# Multi-Objective Optimization with Mayfly Algorithm for Periodic Charging in Wireless Rechargeable Sensor Networks

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## Abstract

**:**

## 1. Introduction

- We find a solution to the problem of wireless energy transfer (WET) by researching the mobile charging demand method, which involves the introduction of two sets of energy variables: emin, which refers to the calculated minimum or lowest energy, and ethresh, which refers to the threshold energy in the node. In addition to this, we present the multi-objective functions as a potential solution to this problem.
- As far as we know, this is the first time the mayfly algorithm has been used in sensor node charging. Optimizing multiple objectives, including minimizing the total energy consumption of sensor nodes, minimizing the total distance traveled by MC, and maximizing vacation time for the mobile charger, is formulated in this work as an optimal problem. Using seven other good performance algorithms, we assessed MA’s efficiency in reducing sensor node energy consumption, mobile charging distance, and vacation time.
- Introduces the concept of a renewable energy cycle in which the remaining energy level of a sensor node’s battery exhibits periodicity over time. We present both the necessary and sufficient conditions for a renewable energy cycle and demonstrate that feasible solutions that meet these requirements can provide renewable energy cycles and, consequently, a long lifetime for sensor networks.

## 2. Literature Review

## 3. Methods

#### 3.1. MC and Travel Path

_{i}(in bits per second), a stationary base station (BS) within the sensor network that serves as the sink node for all data generated by all sensor nodes. All data streams are routed to the base station using a single hope data routing, a rest station (RS) where the mobile charger may recharge its battery and prepare for the next cycle. A mobile charger is used to move around the network and charge the batteries of the sensor nodes. The MC departs out of its home station within the sensor network, traverses the region along a predetermined path, and then returns to its home station at the end of its journey. At certain locations along its path, the MC pauses to charge sensor nodes that are scheduled to be charged during the current cycle (see Figure 1). Before returning to the service station, we suppose that the MC has sufficient energy to sustain its journey, data collection, and nodes energy transfer.

_{n}represents the nodes that must be charged while visited. MC passes thru the Hamiltonian cycle in the Cth cycle, MC passes through the smallest Hamiltonian cycle, which connects nodes in H

_{n}and BS. The shortest Hamiltonian cycle’s traveling path is represented by P

_{n}. D

_{n}signifies the length of path P

_{n}, and t

_{n}represents the time spent across distance D

_{n}. The total time for the MC’s tour cycle is marked by T, while the MC’s vacation time in the Cth cycle is denoted by ${\tau}_{\mathrm{vac}}$. The MC goes from RS to H

_{n}during the Cth cycle, visiting and charging sensor nodes before returning to RS for ${\tau}_{\mathrm{vac}}$. The following formula is used to compute the cycle time T:

_{n}.

#### 3.2. Control Methodology

## 4. Total Energy Consumption Analysis

## 5. Proposed Strategy

#### 5.1. Optimization with Flowing Rate and Data Routing

_{total}in Equation (6). Every node should indeed fulfill the fundamental flow balancing constraint in Equation (8) and the energy consumption model in Equation (9). The optimal challenge can therefore be explained as a linear programming problem as follows:

#### 5.2. The Procedure of Joint Design

#### 5.2.1. Step 1

#### 5.2.2. Step 2

_{k}. To begin, we set the charging period ${T}_{i}$ of each node $i$ ($i\in N$) as follows:

_{k}($1\le k\le g$) and let $\left(i\in {s}_{a}\right)$; the MC will visit node $i$ during the ${\left(n{.2}^{a-1}\right)}^{th}$ trip cycle.

#### 5.2.3. Step 3

Algorithm 1 |

Define the value of T and the number of the visits set |

Initialize P_{max} and P_{min} |

Initialize e_{min} and e_{thresh} |

Set g |

Set the recharging period of node i, T_{i} and classify Z_{k} |

Define Z_{1}, Z_{2}, …, Z_{g} |

For i = 1,2 3,…, n do |

a=$\lfloor lo{g}_{2}\left(\frac{{E}_{max}-{E}_{min}}{{p}_{i}\xb7T}-1\right)\rfloor +1$ |

i $\in $ Za ${T}_{i}={2}^{a-1}\xb7T$ |

End for |

Set the visiting nodes and traveling path of T |

For j = 1, 2, 3,…,${2}^{a-1}$ |

If j is odd, then |

${F}_{j}$ = ${Z}_{1}$ |

else |

write ${F}_{j}$ as ${F}_{j}=n\xb7{2}^{c}$ |

${F}_{j}$ = ${Z}_{1}\cup {Z}_{2}\cup {Z}_{3}\dots {Z}_{c+1}$ |

End if |

For ∀${n}_{i}$ ∈ Fj do |

Charge nodes ${n}_{i}$ to E_{max} |

End for |

End for |

#### 5.3. Mayfly Algorithm

## 6. Results and Discussion

## 7. Conclusions

_{max}. A technique was used for joining each node’s charging duration, the visiting set, and the traveling path during each cycle in work by first constructing a practical optimization problem with a flow rate to determine the energy consumption rate. Then, we demonstrated how the mayfly algorithm can optimally keep the network operational and can dramatically cut total energy consumption while maintaining vacation time ratio performance maximized according to simulations. For the future work to get more performance results, we will study how the nodes can also be charged partially without charging them to the maximum energy level, and we will make a dead node analysis to test which is a good algorithm in terms of how many nodes died according to different network area sizes.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

Abbreviations | Description |

λ | The efficiency of non-radiative energy transfer |

T | MC periodic trip cycle |

H_{n} | Set of nodes that must be visited during the Cth cycle |

E_{min} | General minimum energy in the node |

E_{max} | Maximum energy in the node |

e_{min} | Proposed minimum energy |

e_{thresh} | Proposed threshold energy |

N | Number of sensor nodes |

RS | Rest station |

BS | Base station |

R_{i} | Node i data rate |

p_{i} | Energy consumption rate at sensor node i |

MC | Mobile charger |

P_{k} | Traveling path of MC |

D_{n} | Distance of P_{k} |

t_{n} | Time spent traveling P_{k} |

${\tau}_{vac}$ | Vacation time of MC at the rest station |

µ_{vac} | MC vacation time ratio |

WSN | Wireless sensor network |

WET | Wireless energy transfer |

TSP | Traveling salesman problem |

t_{i} | Charging duration of node i |

P_{total} | System total energy consumption |

D_{total} | Total distance traveled over all cycles |

T_{total} | Total time spent overall cycles |

W_{ij}, W_{iB} | Flow rate coefficient from node i to node j (or base station) |

V_{ij}, V_{iB} | Energy consumption for transmitting a unit of data from node i to node j or base station |

ρ | Constant coefficient |

α | Path loss index |

d_{ij} | Distance between sensor i and sensor j (or base station B) |

β_{1} and β_{2} | Constant coefficients in transmission energy modeling |

(X_{B}, Y_{B}) | Coordinates of the base station |

V | Traveling speed of MCV |

U | Energy transfer rate of MCV |

g | The number of sets needing to be classified |

Z_{k} | The defined set that needs to be classified |

F_{j} | The set of nodes that should be visited during the jth cycle |

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Simulation Parameters | Description of the Abbreviation |
---|---|

Nodes | 50 |

Area length and width | 100–1000 m |

RS, BS | center |

U | 5 W |

V | 7 m/s |

λ | 0.85 |

E_{max} | 10.8 kJ |

E_{min} | 0.05 × E_{max} |

Data rate R_{i} | [1, 10] kb/s |

β_{1} | 50 nJ/b |

β_{2} | 0.0013 pJ/b/m^{4} |

α | 4 |

ρ | 50 nJ/b |

Number of parameters | 20 |

Maximum iterations | 50 |

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**MDPI and ACS Style**

Mukase, S.; Xia, K.
Multi-Objective Optimization with Mayfly Algorithm for Periodic Charging in Wireless Rechargeable Sensor Networks. *World Electr. Veh. J.* **2022**, *13*, 120.
https://doi.org/10.3390/wevj13070120

**AMA Style**

Mukase S, Xia K.
Multi-Objective Optimization with Mayfly Algorithm for Periodic Charging in Wireless Rechargeable Sensor Networks. *World Electric Vehicle Journal*. 2022; 13(7):120.
https://doi.org/10.3390/wevj13070120

**Chicago/Turabian Style**

Mukase, Sandrine, and Kewen Xia.
2022. "Multi-Objective Optimization with Mayfly Algorithm for Periodic Charging in Wireless Rechargeable Sensor Networks" *World Electric Vehicle Journal* 13, no. 7: 120.
https://doi.org/10.3390/wevj13070120