Abstract
Wireless Sensor Networks (WSNs) are pivotal in modern engineering, enabling applications in agriculture, healthcare, and disaster management. However, maintaining these networks in remote or complex environments poses significant challenges. Unmanned Aerial Vehicles (UAVs) have emerged as a promising solution for wireless charging due to their mobility and cost-effectiveness. This paper addresses the critical problem of optimizing UAV charging efficiency in three-dimensional WSNs under energy constraints. We propose a multi-objective optimization model that minimizes charging time while maximizing energy delivery to network devices. To solve this NP-hard problem, we introduce an Enhanced Multi-Objective Particle Swarm Optimization (EMOPSO) algorithm, incorporating chaos theory, Grey Wolf Optimization (GWO), and Cauchy mutation. Simulation results demonstrate the superior performance of EMOPSO compared to existing algorithms, achieving higher precision and stability across varying network scales.
1. Introduction
Unmanned Aerial Vehicles (UAVs) are increasingly utilized in WSNs for tasks such as data collection and wireless charging. Their ability to hover and deliver energy to ground-based sensors makes them indispensable in scenarios where traditional infrastructure is impractical. However, UAVs face inherent limitations, including finite onboard energy and dynamic energy consumption during flight and hovering. Efficient energy allocation is essential to maximize UAV operational longevity and charging effectiveness.
This paper focuses on optimizing UAV charging efficiency by addressing two primary objectives:
- Maximizing Energy Delivery: Ensuring network devices receive sufficient energy to sustain operations.
- Minimizing Charging Time: Reducing the time UAVs spend hovering or traveling to conserve energy.
The proposed solution integrates advanced optimization techniques to balance these competing goals, ensuring robust performance in three-dimensional WSNs.
2. System Model
2.1 Network Architecture
The WSN comprises:
- A UAV with limited onboard energy BB.
- nn randomly distributed network devices DiDi with coordinates (xi,yi,zi)(xi,yi,zi).
- A base station BSBS serving as the UAV’s starting and ending point.
The UAV selects mm hovering positions Hj=(Xj,Yj,Zj)Hj=(Xj,Yj,Zj) to charge devices within a maximum effective charging distance dmaxdmax.
2.2 Charging Model
The charging power σijσij received by device DiDi from UAV at HjHj is modeled as:σij=α(dij+β)2,dij≤dmaxσij=(dij+β)2α,dij≤dmax
where:
- α=GsGrηλ2σ016π2Lpα=16π2LpGsGrηλ2σ0.
- dijdij is the Euclidean distance between DiDi and HjHj.
- σ0σ0 is the UAV’s transmission power.
The total energy E(i)E(i) delivered to DiDi is:E(i)=min{θc,∑j=1mσijtHj}E(i)=min{θc,j=1∑mσijtHj}
where θcθc is the energy capacity of DiDi, and tHjtHj is the hovering time at HjHj.
2.3 Energy Consumption Model
UAV energy consumption includes:
- Movement Energy: Proportional to flight distance ℜℜ:Cmov=μℜ,μ=PmovvCmov=μℜ,μ=vPmovwhere vv is the UAV’s cruising speed.
- Hovering Energy:Chov=∑j=1mPhovtHjChov=j=1∑mPhovtHj
- Charging Energy:Cchar=∑j=1mσ0tHjCchar=j=1∑mσ0tHj
The total energy constraint is:Csum=Cmov+Chov+Cchar≤BCsum=Cmov+Chov+Cchar≤B
3. Multi-Objective Optimization
3.1 Problem Formulation
The optimization problem is defined as:minHj,tHjF={−f1,f2}Hj,tHjminF={−f1,f2}
where:
- f1=∑i=1nE(i)f1=∑i=1nE(i) (maximize energy delivery).
- f2=∑j=1mtHjf2=∑j=1mtHj (minimize charging time).
Subject to:
- UAV energy constraints.
- Device energy thresholds.
- Spatial boundaries for UAV deployment.
3.2 EMOPSO Algorithm
To solve this NP-hard problem, we propose EMOPSO, which enhances traditional MOPSO with:
- ICMIC Chaos Initialization: Ensures uniform distribution of initial solutions:qj+1=sin(ϵπqj),ϵ=0.7qj+1=sin(qjϵπ),ϵ=0.7
- GWO-Based Update: Introduces larger search steps to escape local optima:X(t+1)=X1+X2+X33X(t+1)=3X1+X2+X3where X1,X2,X3X1,X2,X3 are leader solutions.
- Cauchy Mutation: Enhances exploration using heavy-tailed distributions:Sji(t)=mod(Sji(t)⋅(1+Cauchy(0,1)),1)Sji(t)=mod(Sji(t)⋅(1+Cauchy(0,1)),1)
4. Simulation Results
4.1 Experimental Setup
- Network Scale: 100m × 100m × 100m.
- Devices: 50, 75, and 100.
- UAV Parameters: B=250kJ,σ0=200J/s,μ=10J/mB=250kJ,σ0=200J/s,μ=10J/m.
4.2 Performance Comparison
EMOPSO outperforms MOPSO, NSGA-II, MOFPA, and MODA in both objectives:
| Devices | Algorithm | Avg. Energy (J) | Avg. Time (s) |
|---|---|---|---|
| 50 | EMOPSO | -98,699 | 1,154 |
| MOPSO | -84,450 | 1,630 | |
| 75 | EMOPSO | -97,515 | 1,168 |
| MOFPA | -21,038 | 2,400 | |
| 100 | EMOPSO | -95,459 | 1,109 |
| MODA | -73,091 | 2,023 |
4.3 Stability Analysis
EMOPSO exhibits lower standard deviations across 30 runs, confirming robustness.
5. Conclusion
This paper presents a novel multi-objective optimization framework for UAV-assisted WSNs, addressing energy and time efficiency. The EMOPSO algorithm, integrating chaos theory, GWO, and Cauchy mutation, demonstrates superior performance in global search and solution quality. Future work may explore dynamic environments and multi-UAV coordination.