategies in wireless sensor networks. J. Instrum.
**2018**, 39, 216–224. [Google Scholar] - Li, M.; Hu, J. Coverage algorithm for mobile heterogeneous wireless sensor networks under complex conditions. Sens. Microsyst.
**2019**, 38, 124–127+132. [Google Scholar] - Liu, C.; Zhao, Z.; Qu, W.; Qiu, T.; Sangaiah, A.K. A distributed node deployment algorithm for underwater wireless sensor networks based on virtual forces. J. Syst. Archit.
**2019**, 97, 9–19. [Google Scholar] [CrossRef] - Li, F.X.; Islam, A.A.; Jaroo, A.S.; Hamid, H.; Jalali, J.; Sammartino, M. Urban highway bridge structure health assessments using wireless sensor network. In Proceedings of the 2015 IEEE Topical Conference on Wireless Sensors and Sensor Networks (WiSNet), San Diego, CA, USA, 25–28 January 2015; pp. 75–77. [Google Scholar]
- Sun, S.Z.; Xiang, Y.; Dang, X.Y. Research on FBG flow and temperature composite sensor based on the PSO decoupling algorithm. Chin. J. Sci. Instrum.
**2022**, 43, 2–10. [Google Scholar] - Varposhti, M.; Hakami, V.; Dehghan, M. Distributed coverage in mobile sensor networks without location information. Auton. Robot.
**2020**, 44, 627–645. [Google Scholar] [CrossRef] - Cheng, S.; Yuan, F. Coverage control for mobile sensor networks with limited communication ranges on a circle. Automatica
**2018**, 92, 155–161. [Google Scholar] - Zhang, H.D.; Shi, W.R.; Yang, L. Study on equilibrium of particle-based coverage control for mobile sensor network. Chin. J. Sci. Instrum.
**2016**, 37, 1049–1057. [Google Scholar] - Thandapani, P.; Arunachalam, M.; Sundarraj, D. An energy-efficient clustering and multipath routing for mobile wireless sensor network using game theory. Int. J. Commun. Syst.
**2020**, 33, e4336. [Google Scholar] [CrossRef] - Wu, Y.; Liu, K.; Chen, B.; Li, F.; Yao, J. Image reconstruction for electrical impedance tomography using radial basis function neural network optimized with adaptive particle swarm optimization algorithm. Chin. J. Sci. Instrum.
**2020**, 41, 240–249. [Google Scholar] - Si, P.; Wu, C.; Zhang, Y.; Chu, H.; Teng, H. Probabilistic coverage in directional sensor networks. Wirel. Netw.
**2019**, 25, 355–365. [Google Scholar] [CrossRef] - Years, I.R. Distributed Voronoi-Based Self-Redeployment for Coverage Enhancement in a Mobile Directional Sensor Network. Int. J. Distrib. Sens. Netw.
**2013**, 9, 165498. [Google Scholar] - Varposhti, M.; Saleh, P.; Afzal, S.; Dehghan, M. Distributed area coverage in mobile directional sensor networks. In Proceedings of the 2016 8th International Symposium on Telecommunications (IST), Tehran, Iran, 27–28 September 2016; pp. 18–23. [Google Scholar]
- Fan, X.G.; Wang, H.; Hao, X. Coverage Enhancement Algorithm for Directed Sensor Networks. Chin. J. Sci. Instrum.
**2017**, 38, 368–377. [Google Scholar] - Peng, S.; Xiong, Y. An Area Coverage and Energy Consumption Optimization Approach Based on Improved Adaptive Particle Swarm Optimization for Directional Sensor Networks. Sensors
**2019**, 19, 1192. [Google Scholar] [CrossRef] - Esmaeilzadeh, R.; Abbaspour, M. Optimum Temporal Coverage with Rotating Directional Sensors. Wirel. Pers. Commun.
**2019**, 105, 369–386. [Google Scholar] [CrossRef] - Liu, Z.; Ouyang, Z. A Learning Automata-based Algorithm for Area Coverage Problem in Directional Sensor Networks. KSII Trans. Internet Inf. Syst.
**2017**, 10, 4807–4822. [Google Scholar] - Zhang, G.; You, S.; Ren, J.; Li, D.; Wang, L. Local Coverage Optimization Strategy Based on Voronoi for Directional Sensor Networks. Sensors
**2016**, 16, 2183. [Google Scholar] [CrossRef] - Yuen, K.; Kuok, S. Efficient Bayesian sensor placement algorithm for structural identification: A general approach for multi-type sensory systems. Earthq. Eng. Struct. Dyn.
**2015**, 44, 757–774. [Google Scholar] [CrossRef] - Jiang, Y.B.; Wang, W.; He, C.L. Sub-regional Dynamic Optimization Algorithm for Path Coverage of Single Target. Comput. Sci.
**2019**, 46 (Suppl. 2), 369–375. [Google Scholar] - Zhang, J.W.; Wang, Y. Strong barrier coverage algorithm for directional sensor network. J. Electron. Meas. Instrum.
**2017**, 31, 83–91. [Google Scholar] - Duan, S.; Shi, Q.; Wu, J. Multimodal Sensors and ML-Based Data Fusion for Advanced Robots. Adv. Intell. Syst.
**2022**, 4, 2200213. [Google Scholar] [CrossRef] - Wang, C.; Mao, J.; Fu, L.; Guo, N.; Qu, W. Coverage optimization algorithm for three-dimensional directional heterogeneous sensor network. J. Comput. Appl.
**2016**, 36, 2362–2366+2373. [Google Scholar] - Yang, Y.F. Research on Coverage Enhancement Algorithm of Multimedia Sensor Networks Based on 3D Perceptual Model; Northeastern University: Shenyang, China, 2015. [Google Scholar]
- Fan, X.G.; Wang, H.; Zhang, Z.J. A Virtual Force-Directed Particle Swarm Optimization for Coverage Enhancing in directional sensor networks. Chin. J. Sens. Actuators
**2015**, 28, 1720–1726. [Google Scholar] - Jiang, Y.B.; Mei, J.D.; Wang, N.H. Directional Sensor Network Coverage Optimization Algorithm with Modify Virtual Force k. J. Chin. Comput. Syst.
**2018**, 39, 457–462. [Google Scholar]

Parameter | Region Area | Number of Logistics Nodes N | Sensing Radius r | Perception Angle $\mathit{\alpha}$ |
---|---|---|---|---|

value | $500\times 500{\mathrm{m}}^{2}$ | 106 | 60 m | $45\xb0$ |

Parameter | Population Size | Iterations | ${\mathit{w}}_{\mathbf{max}}$ | ${\mathit{w}}_{\mathbf{min}}$ | c_{1} | c_{2} | c_{3} |
---|---|---|---|---|---|---|---|

value | 40 | 50 | 0.9 | 0.4 | 0.729 | 0.729 | 1.414 |

Initial Value | VF | One | Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Fifteen | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

r = 50 | 65.04 | 71.8 | 74.76 | 74.96 | 75.36 | 75.6 | 75.16 | 75.08 | 75.56 | 74.92 | 75.48 | 74.96 | 75.64 | 3.84 |

r = 60 | 66 | 71.96 | 73.12 | 73.4 | 74.2 | 73.88 | 74.24 | 74.44 | 73.84 | 73.52 | 74.72 | 73.48 | 74.4 | 2.24 |

r = 70 | 68.96 | 72.28 | 73.2 | 73.24 | 73.88 | 73.56 | 73.96 | 73.76 | 73.64 | 73.8 | 73.92 | 74.04 | 73.84 | 1.76 |

$\mathsf{\alpha}=30$ | 68.44 | 76.48 | 77.76 | 78.56 | 78.28 | 78.12 | 78.4 | 78.4 | 77.56 | 74.72 | 76.68 | 78.08 | 77.88 | 2.08 |

$\mathsf{\alpha}=45$ | 65 | 70.44 | 71.88 | 72.44 | 72.84 | 72.52 | 72.6 | 72.52 | 72.68 | 72.64 | 72.68 | 72.72 | 72.52 | 2.4 |

$\mathsf{\alpha}=60$ | 69.2 | 72.36 | 72.64 | 72.96 | 73.32 | 73.6 | 73.68 | 73.68 | 74.44 | 74 | 74.76 | 73.96 | 74.08 | 2.4 |

$\mathrm{s}=400\times 400{\mathrm{m}}^{2}$ | 66.69 | 72.75 | 72.94 | 73.12 | 74.06 | 73.44 | 74.13 | 74.31 | 74.94 | 75 | 74.56 | 75.06 | 74.75 | 2.31 |

$\mathrm{S}=500\times 500{\mathrm{m}}^{2}$ | 64.72 | 70.2 | 71.76 | 71.96 | 72.96 | 72.72 | 73.52 | 73.56 | 73.8 | 74.24 | 73.56 | 74.12 | 73.64 | 4.04 |

$\mathrm{S}=600\times 600{\mathrm{m}}^{2}$ | 65.14 | 70.56 | 74.44 | 74.69 | 75.36 | 75.14 | 75.31 | 75.61 | 75.25 | 74.89 | 75.42 | 75.14 | 75.67 | 5.11 |

$\mathrm{S}=700\times 700{\mathrm{m}}^{2}$ | 66.22 | 71.5 | 75.84 | 75.69 | 76.22 | 76 | 76.33 | 76.29 | 76.1 | 75.55 | 76.2 | 75.16 | 76.27 | 4.83 |

Algorithm | Mean Coverage Rate | Maximum Coverage |
---|---|---|

Algorithm in this paper | 80.61% | 84.2% |

LAASD | 75.5% | - |

VF-PSO | 75% | 78% |

OSRCEA | 73.8% | - |

PSO | 70.13% | 70.52% |

VF | 64.64% | 64.64% |

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## Share and Cite

**MDPI and ACS Style**

Zhu, L.; Lin, L.; Liang, Q.; Lu, Y.; Tan, H.; Ma, X.; Zhang, D.
Overlay Optimization Algorithm for Directed Sensor Networks with Virtual Force and Particle Swarm Optimization Synergy. *Electronics* **2023**, *12*, 4332.
https://doi.org/10.3390/electronics12204332

**AMA Style**

Zhu L, Lin L, Liang Q, Lu Y, Tan H, Ma X, Zhang D.
Overlay Optimization Algorithm for Directed Sensor Networks with Virtual Force and Particle Swarm Optimization Synergy. *Electronics*. 2023; 12(20):4332.
https://doi.org/10.3390/electronics12204332

**Chicago/Turabian Style**

Zhu, Lingjian, Li Lin, Qi Liang, Yaling Lu, Haonan Tan, Xuan Ma, and Dongya Zhang.
2023. "Overlay Optimization Algorithm for Directed Sensor Networks with Virtual Force and Particle Swarm Optimization Synergy" *Electronics* 12, no. 20: 4332.
https://doi.org/10.3390/electronics12204332