## 6 Simulation Results  
### Experimental Settings  
The robustness and effectiveness of the proposed algorithm will be validated in this section. In the context of real-world applications, the deployment of UAVs and IoT devices is subject to variability in terms of quantity, device types, and geographical distribution, contingent upon the specific mission requirements. To enhance the realism of the simulation and to assess the robustness of the proposed algorithm, it is imperative to consider adiverse range of scenarios. Hence, multiple scenarios are introduced and listed in Table 3, totaling eight scenarios. Two distinct IoT-device-distribution characteristics are presented in Figure 6. Specifically, scenarios 1, 2, 5, and 6 exhibit sparse IoT device distribution, while scenarios 3, 4, 7, and 8 feature dense distribution. The number of IoT device types is set to 2 and 3, addressing dual-objective and three-objective optimization, respectively. For three-objective problems (scenarios 5-8), the expansion of solution space dimensions results in a wider spread of optimal solutions, elevating search difficulty. Thus, the population size \(M\) is increased to enhance solution space exploration. The number of different types of IoT devices varies in each scenario, as detailed in Table 3. For the number of UAVs, 1 and 3 are set. It is important to note that when the number of UAV is 1, there is no need to consider the association selection of UAV relay by IoT devices. In scenarios with three UAVs (scenarios 2, 4, 6, and 8), the search for optimal solutions becomes more challenging. To address this, the base of decay rate \(b\) is decreased to improve search precision in the solution space, with its value determined through rigorous pre-experimental analysis. Other simulation parameters are outlined in Table 4. The environmental parameters were set based on references from the relevant literature [29; 44; 45], while the algorithm parameters were determined through multiple preliminary experiments to obtain relatively reasonable values. All simulation experiments were conducted utilizing Python 3.9, with the subsequent visualization of results executed through the Matplotlib library. Furthermore, portions of the experimental content in this paper have previously appeared in a conference paper [46]. However, the scope was limited to just two experimental scenarios, two comparative algorithms, two objective functions, and a single number of UAVs, neglecting the correlation between UAVs and IoT devices. In order to verify the effectiveness of the algorithm, MOEA/D-MFAR was compared with three classic multi-objective optimization algorithms. The benchmark algorithms used in our study are as follows:  
* MOEA/D: As originally proposed [40], it employs a genetic algorithm for solution generation. This algorithm is also applied to similar SAGIN [32] scenarios. * NSGA-II [47]: The Non-dominated Sorting Genetic Algorithm II (NSGA-II), which includes an elite screening mechanism and a rapid non-dominated sorting technique, is utilized to ensure convergence while preserving search efficiency. This algorithm is also integrated into comparative experiments within the context of airship observation ground missions [39]. * MOPSO [48]: Multi-objective Particle Swarm Optimization (MOPSO), a variant of the Particle Swarm Optimization algorithm, is specifically designed to tackle multi \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Number of Types of IoT** & \multirow{2}{*}{**Number of UAV**} & **Distribution** & **The Respective Quantities of Different Types of IoT Devices** \\  & **Devices** & & **of IoT Devices** & **of IoT Devices** \\ \hline
1 & 2 & 1 & sparse & 10, 10 \\
2 & 2 & 3 & sparse & 10, 10 \\
3 & 2 & 1 & dense & 10, 6 \\
4 & 2 & 3 & dense & 10, 6 \\
5 & 3 & 1 & sparse & 10, 10, 10 \\
6 & 3 & 3 & sparse & 10, 10, 10 \\
7 & 3 & 1 & dense & 10, 8, 6 \\
8 & 3 & 3 & dense & 10, 8, 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Details of the eight scenarios. objective problems.