## 5 Simulation and Numeric Results
### Performance  
This section compares the change trend of flight path between MAC-NSGA II, NSGAIII, and MOEA/D when the number of SDs increases from 100 to 1000. As shown in Figure 4, when the number of UAVs is 6, the longest trajectory of MAC-NSGA II is the shortest among the three algorithms, and the difference is not obvious as the network size is small. However, the longest path of the other two algorithms can be as high as 1.5 times of the proposed algorithm with the increase of network size. In terms of average growth rate, the proposed algorithm recorded about 40%, and the other two algorithms are also significantly higher, which are 47% and 48% respectively. The reason for this phenomenon is that the other two algorithms have no practical strategy to adjust the path structure, while the min-max framework is introduced into the proposed algorithm to further reduce the longest trajectory of UAVs and balance the flight load between UAVs. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(N\) & \(\{100,200,\cdots,1000\}\) & \(h_{0}\) & \((200,200)\) \\ \(\mathrm{A}(\mathrm{m}^{2})\) & 0.503 & \(v_{0}\) & 4.03 \\ \(U_{tip}(\mathrm{m/s})\) & 120 & \(d_{0}\) & 0.6 \\ \(s\) & 0.05 & \(\rho(\mathrm{kg/m}^{3})\) & 1.225 \\ \(H(\mathrm{m})\) & 20 & \(P_{how}(\mathrm{W})\) & 13.7 \\ \(V_{e}(\mathrm{m/s})\) & 10 & \(P_{move}(\mathrm{W})\) & 30 \\ \(\eta^{\prime}\) & 90\% & \(P_{tra}(\mathrm{W})\) & 3 \\ \(M(\mathrm{m}^{2})\) & \(400\times 400\) & \(p_{0}(\mathrm{dB})\) & \(-60\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters. Figures 5 and 6 also reveal the results of the longest trajectory and average trajectory at different network scales when the number of UAVs is 6, 9, 12, and 15. It is not difficult to see that the performance of the 15 UAVs in the large-scale network outperforms the other three conditions in both the longest trajectory and the average trajectory. The reason is that in a small-scale network, a handful of UAVs can realize power and information transmission. In this case, increasing UAVs can reduce the number of SDs traversed by each UAV, yet its flight trajectory cannot be significantly reduced, which is actually a wasteful strategy. Nevertheless, in a large-scale network, as the number of SDs grows exponentially, the original UAVs can only complete their missions by expanding their flight range and increasing the number of SDs serving them, which is more time-consuming and more burdensome. If the scale of UAVs is expanded, the flight load of each UAV can be reduced and the energy efficiency can be improved. Figure 7 shows the worst value and median value of the Pareto optimal solution for the average delay of the longest trajectory information collection of six UAVs under different network scales. The maximum delay of MACO-NSGA II decreases by 27.7% and 43.4% compared with NSGAIII and MOEA/D, respectively, while the median value decreases by 25.3% and 43%, respectively. The reason is that although the other two algorithms can optimize more than two targets at the same time, they do not have a separate path optimization framework. In addition, it can be found that with the increase of network size, the average time delay of the three algorithms is significantly reduced. This is because when the distribution area remains unchanged, the increase in the number of SDs means that the distribution density becomes larger, thus shortening the distance of the hovering point of a UAV. Figure 4: The longest trajectory of 6 UAVs with different algorithm. Figure 5: The longest trajectory of 6, 9, 12, and 15 UAVs. Figure 6: The average trajectory of 6, 9, 12, and 15 UAVs. Table 5 demonstrates the optimal value, worst value, mean value and median value of the energy efficiency of the longest trajectory under 20 scenarios. Due to space limitation, only the optimal and median values of the two comparison algorithms are given.