## 5 Simulation Results  
The main simulation parameters are listed in Table 1[14,16,18]. The simulation environment in this paper is based on MATLAB and is employed for computational simulation to validate the effectiveness of the proposed algorithm. It is assumed that in a square area with an extent denoted as \(500\) m \(\times\)\(500\) m, GPFs are randomly distributed. Each GPF is characterized by specific real-time and non-real-time communication throughput requirements. Three APs are assumed to fly within this area at an altitude denoted as \(H_{u}=100\) m, aiming to establish LoS communication with GPFs. Additionally, an LEO satellite serves as a cloud server data center, processing real-time power business data from GPFs. Specifically, the APs depart from a predefined starting position and, within a specified time denoted as \(T\), fulfill the communication requirements of all GPFs. The specific simulation parameters are detailed in Table 1.  
The number of algorithm iterations \(N_{\text{epi}}\), discretization state parameters \(K\) and \(L\), and distance scaling factors \(\rho\) in Tables 2 and 3 are reasonably set, taking into account factors such as the size of the simulation environment equipment, computer computing power, and simulation time. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(N\) & 10 & \(W\) & \(50\,\mathrm{kHz}\) \\ \(M\) & 3 & \(p_{max}\) & \(41\) dBm \\ \(H_{u}\) & 100 m & \(T\) & \(100\) s \\ \(v_{max}\) & 10 m/s & \(H_{s}\) & \(250\) km \\ \(g_{0}\) & \(1.4\times 10^{-4}\) & \(L_{M}\) & \(3\) \\ \(\sigmaFigure 3 depicts the flight paths of three APs in the system when accommodating 10 GPFs. It can be observed that the APs tend to move towards regions with denser GPF positions. Additionally, the three APs predominantly serve distinct groups of GPFs. As the remaining throughput requirements of GPFs change, the APs continuously adjust their positions. While meeting the demands of the majority of GPFs, efforts are made to consider GPFs with a higher remaining throughput. This indicates that through optimized flight paths, APs can enhance service provision for GPFs, consequently improving the overall system energy efficiency. In Figure 4, the variation of the overall system energy efficiency with the number of training episodes is compared under different exploration rates. To visually represent this variation more intuitively, Figure 5 averages the obtained actual energy efficiency values every 10 episodes to obtain the corresponding fluctuation curve. It can be observed in the graph that when the exploration rate is relatively high, the algorithm converges to a lower maximum energy efficiency value. However, the exploration of possible action strategies is more thorough. As the exploration rate decreases, the convergence speed of the algorithm decreases, but it can converge to higher energy efficiency values. The proposed algorithm incorporates a decreasing exploration rate with an increasing number of training episodes. It initially sacrifices energy efficiency to enhance convergence speed, and after a sufficiently thorough exploration of the policy, it converges to the globally optimal energy efficiency value, aiming to improve the algorithm's performance. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline \(N_{\text{epi}}\) & 300 \\ \(K\) & 17 \\ \(\rho\) & \(6\times 10^{-9}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Algorithm 1 simulation parameters. Figure 3: The positions of GPFs and the flight paths of APs in the simulated scenario. To illustrate the effectiveness of the proposed algorithm in this paper, the algorithm is compared with the following three algorithms:  
1. Random Path Algorithm (RP algorithm): Within the state space defined in Algorithm 1, the movement of each AP is set to move towards a random GPF in each time slot. To facilitate comparison, the device association and power control strategy of Algorithm 2 remain unchanged. 2.