## 6 Simulation Results
### Verification of Decay Rate Mechanism  
Initially, we assessed the impact of the decay rate mechanism on the overall evolutionary process. Eight scenarios were examined through two sets of experiments: MOEA/D-MFAR with the decay rate mechanism and MOEA/D-MFAR without the decay rate mechanism (MOEA/D-MFAR-ndr). The parameter configurations for these experiments align with the specifications outlined in Table 4. The Pareto fronts (PFs) resulting from the experiments across the eight simulation scenarios are depicted in Figure 7. The red scattered points denote the performance of MOEA/D-MFAR, while the green scattered points represent MOEA/D-MFAR-ndr performance. Evidently, no matter what scenario settings, the presence of the decay rate mechanism enhances the performance of the obtained PFs. The PFs comprising red scatter points consistently appear closer to the top-right corner compared to their green counterparts. Notably, the red PFs entirely dominate the green PFs, signifying that the IoT devices achieve a higher channel rate with the aid of the decay rate mechanism. Furthermore, the red frontiers display a noticeably denser distribution than the green ones, indicating a larger number of feasible solutions. These solutions accommodate varying demand scenarios. To quantify the performance of the obtained PFs, we computed and presented the hypervolume (HV) values and the number of solutions in Table 5. HV serves as a quantitative index assessing the quality of PFs, with larger HV values indicating superior performance. All HV calculations herein use (0, 0) as the reference point. The comparative analysis reveals consistently smaller HV for MOEA/D-MFAR-ndr than for MOEA/D-MFAR, emphasizing the advantageous impact of the decay rate mechanism, and the number of feasible solutions will be greatly increased, aided by the decay rate mechanism. The HV values corresponding to each epoch are logged and illustrated in Figure 8. This approach allows for the visualization of PF performance and facilitates the observation of the convergence process. The red curves depict the HV fluctuations for the algorithm incorporating a decay rate mechanism, whereas the green curves represent the algorithm devoid of a decay rate mechanism. Evidently, in comparison to the red curves, the red curves ultimately attain a higher HV value, indicating a faster convergence speed. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Height of UAV and LEO satellite & 100 m, 1000 km \\ System bandwidth \(B\) & 1 MHz \\ Channel gain per unit distance \(g_{0}\) & \(1.42\times 10^{-4}\) \\ Total transmission power of UAV \(P^{U}\) & 50 W \\ Transmission power of IoT device \(P^{I}\) & 1 W \\ Noise power spectral density \(N_{0}\) & \(-174\) dBm/Hz \\ Population size \(M\) & 100 for scenarios 1,2,3,4 \\  & 120 for scenarios 5,6,7,8 \\ Iteration steps \(E\) & 100 \\ Neighborhood Size \(S\) & 5 \\ \(c_{1},c_{2},c_{3},c_{4}\) & 0.1, 0.5, 0.5, 0.5 \\ Base of decay rate \(b\) & 0.8 for scenarios 1,3,5,7 \\  & 0.7 for scenarios 2,4,6,8 \\ \(PB_{um},PB_{dm},PB_{cm}\) & 0.5, 0.5, 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation parameters. Figure 7: PFs obtained by MOEA/D-MFAR and MOEA/D-MFAR-ndr. **(a)** Scenario 1. **(b)** Scenario 2. **(c)** Scenario 3. **(d)** Scenario 4. **(e)** Scenario 5. **(f)** Scenario 6. **(g)** Scenario 7. **(h)** Scenario 8. Moreover, to assess the fairness of resource allocation among IoT devices of the same type, we computed the average standard deviation of the channel rate (ASDR) and present the results in Table 6. For the \(t\)-th type of IoT devices, \(n\in\{1,\ldots,N_{t}\}\), the ASDR calculation formula is described as Formula (36), where \(N_{s}\) is the number of solutions in EP, and  
Figure 8: HV curves of MOEA/D-MFAR and MOEA/D-MFAR-ndr in eight scenarios. (**a**) Scenario 1. (**b**) Scenario 2. (**c**) Scenario 3. (**d**) Scenario 4. (**e**) Scenario 5. (**f**) Scenario 6. (**g**) Scenario 7. (**h**) Scenario 8.  
is the sequence number of the solution.