## 5 Test Experiments of Benchmark Function Sets
### Results on 30D Functions  
The proposed GLLCSA displays the lowest average value of the 30 functions, and the detailed comparison results of GLLCSA and the other eleven peers can also be seen in Table 5. In other words, the improved algorithm can obtain better results than the other algorithms on every test function. Moreover, the results of F2, F3, F5, F7, F8, F10, F14, F17, F18, F21, F23-F29 bear out the ability of this method to obtain the highest quality solutions. Compared with the other competitive algorithms, the statistical performance of GLLCSA is verified by the CEC 2014 benchmark functions. For further statistical comparison, according to the ARV index, the ranking of the 12 algorithms is shown in Table 6. According to the statistical value of ARV, when searching for the minimum value of the function, GLLCSA is better than the other methods, followed by IGWO, CGPSO, OBLGWO, PSO, BA, GWO, RCBA, CBA, MFO, SCA, and CESCA. In Table 7, the Wilcoxon signed-rank test [101] is given, which indicates whether the difference between GLLCSA and the other algorithms is significant. As can be seen from the table, the experimental results of GLLCSA have a better performance than SCA and CESCA in all test functions. In conclusion, compared with SCA, CESCA, and the other nine algorithms, the GLLCSA achieves the best results for these test functions. In addition, to display the significant advantages of GLLCSA, Figure 3 shows the convergence rates of IGWO, CGPSO, OBLGWO, PSO, BA, GWO, RCBA, CBA, MFO, SCA, and CESCA on 30 benchmarks. As shown in the figure, for the problems of F2, F3, etc., it can be seen from the convergence curve that, compared with the other algorithms, GLLCSA can improve both the convergence speed and the convergence accuracy based on the original SCA. Furthermore, the GLLCSA can reach the optimal solution when dealing with F5, F8, F10, F17, F18, F21, F27, F28, and F29. Since both F12 and F13 are multimodal functions, it is obvious to notice that there are many locally optimal solutions for these two functions. Although GLLCSA also falls into the optimal local solution, its convergence speed and accuracy are optimal when compared to the other algorithms. It is proved that \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Function** & **Dim** & **Range** & \(f_{min}\) \\ \hline \(f_{14}(x)=(\frac{1}{500}+\sum\limits_{j=1}^{25}\frac{1}{j+\sum\limits_{j=1}^{ 2}\left(x_{j}-a_{ij}\right)}^{5})\) & 2 & \([-65,65]\) & 1 \\ \hline \(f_{15}(x)=\sum\
olimits_{i=11}^{11}\left[a_{i}-\frac{x_{1}\left(b_{i}^{2}+b_{ x2}\right)}{b_{i}^{2}+b_{x3}\times 4}\right]\) & 4 & \([-5,5]\) & 0.00030 \\ \hline \(f_{16}(x)=4x_{1}^{2}-2.1x_{1}^{4}+\frac{1}{5}x_{1}^{3}+x_{1}x_{2}-4x_{2}^{2}+4 x_{2}^{4}\) & 2 & \([-5,5]\) & \(-1.0316\) \\ \hline \(f_{17}(x)=(x_{2}-\frac{5.1}{4\pi^{2}}x_{1}^{2}+\frac{5}{\pi}x_{1}-6)^{2}+10 \left(1-\frac{1}{8\pi}\right)cosx_{1}+10\) & 2 & \([-5,5]\) & 0.398 \\ \hline \(f_{18}(x)=[1+(x_{1}+x_{2}+1)^{2}(19-14x_{1}+3x_{1}^{2}\) & & & \\  \(-14x_{2}+6x_{1}x_{2}+3x_{2}^{2})]\times[30\) & 2 & \([-2,2]\) & 3 \\  \(+(2x_{1}-3x_{2})^{2}\) & & & \\  \(\times(18-32x_{1}+12x_{1}^{2}+48x_{2}\) & & & \\  \(-36x_{1}x_{2}+27x_{2}^{2})]\) & & & \\ \hline \(f_{19}(x)=-\sum\limits_{i=1}^{4}c_{i}exp(-\sum\limits_{j=1}^{3}a_{ij}\left(x_{ j}-p_{ij}\right)^{2})\) & 3 & \([1,3]\) & \(-3.86\) \\ \hline \(f_{20}(x)=-\sum\limits_{i=1}^{4}c_{i}exp(-\sum\limits_{j=1}^{6}a_{ij}\left(x_{ j}-p_{ij}\right)^{2})\) & 6 & \([0,1]\) & \(-3.32\) \\ \hline \(f_{21}(x)=-\sum\limits_{i=1}^{5}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & 4 & \([0,10]\) & \(-10.1532\) \\ \hline \(f_{22}(x)=-\sum\limits_{i=1}^{7}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & 4 & \([0,10]\) & \(-10.4028\) \\ \hline \(f_{23}(x)=-\sum\limits_{i=1}^{10}\left[(X-a_{i})(X-a_{i})^{T}+c_{i}\right]^{-1}\) & 4 & \([0,10]\) & \(-10.5363\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simple multimodal functions. the CSA based on GLL has a good exploration in avoiding LO. Therefore, the GLLCSA has more advantages than the original CSA.