# Swarm Intelligence Techniques for Mobile Wireless Charging

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## Abstract

**:**

## 1. Introduction

## 2. Related Works and Comparison

#### 2.1. Swarm Intelligence (SI)-Based Techniques

#### 2.2. Energy Provisioning Using MCs in WRSNs

## 3. The Network Model

#### 3.1. Network Elements

#### 3.2. The Deployment and Energy Model

#### Uniform and Non-Uniform Deployment

#### 3.3. Recharge by Adaptive Network Partitioning and Clustering

- The first partition is conducted. This method is like that in [9] and follows a uniform division of the network into c parts. Unlike [9], our method uses a dynamic selection of the cluster centroids, where CHs can be in each region of the network. These nodes are located at the center of each region. Besides, we evaluate the distance ${r}^{\prime}$ and the shortest hop routing ${\u0125}^{\prime}$ from each node to the cluster centroids. ${{r}^{\prime}}_{jk}$ denotes the distance between node j and cluster centroid k, where $j\in N,k\in c$.
- The second partition is conducted. Firstly, we evaluate the weight ${W}_{jk}$ of each node j to k. Here, ${W}_{jk}=\alpha {R}_{jk}+\psi {\u0124}_{jk}$; $\alpha +\psi =1,0\le \alpha ,\psi \le 1,\u2371j\in N,\u2371k\in \left[1,c\right]$. We define $\alpha $ and $\psi $ as part of the distance and routing hop priorities, respectively, and ${R}_{jk}$ is the serial number of the distance ${{r}^{\prime}}_{jk}$ from node j to cluster centroid k. If ${R}_{jk}=1$ denotes the minimum value of ${{r}^{\prime}}_{jk}$, ${R}_{jk}=c$ denotes the maximum distance ${{r}^{\prime}}_{jk}.$ We denote $\u236b=\frac{\alpha}{\psi}$ as the ratio of $\alpha $ and $\psi $. If $\u236b\to \infty $, our algorithm only considers a routing hop. On the contrary, our algorithm can also consider distance when $\u236b\to 0$. In this case, we jointly consider the routing hop and distance to make $\u236b=1$. Next, the smallest ${W}_{jk}$ is chosen, owing to its partitioning, and the node j is assigned to the kth region. This whole process is repeated until all the nodes in the network are partitioned. The proposed network partitioning and clustering method can be summarized in Algorithm 1.

Algorithm 1: Node-partition algorithm based on cluster centroids. |

Let S sensor-nodes and c cluster centroids be inputted We denote the output as: min $\left[{W}_{j}{}^{1}\dots ,{W}_{j}{}^{c}\right]$ Calculate distance ${{r}^{\prime}}_{jk}$ and the shortest hop ${{\u0125}^{\prime}}_{jk}$ between node j and centroid k where $j\in S,k\in c$. Arrange $\left({{r}^{\prime}}^{1}{}_{j},\dots ,{{r}^{\prime}}^{c}{}_{j}\right)$ and $\left({{\u0125}^{\prime}}^{1}{}_{j},\dots ,{{\u0125}^{\prime}}^{c}{}_{j}\right)$ in ascending order ${R}_{jk}$ denotes the distance of the serial number and ${\u0124}_{jk}$ is the routing hop serial number of node j to centroid k. While $N\ne \u0275$ Calculate ${W}_{jk}=\alpha {R}_{jk}+\psi {\u0124}_{jk},\alpha +\psi =1,0\le \alpha ,\psi \le 1,\u2371j\in S,\u2371k\in \left[1,c\right],$ ${W}_{jk}=\mathrm{min}\left[{W}_{j}{}^{1}\dots ,{W}_{j}{}^{c}\right]$, the node j is assigned to the kth region. $S=S-j$ End |

#### 3.4. Charging Model and Strategy for MCs

## 4. Recharge Optimization Problem with Multiple Mobile Chargers (ROPMMCs)

_{r}= {1, 2, … s

_{r}}, where each sensor-node is capable of storing E units of energy for each ${\mathrm{s}}_{r}\in {\mathrm{S}}_{r}$ in a list L

_{s}of pairs $\left({t}_{{s}_{r}}^{r},{e}_{{s}_{r}}^{r}\right),r\ge 1$, where ${t}_{{s}_{r}}^{r}$ represents the time taken to generate the $r\mathrm{th}$ message of ${s}_{r}$, and ${e}_{{s}_{r}}^{r}$ is the energy expended by the sensor-node in its message transmission. We consider a graph, G = (U, V), where ${U}_{j}\left(j\in {S}_{r}\right)$ is the location of the sensor-nodes j to be visited, and V is the set of edges. Each edge ${V}_{j,k}$ has a traveling energy cost ${e}_{j,k}$ which varies directly with the distance between the nodes j and k, and a latency cost ${c}_{jk}={t}_{j}+{t}_{jk}$, where ${t}_{j}$ is the recharge time of node j from its current energy status to its full capacity, and ${t}_{jk}$ is the traveling time from node j to node k. The recharge capacity ${R}_{c}$ of an MC is used to determine the maximum number of sensor-nodes to be recharged before the MC’s energy is depleted. We note that different MCs could have varying recharge capacities during the run. We also consider an $\left|{S}_{r}\left|\times \right|{S}_{r}\right|$ matrix R, where ${R}_{j,k}$ is the distance between sensors j and k and an MC, M, which can recharge a sensor-node to its initial energy in a timely manner. If we assume that the MC moves at a constant speed v, then the time of travel between j and k can be calculated as $\frac{{R}_{j,k}}{v}$. The MCROP is to determine the feasibility of scheduling an MC for node-energy replenishment to minimize/avoid packet loss arising from insufficient energy.

## 5. MCs Coordination and Charging Traversal Strategies

#### 5.1. Percentage of Energy Available to the MCs

#### 5.2. Partial vs. Full Charging

#### 5.3. Coordination Strategy

- Distributed coordination: Here, the MCs perform distributed coordination among themselves and assume limited network knowledge. The network area is split into slices as shown in Figure 3a, and each slice is assigned to an MC. Each MC can adjust their slice limits to suit their region of interest, either by increasing or shrinking the slice. The MCs, in a distributive manner, define their slice limits in accordance with the size of the region of interest. Hence, an MC with a lower energy status provides its neighbor with a portion of its region of interest for charging. Besides, the energy levels of the MCs determine which of them should reduce their region of interest. Figure 7 shows the distributed form of coordination. Specifically, Figure 7a–c depicts distributed coordination before, during, and after the coordination, respectively.
- Centralized coordination: We can distinguish two kinds of centralized coordination. (a) The MCs assume local network knowledge (LNK), and (b) the MCs assume global network knowledge (GNK). In (a), the coordination process uses information from all MCs, including their energy status and position. Essentially, each MC is assigned to a network region. Using Equation (1), the initial deployment coordinates are $\left(m,n\right)=\left\{\frac{\Re}{2}\mathrm{cos}\left(\frac{\pi}{\mathrm{n}}\left(2p-1\right)\right),\frac{\Re}{2}\mathrm{sin}\left(\frac{\pi}{\mathrm{n}}\left(2p-1\right)\right)\right\}$ where p = {1, 2, … n}. The network area is split into slices, as shown in Figure 3a (e.g., for n = 8 chargers) with one MC assigned to each slice. During the initialization of the coordination process, we calculate the region of each MC. An MC is assigned to a regional area equivalent to its present energy status to balance the energy dissipation among the MCs. To calculate the regional area of an MC k we compute the central angle ${\varphi}_{k}$ corresponding to the slice of the MC. That is, ${\varphi}_{k}=2\pi .\frac{{E}_{k}}{{\sum}_{k=1}^{N}{E}_{k}}$, where $\sum _{k=1}^{N}{\varphi}_{k}=2\pi $. In the case of global knowledge, the MCs assume global network knowledge and obtain the most updated energy information from sensors, which they use to make real-time decisions. The energy information is aggregated by CHs (special nodes in the network acting as representatives of the partitioned network areas). The MCs communicate with each other to update their energy status and positions. To avoid charging conflicts (already discussed in Section 3.4) where MCs select the same node for charging, the sink can be used to store and update each node’s availability, as well as prioritizing their charging requests. This can be done by maintaining a 0–1 node list wherein a node is assigned a value of 1 (locked) when selected for charging and is returned to a value of 0 after being charged. Using this method, an MC can simply communicate with the sink, ignore nodes that have already been chosen by other MCs, and inform the sink of the energy status of the node it has selected. The global knowledge coordination strategy is expected to outperform all other strategies exploiting local knowledge, since the assumption of global network knowledge further extends the MC’s coordinating abilities. However, this strategy would be unrealistic and would not be feasible for real LS-WSNs, as it introduces a high communication overhead whereby every node has to propagate their energy status to the MC, and nodes and MCs have to communicate their status over large distances. This does not scale well with LS-WSNs. Thus, the global knowledge charger studied presents an online solution that minimizes, in each round, the product of each node’s energy and its distance from the present position of the MC. Simply put, for each moving step, the global charger reduces the following [22]: $\mathrm{min}\left\{\left(1+\frac{{E}_{\mathrm{curr}}}{{E}_{\mathrm{init}}}\right).\left(1+\frac{{\u0256}_{curr}}{2R}\right)\right\}$ where ${E}_{\mathrm{curr}}$, ${E}_{\mathrm{init}}$, and ${\u0256}_{curr}$ are the current energy, initial energy, and current transmission distances of each sensor, respectively.

#### 5.4. The Charging Traversal Strategy

#### 5.5. The MC’s Movement Energy and Charging Costs

## 6. Simulation Results and Analysis

#### 6.1. The Packet Delivery Ratio (PDR) and the Total Packets Delivered

#### 6.2. The Energy Consumption of the Sensor-Nodes and MCs

#### 6.3. Throughput

#### 6.4. Network Lifetime

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 7.**MC distributed coordination. (

**a**) Before the coordination, (

**b**) during the coordination, (

**c**) after the coordination.

Notation | Description |
---|---|

𝓝 | The number of sensor-nodes |

⍲ | Area of circular sensing field |

$\Re $ | Radius of circular sensing field |

n | Number of mobile chargers |

$\S $ | Density of network |

ɖ | Transmission range of sensor-nodes |

δ | Rate of packet generation by sensor-nodes |

${R}_{c}$ | Recharge capacity of the MC |

v | Speed of the MC |

${E}_{j}$ | The residual energy of the sensor-node j before charging |

${\mathrm{t}}_{v}$ | The charging time of the MC |

${P}_{t}$ | The transmit power |

${\mathrm{R}}_{\mathrm{mc}}$ | The charging radius of the MC |

${P}_{L}$ | The polarization loss |

$\u014b$ | The rectifier efficiency |

$\u03fb$ | An adjustable parameter |

${G}_{t}$ | Transmit gain |

${G}_{r}$ | Receive gain |

$\lambda $ | Wavelength |

ɤ | Message (in bits) transmitted or received |

${\u0256}^{\beta}$ | Power needed to transmit a message |

${\u0194}_{\mathrm{m},\mathrm{n}}$ | Relative density |

${\mathrm{E}}_{0}$ | Initial energy of the sensors |

$\u213e$ | Recharge time of the sensor-node’s battery |

${\mathsf{\psi}}_{\mathrm{s}}$ | Battery capacity of the sensor-nodes |

${E}_{r}$ | Total energy replenished into the network |

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## Share and Cite

**MDPI and ACS Style**

Ijemaru, G.K.; Ang, K.L.-M.; Seng, J.K.P.
Swarm Intelligence Techniques for Mobile Wireless Charging. *Electronics* **2022**, *11*, 371.
https://doi.org/10.3390/electronics11030371

**AMA Style**

Ijemaru GK, Ang KL-M, Seng JKP.
Swarm Intelligence Techniques for Mobile Wireless Charging. *Electronics*. 2022; 11(3):371.
https://doi.org/10.3390/electronics11030371

**Chicago/Turabian Style**

Ijemaru, Gerald K., Kenneth Li-Minn Ang, and Jasmine Kah Phooi Seng.
2022. "Swarm Intelligence Techniques for Mobile Wireless Charging" *Electronics* 11, no. 3: 371.
https://doi.org/10.3390/electronics11030371