## 4 Analysis of Experimental Results
### Cognitive Radio Application
#### 4.2.1 IGEO Problem Solving Model
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Algorithm**} \\ \cline{2-9}  & **GWO** & **PSO** & **SCA** & **SSA** & **WOA** & **GEO** & **GEO\_DLS** & **IGEO** \\ \hline x1 & 1.5 & 0.969826 & 1.5 & 1.5 & 1.5 & 0.5 & 0.5 & 0.5 \\ x2 & 0.5 & 1.159815 & 0.5 & 0.5 & 0.5 & 1.5 & 0.5 \\ x3 & 0.5 & 0.752953 & 0.5 & 0.5 & 0.5 & 1.5 & 0.5 \\ x4 & 1.5 & 1.188875 & 1.5 & 2 & 1.5 & 1.5 & 1.5 & 0.5 \\ x5 & 0.5 & 0.650562 & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 \\ x6 & 2 & 1.4745 & 2 & 2 & 2 & 0.5 & 1.5 & 0.5 \\ x7 & 0.5 & 0.613342 & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 \\ x8 & 0.537 & 0.238309 & 0.537 & 0.537 & 0.537 & 0.345 & 0.192 & 0.192 \\ x9 & 0.192 & 0.272645 & 0.345 & 0.192 & 0.345 & 0.192 & 0.345 & 0.192 \\ x10 & 0 & \(-1.22153\) & 0 & 0 & 0 & \(-30\) & \(-30\) & \(-30\) \\ x11 & 0 & \(-4.66199\) & 0 & 0 & 0 & \(-30\) & \(-30\) & \(-30\) \\ Best & 24.425 & 27.32353 & 24.425 & 26.43 & 24.425 & 22.255 & 22.255 & 21.8829 \\ Mean & 27.7745 & 33.02376 & 24.425 & 28.02457 & 27.27683 & 23.388 & 23.058 & 22.67033 \\ Std & 1.629772 & 11.50943 & 7.23 \(\times\)\(10^{-15}\) & 1.185854 & 1.377264 & 0.950917 & 1.132364 & 0.765726 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Comparison of the best results and the statistical results obtained using different optimizers for the car side impact design problem. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**Algorithm**} \\ \cline{2-9}  & **GWO** & **PSO** & **SCA** & **SSA** & **WOA** & **GEO** & **GEO\_DLS** & **IGEO** \\ \hline x1 & 50 & 56.41491 & 50 & 50 & 50 & 10 & 10 & 10 \\ x2 & 80 & 57.61318 & 80 & 80 & 80 & 57.15807 & 10 & 34.67102 \\ x3 & 1.499999 & 1.821976 & 1.499985 & 1.5 & 1.5 & 1.494375 & 5 & 2.340662 \\ x4 & 5 & 6.412176 & 5 & 5 & 5 & 5 & 0.9 & 0.9 \\ Best & 0.012295 & 0.010767 & 0.012295 & 0.012295 & 0.001644 & 0.001644 & 0.001644 \\ Mean & 0.012295 & 0.025111 & 0.012295 & 0.012295 & 0.012295 & 0.00195 & 0.002334 & 0.001644 \\ Std & \(3.11\times 10^{-12}\) & 0.008798 & \(4.62\times 10^{-10}\) & \(1.68\times 10^{-13}\) & \(5.62\times 10^{-16}\) & 0.000216 & 0.001078 & \(8.82\times 10^{-19}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 15: Comparison of best results and the statistical results obtained using different optimizers for I beam design problem. #### 4.3.5 Three-Bar Truss Design Problem

In the classic three-bar truss engineering design problem, the aim is to minimize the weight of a symmetrical light bar structure that is subject to constraints on stress, deflection, and buckling. The mathematical model for this problem is presented in Appendix B, and the structural diagram can be found in Appendix A. Table 18 presents the results of various optimization algorithms, including GWO, PSO, SCA, SSA, WOA, GEO, and GEO_DLS, as well as the comparison algorithm GEO_DLS, and IGEO for the three-bar truss design problem. The table indicates that IGEO achieved the best results, with a minimum value of 259.8111. ## 5 Conclusions

The principle and position update formula of the original golden eagle optimization method were explored, and a hybrid golden eagle optimization algorithm (IGEO) based on Arnold mapping and nonlinear convex decreasing weight was proposed. Using 12 benchmark functions, CEC2021, and the Wilcoxon, Friedman, and Holm tests, it was confirmed that the proposed IGEO has better search performance and stronger resilience. Additionally, the impact of the single-strategy method on the algorithm was also studied. After conducting simulation tests, the enhanced IGEO was applied to the model of the traditional cognitive radio spectrum allocation problem. It was discovered that IGEO had the best overall performance, and was able to allocate the spectrum well when compared to GA, PSO, and other methods. To test the proposed IGEO's problem-solving abilities, five real-world technical design problems were also addressed, and the solutions were contrasted with other methods.