## 4 Analysis of Experimental Results
### Simulation Experiment
#### 4.1.4 Comparative Analysis of Different Strategy Algorithms  
To explore the effectiveness of the proposed algorithm and study the impact of different strategies on the golden eagle optimizer algorithm, ablation experiments were conducted. GEO with a single strategy includes GEO with nonlinear weights (wGEO) and GEO with global optimization strategy (pGEO). The experimental parameter settings were consistent with those presented in Table 3. The experimental algorithms included GEO, wGEO, pGEO, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & **CMA-ES-RIS** & **FMMPA** & **EIW\_PSO** & **L-SHADE** & **GEO\_DLS** & **IGEO** \\ \hline Value & 4.10 & 1.60 & 5.10 & 3.50 & 3.80 & 2.90 \\ Rank & 5 & 1 & 6 & 3 & 4 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: [PERSON] ranking under CEC2021 comparison. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(i\) & **Sample 1 vs. Sample 2** & \begin{tabular}{c} **–** \\ **z** \\ \end{tabular} & \begin{tabular}{c} **–** \\ **p** \\ \end{tabular} & \begin{tabular}{c} **–** \\ **\alpha/i** \\ \end{tabular} & \
\begin{tabular}{c} **Null Hypothesis (Ho)** \\ \end{tabular} &
\begin{tabular}{c} **Conclusion** \\ **\end{tabular} \\ \hline
1 & IGEO-L-SHADE & 0.600 & 0.473289 & 0.05 & & \\
2 & IGEO-GEO\_DLS & 0.900 & 0.282059 & 0.025 & All algorithms have & Ho accepted for \(\alpha=5\%\) \\
3 & IGEO-CMA-ES-RIS & 1.200 & 0.151494 & 0.016667 & similar distributions & since \(\overline{p}>\alpha/\)i \\
4 & IGEO-FMMPA & 1.300 & 0.120233 & 0.0125 & with little difference & Ho rejected for \(\alpha=5\%\) \\
5 & IGEO-EIN\_PSO & 2.200 & 0.008551 & 0.01 & & since \(\overline{p}<\alpha/\)i \\  & N & 10 & \(\chi^{2}\) & 19.943 & \\  & Free degree & 5 & \(p\)-value & \(<\)0.05 & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Subsequent Holm verification results for all algorithms under CEC2021. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **CMA-ES-RIS** & **FMMPA** & **EIW\_PSO** & **L-SHADE** & **GEO\_DLS** & **IGEO** \\ \hline Value & 4.10 & 1.60 & 5.10 & 3.50 & 3.80 & 2.90 \\ Rank & 5 & 1 & 6 & 3 & 4 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: [PERSON] ranking under CEC2021 comparison. and IGEO. Each algorithm was independently run 50 times on each of the 12 test functions selected in this article. The experimental results are presented in Table 13.  
The results presented in Table 13 indicate that the optimization accuracy when using a nonlinear convex decreasing weight strategy or a global optimization strategy individually is inferior to that when using the mixed strategy, with a significant difference in optimization accuracy despite having the same running time. For F1, F2, F7, F9, and F11, IGEO demonstrated absolute superiority, achieving the highest optimization accuracy. For F3 to F6, wGEO, pGEO, and IGEO exhibited similar search accuracy, which was significantly better than that of GEO. For F8, F10, and F12, pGEO and IGEO exhibited similar performance. To verify the performance of IGEO in terms of convergence speed and search accuracy, Figure 6 presents the average convergence curves of the benchmark functions. Similarly, since the optimal value of function F8 is \(-1\), the absolute value of all results is taken when drawing the visualization. Compared with wGEO and pGEO, IGEO exhibits faster convergence on F3 to F6, although the convergence precision is the same. IGEO and pGEO achieve identical performance on F8. For F10 and F12, IGEO demonstrates a slight advantage in terms of convergence speed, while the average optimal value and standard deviation are close to the theoretical optimal value. Furthermore, IGEO performs optimally on the other functions. Combining the exploration of the value of m described in Section 3.2 and the two numerical experiments reported in Sections 4.1.2 and 4.1.3, it can be concluded that the nonlinear convex decreasing weight mainly affects the convergence speed of the algorithm, indicating the algorithm's ability to perform exploration.