## 7 Experimentation and Analysis  
### Algorithm Performance Validation  
In this section, the performance of the GLSOAG is verified and comparatively analyzed. The experiments are conducted to compare the GLSOAG proposed in this paper with the classical SOA, classical PSO and BSA. Simulation experiments are conducted for the four algorithms based on the classical test function set IEEE CEC2005 [32] shown in Table 4 and the algorithm iteration results are recorded in Table 5. In addition, the comparison of test function images and algorithm convergence curves are shown in Figure 9 to visualize the advantages of the algorithms in convergence speed and convergence accuracy. Due to space constraints, this section only conducts simulation experiments on test functions F1 to F12 from IEEE CEC2005, with the results for test functions F13 to F23 presented in Appendix B. Furthermore, we demonstrate the simulation results of running the 4 algorithms once on all test functions with a maximum of 500 iterations in Appendix A, to reflect a more aggressive performance comparison of the algorithms.  
Figure 9: _Cont._  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Function** & **Dim** & **Interval** & \(\mathbf{f_{min}}\) \\ \hline F1 & \(F_{1}(x)=\sum_{i=1}^{n}x_{i}^{2}\) & 30 & \([-100,100]^{n}\) & 0 \\ F2 & \(F_{2}(x)=\sum_{i=1}\lvert x_{i}\rvert+\prod_{i=1}^{n}\lvert x_{i}\rvert\) & 30 & \([-10,10]^{n}\) & 0 \\ F3 & \(F_{3}(x)=\sum_{i=1}\left(\sum_{j=1}^{i}x_{j}\right)^{2}\) & 30 & \([-100,100]^{n}\) & 0 \\ F4 & \(F_{4}(x)=\max_{i}\{\lvert x_{i}\rvert,1\leq i\leq n\}\) & 30 & \([-100,100]^{n}\) & 0 \\ F5 & \(F_{5}(x)=\sum_{i=1}^{n-1}\left[100\big{(}x_{i+1}-x_{i}^{2}\big{)}^{2}+(x_{i}- 1)^{2}\right]\) & 30 & \([-30,30]^{n}\) & 0 \\ F6 & \(F_{6}(x)=\sum_{i=1}^{n}(\lvert x_{i}+0.5\rvert)^{2}\) & 30 & \([-100,100]^{n}\) & 0 \\ F7 & \(F_{7}(x)=\sum_{i=1}^{n}x_{i}^{4}+\text{random}[0,1)\) & 30 & \([-1.28,1.28]\) & 0 \\ F8 & \(F_{8}(x)=\sum_{i=1}^{n}x_{i}\sin\left(\sqrt{\lvert x_{i}\rvert}\right)\) & 30 & \([-500,500]^{n}\) & \(-12,569.5\) \\ F9 & \(F_{9}(x)=\sum_{i=1}^{n}\left[x_{i}^{2}-10\cos(2\pi x_{i})+10\right)\big{]}\) & 30 & \([-5.12,5.12]^{n}\) & 0 \\ F10 & \(F_{10}(x)=\)20 & \(\exp\left(-0.2\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_{i}^{2}}\right)-\exp\left( \frac{1}{n}\sum_{i=1}^{n}\cos(2\pi x_{i})\right)+20+e\) & 30 & \([-32,32]\) & 0 \\ F11 & \(F_{11}(x)=\frac{1}{4000}\sum_{i=1}^{n}x_{i}^{2}-\prod_{i=1}^{n}\cos\left( \frac{x_{i}}{\sqrt{i}}\right)+1\) & 30 & \([-600,600]\) & 0 \\  & \(F_{12}(x)=\frac{x}{n}\Bigg{\{}10\sin^{2}(\pi y_{i})+\sum_{i=1}^{n-1}(y_{i}-1)^ {2}\Big{[}1+10\sin^{2}(\pi y_{i+1})\Big{]}+(y_{n}-1)^{2}\Bigg{\}}+\) & & \\ F12 & \(\sum_{i=1}^{n}u(x_{i},10,100,4)\); & 30 & \([-50,50]^{n}\) & 0 \\  & \(y_{i}=1+\frac{1}{4}(x_{i}+1);u(x_{i},a,k,m)=\begin{cases}k(x_{i}-a)m,&x_{i}>a,\\ 0,&-a\leq x_{i}\leq a,\\ k(-x_{i}-a)m,&x_{i}<-a\end{cases}\) & 30 & \([-50,50]^{n}\) & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Set of test functions [32].  
Figure 9: Algorithm effect diagram. In it, subplots F1 to F12 respectively represent the average curve variation effect diagrams of SOA, GLSOA, PSO, and BSA algorithms on test functions F1 to F12, obtained from 30 consecutive rounds of experiments with 200 iterations per round.