# Dynamic Deployment of Wireless Sensor Networks by Biogeography Based Optimization Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. WSN Dynamic Deployment Problem and Sensor Detection Model

_{i}is the coverage of a sensor i, S is the set of the nodes, and A is the total size of the area of interest. The reason why a union operation is used rather than a plus operation, is that every grid point is calculated only once.

_{i}is positioned at (x

_{i}, y

_{i}). For any point P at (x, y), Euclidean distance between s

_{i}and P is d(s

_{i}, P). The binary sensor model [25] is shown by Equation (2):

_{xy}(s

_{i}) is the coverage of a grid point P by sensor s

_{i}, d(s

_{i}, P) is Euclidean distance. For simplicity, but without loss of generality, we use the binary sensor model to confirm the effectiveness of BBO in solving the sensor deployment.

## 3. Dynamic Deployment of Wireless Sensor Networks with Biogeography-Based Optimization

- Detection radii of the sensors are all identical (r);
- All of the sensors have ability to communicate with other sensors;
- WSN consists of both mobile and static sensors.

_{i}. The modified probability X

_{i}is proportional to its immigration rate λ

_{i}, and the source of the modified probability from X

_{j}is proportional to the emigration rate μ

_{j}. The migration operator is shown in Figure 1(a).

**Figure 1.**(

**a**) The habitat migration operator algorithm. (

**b**) The habitat mutation operator algorithm.

- - Initialize the parameters: detection radius r, size of the area of interest A, number of mobile sensors m, number of static sensors s, population size NP, maximum number of iterations MaxGeneration, divided grid size GridSize, maximum variation rate m
_{max}, migration rate p_{mod}, the maximum capacity of habitat species S_{max}, maximum of immigration operator I and maximum of emigration operator E and the maximum of elite individuals retained z. - - Deploy the s static sensors at random.
- - Determine the positions of m mobile sensors randomly for each Habitat X
_{i}using Equation (3) where j = 1, 2,…, 2m: - - Evaluate the fitness value (HSI, i.e., coverage rate) for each individual.
- - t = 0
- -
**REPEAT**- - Sort the population from worst to best according to its HSI.
- - For each individual, map the HSI to the number of species using Equation (4), where m
_{max}is a user-defined parameter, P_{s}and P_{max}is migration rate for S species and max species respectively: - - Calculate the immigration rate λ
_{i}and the emigration rate μ_{i}for each individual x_{i}. - - Modify the population with the migration operator shown in Figure 1(a).
- - Update the probability of each individual.
- - Mutate the population with the mutation operator shown in Figure 1(b).
- - Evaluate the fitness for each individual.
- - Memorize the best solution achieved so far.
- - t = t + 1

- -
**UNTIL**t = MaxNumber

_{1}, X

_{2},…, X

_{NP}. x

_{i}is the initial position of Sensor s

_{i}determined by Equation (3), where x

_{i}=(x

_{i,}

_{1}, x

_{i,}

_{2},⋯, x

_{i,j}, ⋯, x

_{i,}

_{2m-1}, x

_{i,}

_{2m}), 1 ≤ j ≤ 2m. In our work, min

_{j}and max

_{j}are 0 and 100, respectively. S

_{max}is the largest possible number of species that the habitat can support. The immigration rate and the emigration rate are functions of the number of species in the habitat and are represented by migration rate p

_{mod}for simplicity, whose maximum is a user-defined parameter m

_{max }in Equation (4).

1 | 2 | 3 | 4 | 5 | 6 | ⋯ | 2m − 1 | 2m |
---|---|---|---|---|---|---|---|---|

x_{1} | y_{1} | x_{2} | y_{2} | x_{3} | y_{3} | ⋯ | x_{m} | y_{m} |

## 4. Simulation Results

_{e}is 0.5 × r = 3.5 m, size of the area which is a square region A (100 m × 100 m) is 10,000 m

^{2}.

_{max}and migration rates p

_{mod}for each island is 1 and mutation probability is 0.005. The ABC algorithms’ population size NP is 30, limit parameter for the scout is taken as 100. SGA algorithms’ population size NP is 30, crossover probability is taken 1, and initial mutation probability is 0.01. The Homo-H-VFCPSO algorithms’ control parameters are set as in [13]. We did some fine tuning on each of the optimization algorithms except BBO to obtain optimal performance, but we did not make any special efforts to tune the algorithm BBO, because Simon [16] has demonstrated that BBO is insensitive to the control parameter.

Initial coverage of stationery sensors | ABC | BBO | SGA | Homo-H-VFCPSO | ||

MG = 50 | Mean | 0.6823 | 0.8367 | 0.8641 | 0.8262 | 0.8013 |

Std | 0.0254 | 0.0155 | 0.0134 | 0.0195 | 0.0158 | |

Best | 0.7275 | 0.8728 | 0.9007 | 0.864 | 0.882 | |

Worst | 0.6224 | 0.8049 | 0.8299 | 0.7699 | 0.8129 | |

Time(s) | - | 31.7 | 15.61 | 15.35 | 17.03 | |

MG =100 | Mean | 0.6762 | 0.854 | 0.8711 | 0.8375 | 0.8609 |

Std | 0.0248 | 0.0853 | 0.0868 | 0.0839 | 0.0889 | |

Best | 0.7434 | 0.8896 | 0.9097 | 0.8769 | 0.8976 | |

Worst | 0.6138 | 0.8115 | 0.8299 | 0.7962 | 0.7692 | |

Time(s) | - | 80.55 | 36.97 | 35.36 | 36.53 | |

MG = 500 | Mean | 0.683 | 0.8889 | 0.9184 | 0.8602 | 0.8536 |

Std | 0.0262 | 0.0885 | 0.0118 | 0.0856 | 0.0865 | |

Best | 0.7346 | 0.9218 | 0.9519 | 0.8922 | 0.8299 | |

Worst | 0.6131 | 0.8501 | 0.8798 | 0.8277 | 0.8188 | |

Time(sec) | - | 356.77 | 173.28 | 175.07 | 185.15 | |

MG = 1000 | Mean | 0.3783 | 0.8959 | 0.929 | 0.8709 | 0.8906 |

Std | 0.0241 | 0.0891 | 0.0122 | 0.0871 | 0.079 | |

Best | 0.7495 | 0.9327 | 0.9523 | 0.9112 | 0.8989 | |

Worst | 0.6224 | 0.8636 | 0.8956 | 0.8287 | 0.8829 | |

Time(s) | - | 724.96 | 346.91 | 349.73 | 356.36 |

**Figure 2.**Best solutions of ABC: (

**a.1**) iteration #50, (

**a.**

**2**) iteration #100, (

**a.**

**3**) iteration #500, (

**a.**

**4**) iteration #1000. Best solutions of BBO: (

**b.1**) iteration #50, (

**b.**

**2**) iteration #100, (

**b.**

**3**) iteration #500, (

**b.**

**4**) iteration #1000. Best solutions of SGA: (

**c.1**) iteration #50, (

**c.**

**2**) iteration #100, (

**c.**

**3**) iteration #500, (

**c.**

**4**) iteration #1000. Best solutions of Homo-H-VFCPSO: (

**c.1**) iteration #50, (

**c.**

**2**) iteration #100, (

**c.**

**3**) iteration #500, (

**c.**

**4**) iteration #1000.

**Figure 3.**Average development of the populations through the different iterations for ABC, BBO, Homo-H-VFCPSO and SGA algorithms in 100 Monte Carlo simulations:

**(a)**iteration #50, (

**b**) iteration #100, (

**c**) iteration #500, (

**d**) iteration #1000.

## 5. Conclusions and Future Work

## Acknowledgments

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**MDPI and ACS Style**

Wang, G.; Guo, L.; Duan, H.; Liu, L.; Wang, H.
Dynamic Deployment of Wireless Sensor Networks by Biogeography Based Optimization Algorithm. *J. Sens. Actuator Netw.* **2012**, *1*, 86-96.
https://doi.org/10.3390/jsan1020086

**AMA Style**

Wang G, Guo L, Duan H, Liu L, Wang H.
Dynamic Deployment of Wireless Sensor Networks by Biogeography Based Optimization Algorithm. *Journal of Sensor and Actuator Networks*. 2012; 1(2):86-96.
https://doi.org/10.3390/jsan1020086

**Chicago/Turabian Style**

Wang, Gaige, Lihong Guo, Hong Duan, Luo Liu, and Heqi Wang.
2012. "Dynamic Deployment of Wireless Sensor Networks by Biogeography Based Optimization Algorithm" *Journal of Sensor and Actuator Networks* 1, no. 2: 86-96.
https://doi.org/10.3390/jsan1020086