# Joint Power Charging and Routing in Wireless Rechargeable Sensor Networks

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## Abstract

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## 1. Introduction

- We present a novel joint optimization model including both charging efficiency and routing, rather than the typical charging optimization problem considering only the predefined data-gathering route.
- We propose a genetic algorithm (GA)-based optimization framework to find the optimal routing tree, in which the specific many-to-one routing tree is coded as an individual for evolution. We design an efficient individual encoding scheme and effective constraints handling mechanisms to achieve quick convergence.
- We then propose a heuristic algorithm to find the optimal resident locations with the given routing tree. By calculating the minimum moving distance and total charging time to evaluate the fitness of each individual, the evolution process of the GA is thus guided.
- We evaluate the proposed algorithms with extensive simulations and study the impact of multiple environmental factors, including the number of sensors and the types of routing tree. Our simulation results have showed that our proposed algorithm achieves a substantial improvement compared with the predefined route.

## 2. System Model and Problem Formulation

#### 2.1. System Model

#### 2.2. Routing Constraints

#### 2.3. Energy Charging Cycle

#### 2.4. Problem Formulation

**Charging efficiency problem**: Charging efficiency is conventionally regarded as the ratio between the working time and charging schedule. On the basis of this criterion, the objective of this problem is to maximize the charging efficiency for the networks. This can be achieved by searching the optimal resident locations, the optimal routing tree and the optimal traveling path. This problem is formulated as

## 3. Optimization Algorithms

#### 3.1. Heuristic Algorithm for Optimal Charging

**Definition**

**1.**

**Definition**

**2.**

Algorithm 1: Heuristic algorithm for resident location selection |

#### 3.2. Joint Optimization of Routing and Charging

#### 3.2.1. Individual Encoding

Algorithm 2: Population initialization |

#### 3.2.2. Fitness Functions and Natural Selection

#### 3.2.3. Crossover and Mutation

#### 3.2.4. Replacement

Algorithm 3: Joint optimization based on genetic algorithm |

## 4. Numerical Results

#### 4.1. Convergence Behavior

#### 4.2. Total Traveling Distance

#### 4.3. Routing

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**A mobile charger periodically visits each resident location once and charges those nodes in its charging radius.

Parameters | Value |
---|---|

The initial energy of sensor n, ${E}_{i}^{n}$ | 10,800 J |

The minimum energy for working, ${E}_{min}$ | 540 J |

The mobile speed, V | 5 m/s |

The full charging ratio, ${u}_{Full}$ | 5 W |

The minimum charging ratio, ${U}_{min}$ | 1 J |

The charging radius, ${R}_{v}$ | 2.7 m |

The sensing ratio of node, n ${\lambda}_{n}$ | 1∼10 kbps |

The number of sensors, N | 20∼80 |

Distance-independent constant term, ${\beta}_{1}$ | $50\times {10}^{-9}$ J/b |

Coefficient of distance-dependent constant term, ${\beta}_{2}$ | $0.0013\times {10}^{-12}$ J/(bm${}^{4}$) |

Pass-loss index , $\alpha $ | 4 |

Energy consumption for receiving per data rate, ${C}_{i}^{r}$ | $50\times {10}^{-9}$ J/b |

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**MDPI and ACS Style**

Jia, J.; Chen, J.; Deng, Y.; Wang, X.; Aghvami, A.-H. Joint Power Charging and Routing in Wireless Rechargeable Sensor Networks. *Sensors* **2017**, *17*, 2290.
https://doi.org/10.3390/s17102290

**AMA Style**

Jia J, Chen J, Deng Y, Wang X, Aghvami A-H. Joint Power Charging and Routing in Wireless Rechargeable Sensor Networks. *Sensors*. 2017; 17(10):2290.
https://doi.org/10.3390/s17102290

**Chicago/Turabian Style**

Jia, Jie, Jian Chen, Yansha Deng, Xingwei Wang, and Abdol-Hamid Aghvami. 2017. "Joint Power Charging and Routing in Wireless Rechargeable Sensor Networks" *Sensors* 17, no. 10: 2290.
https://doi.org/10.3390/s17102290