# The Optimization of UAV-Assisted Downlink Transmission Based on RSMA
## 5 Simulation Analysis
### Simulation Analysis of MD-AFSA Algorithm Performance  
In this study, the AFSA algorithm is improved and designed, and the MD-AFSA algorithm is proposed to improve the optimization ability and convergence speed of the algorithm, and realize the optimal solution of UAV deployment position. In the experiment, some test functions introduced in reference [26] are selected to analyze and compare the performance of the algorithm. The information of the selected test functions is shown in Tables 1 and 2. The standard AFSA and the dynamic strategy and memory strategy proposed in this paper are tested on the test functions in Tables 1 and 2, respectively. Figure 3 shows the test results of single extreme function. In Figure 3, AFSA represents the standard artificial fish school algorithm, M-AFSA represents the memory strategy proposed in this paper to the standard artificial fish school algorithm, D-AFSA represents the dynamic step size and dynamic field strategy proposed in this paper to the standard artificial fish school algorithm, and MD-AFSA represents the dynamic memory fish school algorithm proposed in this paper. According to Figure 3, it can be seen that D-AFSA usually has a good convergence speed in the early stage of algorithm iteration, but the convergence speed is even lower than that of AFSA in the late stage of algorithm iteration; compared with D-AFSA and AFSA, M-AFSA can achieve faster convergence speed and lower error; the convergence speed of MD-AFSA in the iteration process of algorithm is close to that of M-AFSA (slightly lower in the early stage of F3), but it has a lower error. The final error of three single-extreme functions after 100 iterations using different optimization algorithms is shown in Table 3. In this test, the error is defined as the difference between the sought objective function value and the actual minimum value. On the F1 function, the solution error of MD-AFSA is reduced by 99.63% \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **Function Expression** & **Range** & **Minimum Value** \\ \hline Step & \(F_{1}(x)=\sum\limits_{i=1}^{D}{(x_{i}+0.5)^{2}}\) & \([-100,100]^{D}\) & 0 \\ Schwefel 2.22 & \(F_{2}(x)=\sum\limits_{i=1}^{D}{|x_{i}|}+\prod\limits_{i=1}^{D}{|x_{i}|}\) & \([-10,10]^{D}\) & 0 \\ Cigar & \(F_{3}(x)=x_{1}^{2}+10^{6}\sum\limits_{i=2}^{D}{x_{i}^{6}}\) & \([-100,100]^{D}\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Single extremum test function. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Function** & **Function Expression** & **Range** & **Minimum Value** \\ \hline Himmelblau & \(F_{4}(x)=\frac{1}{D}\sum\limits_{i=1}^{D}{\left(x_{i}^{4}-16x_{i}^{2}+5x_{i} \right)}\) & \([-5,5]^{D}\) & \(-78.3326\) \\ Schaffer & \(F_{5}(x)=0.5+\frac{\left(sin{\left\langle\sum_{i=1}^{D}x_{i}^{2}\right\rangle} ^{2}-0.5}{\left(1+0.001\left(\sum_{i=1}^{D}x_{i}^{2}\right)\right)^{2}}\) & \([-100,100]^{D}\) & 0 \\ Alpine & \(F_{6}(x)=\frac{D}{i=1}{|x_{i}\sin(x_{i})+0.1x_{i}|}\) & \([-10,10]^{D}\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multi-extremum test function. Figure 3: Single Extremum Function Test. compared with AFSA; on the F2 function, the solution error of MD-AFSA is reduced by 98.68% compared with AFSA; on the F3 function, the solution error of MD-AFSA is reduced by 91.76% compared with AFSA. In Figure 4, the meaning of each curve is consistent with that of Figure 3. In the multi-extreme function test, D-AFSA still performs poorly, even lower than the standard AFSA algorithm; M-AFSA and MD-AFSA have better performance than AFSA and D-AFSA; On the basis of M-AFSA, MD-AFSA incorporates dynamic step size and dynamic field of view strategies, which is conducive to faster convergence and algorithm optimization. The final errors of the three multi-extreme functions after 100 iterations using different optimization algorithms are shown in Table 4. The analysis shows that MD-AFSA has the lowest error only in all test functions.