# Dynamic Hierarchical Energy-Efficient Method Based on Combinatorial Optimization for Wireless Sensor Networks

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. The System Model

#### 3.1. Network Model

- (1)
- The BS and all sensor nodes are stationary after deployment, and are equipped with a Global Positioning System (GPS) unit. Hence, these nodes are location-aware.
- (2)
- All properties for each sensor node are identical, while the BS is manually maintained and has enough energy to support continuous operations, with its energy denoted as ${\epsilon}_{0}$.
- (3)
- Provided with sufficient energy, each node can control the transmission power according to the distance between the transmitter and the receiver.
- (4)
- The amount of transmission data is exactly equal for each sensor node of valid routes.

#### 3.2. Sensor Energy Model

## 4. Proposed Protocol

#### 4.1. Constructing the Hierarchical Network Structure

#### 4.2. Establishing the Feasible Routing Set

#### 4.3. Obtaining the Optimal Route

## 5. Performance Evaluation

#### 5.1. Experimental Setup

#### 5.2. Node Energy Consumption and Wireless Sensor Network Longevity for the Dynamic Hierarchical Protocol Based on Combinatorial Optimization Algorithm

#### 5.3. Wireless Sensor Network Longevity versus the Width of the Sensing Field and the Number of Sensor Nodes

#### 5.4. Efficiency and Computational Complexity Discussion

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**One-hundred sensor nodes’ random distribution in the deployment scenario of a 100 m × 100 m square region, and the coordinate (50, 50) of the BS.

**Figure 3.**Averages of sensor nodes’ energy consumption for one transmission round in the dynamic hierarchical protocol based on combinatorial optimization (DHCO) algorithm.

**Figure 4.**Percentage of live sensor nodes with sensor nodes of a random distribution for various algorithms in the deployment scenario of a $100\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\times 100\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$ square region and the coordinate (50, 50) of the BS: (

**a**) 100 sensor nodes of a random distribution, and (

**b**) 200 sensor nodes of a random distribution.

**Figure 5.**Comparison of transmission rounds with different dead sensor nodes for various algorithms in the deployment scenarios of 100 sensor nodes of a random distribution and the coordinate (50, 50) of the BS: (

**a**) at the 40% dead-sensor-nodes level for different widths of the sensing field, and (

**b**) at the 80% dead-sensor-nodes level for different widths of the sensing field.

**Figure 6.**Comparison of transmission rounds with different dead sensor nodes for various algorithms in the deployment scenarios of the $100\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\times 100\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$ square region and the coordinate (50, 50) of the BS: (

**a**) at the 40% dead-sensor-nodes level for different numbers of sensor nodes, and (

**b**) at the 80% dead-sensor-nodes level for different numbers of sensor nodes.

**Figure 7.**Comparison of the mean time and standard deviation of the computational complexity for each transmission round in the deployment scenarios of the $100\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}\times 100\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$ square region and the coordinate (50, 50) of the BS: (

**a**) mean time for diverse numbers of sensor nodes, and (

**b**) standard deviation of the computational complexity for diverse numbers of sensor nodes.

Properties | Values |
---|---|

Initial node energy | 0.5 J |

Electronics energy, ${E}_{elec}$ | 50 nJ/bit |

Consumption loss for ${d}^{2}$, ${\epsilon}_{fs}$ | 10 pJ/bit/m${}^{2}$ |

Consumption loss for ${d}^{4}$, ${\epsilon}_{amp}$ | 0.0013 pJ/bit/m${}^{4}$ |

Data aggregation energy | 50 nJ/bit/signal |

Packet size, l | 400 bit |

The optimal communication radius, ${r}_{s}$ | 40 m |

The threshold distance, ${d}_{0}$ | 75 m |

The minimum residual node energy, $\widehat{\epsilon}$ | $5\phantom{\rule{4pt}{0ex}}\mathsf{\mu}$J |

The initial probability p of being a CH | 0.05 |

The maximum number of iterations in HEED | 12 |

The population size in GASONeC | 30 |

The generation size in GASONeC | 30 |

The crossover probability in GASONeC | 0.8 |

The mutation probability in GASONeC | 0.006 |

Duty cycle $\gamma $ in DCFR | 10% |

Duration of a data period ${T}_{r}$ in DCFR | 10 s |

Energy consumption rate for idle listening ${E}_{idle}$ in DCFR | 0.88 mJ/s |

Width of Square Region | Location of BS | Number of Nodes | Mean Time | Standard Deviation |
---|---|---|---|---|

100 m | (50 m, 50 m) | 100 | 0.00479 s | 0.00011 |

100 m | (50 m, 50 m) | 120 | 0.00494 s | 0.00014 |

100 m | (50 m, 50 m) | 140 | 0.00603 s | 0.00018 |

100 m | (50 m, 50 m) | 160 | 0.00703 s | 0.00016 |

100 m | (50 m, 50 m) | 180 | 0.00803 s | 0.00012 |

100 m | (50 m, 50 m) | 200 | 0.00937 s | 0.00013 |

100 m | (100 m, 100 m) | 100 | 0.00417 s | 0.00015 |

100 m | (150 m, 150 m) | 100 | 0.00407 s | 0.00014 |

100 m | (200 m, 200 m) | 100 | 0.00393 s | 0.00009 |

100 m | (250 m, 250 m) | 100 | 0.00408 s | 0.00012 |

200 m | (50 m, 50 m) | 100 | 0.00409 s | 0.00015 |

300 m | (50 m, 50 m) | 100 | 0.00389 s | 0.00008 |

400 m | (50 m, 50m) | 100 | 0.00411 s | 0.00011 |

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**MDPI and ACS Style**

Chang, Y.; Tang, H.; Cheng, Y.; Zhao, Q.; Yuan, B.L.a.
Dynamic Hierarchical Energy-Efficient Method Based on Combinatorial Optimization for Wireless Sensor Networks. *Sensors* **2017**, *17*, 1665.
https://doi.org/10.3390/s17071665

**AMA Style**

Chang Y, Tang H, Cheng Y, Zhao Q, Yuan BLa.
Dynamic Hierarchical Energy-Efficient Method Based on Combinatorial Optimization for Wireless Sensor Networks. *Sensors*. 2017; 17(7):1665.
https://doi.org/10.3390/s17071665

**Chicago/Turabian Style**

Chang, Yuchao, Hongying Tang, Yongbo Cheng, Qin Zhao, and Baoqing Li andXiaobing Yuan.
2017. "Dynamic Hierarchical Energy-Efficient Method Based on Combinatorial Optimization for Wireless Sensor Networks" *Sensors* 17, no. 7: 1665.
https://doi.org/10.3390/s17071665