# Tethered Balloon Cluster Deployments and Optimization for Emergency Communication Networks
## 5 Simulation Validations and Discussion
### Simulation Results  
Figure 2 shows the effect of MOPSO and SA on target coverage rate and system energy efficiency when the number of deployed balloons increases from 1 to 10, and both algorithms show an increasing trend. However, MOPSO consistently shows a significant advantage, with a 19.43% and 25.7% improvement in coverage and energy efficiency, respectively, compared to SA. This considerable performance difference can be explained by the properties of MOPSO and SA. MOPSO can optimize multiple conflicting objective functions simultaneously, maintaining the diversity of solutions during the search process and thus exploring the solution space more efficiently. It can quickly converge to the global optimal solution set through the information exchange between particles and the guidance of the global optimal solution. In contrast, although SA is simple, its completely stochastic nature makes it difficult to effectively utilize the structural information of the problem and often requires a large number of iterations to find a better solution in complex multi-objective optimization. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Symbol** & **Definition** & **Value** \\ \hline \(x_{min},x_{max},y_{min},y_{max}\) & Simulation area & 100 km \(\times\) 100 km \\ \(h_{min},h_{max}\) & Minimum and maximum heights of balloons & 400–1000 m \\ N & Number of balloons & 1–10 \\ \(M\) & Number of users & 100 \\ \(\Lambda\) & SINR threshold & 8 dB \\ \(f_{c}\) & Carrier frequency & 2.4 GHz \\ \(B\) & Total bandwidth & 100 MHz \\ \(c\) & The speed of light & 3 \(\times\) 108 m/s \\ \(P_{min},P_{max}\) & Minimum and maximum transmit power & 60–100 W \\ \(\eta_{LoS}\) & Additional path loss under LoS & 1 dB \\ \(\eta_{NLoS}\) & Additional path loss under NLoS & 20 dB \\ \(a\) & Environmental impact factor & 9.6 \\ \(b\) & Environmental impact factor & 0.2 \\ \(d_{min}\) & Minimum distance between adjacent balloons & 500 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Primary simulation parameters. Figure 2: Comparison of MOPSO and SA for coverage rate and energy efficiency. Figure 3 illustrates the coverage and energy efficiency versus iterations of MOPSO and SA with a fixed number of balloons of 10. The two algorithms are significantly different in terms of convergence speeds. MOPSO shows a stepwise increase, which means that it finds better solutions at each iteration step and gradually approaches the optimal solution set. After 130 and 300 iterations, the coverage and energy efficiency stabilized at 96% and 16.84 Mbps/W, respectively, which indicates that they found a deployment scheme that maximized the coverage and energy efficiency while satisfying the constraints. The coverage and energy efficiency of SA, although reaching higher values early at about 50 iterations, do not converge and continue to increase in the subsequent 300 and 500 iterations with a slightly upward trend and stabilize at 83% and 12.48 Mbps/W, respectively, after 500 iterations. Because SA generates a new solution randomly at each iteration and cannot use the previous information to guide the search direction, the convergence speed is very slow. There is a large gap between its overall performance and that of MOPSO, which shows a faster convergence speed due to its ability to use inter-particle collaboration and information sharing to search the solution space. Figure 4 depicts the final positions of ten balloons deployed and their coverage under MOPSO calculation after 1000 iterations. It can be seen that the target coverage rate at this point is 96%, which matches the data at the end of MOPSO curves in Figures 1(a) and 2(a). The high-altitude tethered balloon communication system involves several interacting objectives such as energy efficiency and coverage, and MOPSO can effectively balance these objectives to find a more optimal deployment plan. This result is of great significance for the deployment of practical systems, implying that higher system performance can be achieved with MOPSO under the same resource input.