## 3 Experimental Results and Discussion
### Computational Time and Space Complexity Analyses  
The total amount of memory used by an algorithm points out the space complexity of that algorithm through the optimization process. The Big O notation of GSLEO-AEFA space complexity can be considered as O (Maxiteration \(\times\)\(N\)\(\times\)\(D\)) where Maxiteration is the number of iterations, \(N\) is the number of agents in the population and \(D\) is the dimension.  
With respect to the computational time, GSLEO-AEFA and the counterpart algorithms are analyzed and the results are shown in Table 8. Out of 23 benchmark functions analyzed,  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Test** & **Dimension** & **GSLEO-AEFA** & **AEFA** & **PSO** & **DE** & **JAYA** & **SCA** & **CS** \\ \hline [PERSON] value & 30 & 1.7 & 4.74 & 4.3 & 3.35 & 5.07 & 5.33 & 3.52 \\ [PERSON] rank & & 1 & 5 & 4 & 2 & 6 & 7 & 3 \\ \hline [PERSON] value & 50 & 1.31 & 5.69 & 3.31 & 3.69 & 4 & 5.92 & 4.08 \\ [PERSON] rank & & 1 & 6 & 2 & 3 & 4 & 7 & 5 \\ \hline [PERSON] value & 100 & 1 & 5.69 & 3.08 & 4.62 & 3.69 & 5.77 & 4.15 \\ [PERSON] rank & & 1 & 6 & 2 & 5 & 3 & 7 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Friedman test for dimension 30, 50, and 100 dimensions for 20 functions.  
for 22 functions, GSLEO-AEFA needs higher CPU time than the others. As a consequence of its hybrid nature, the algorithm GSLEO-AEFA requires more time to figure out the optimization. On the other hand, in terms of precise solutions, GSLEO-AEFA produces high quality results and a researcher may negotiate between the high solution quality and the computational time depending on the problem specifications.  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline  & **GSLEO-AEFA** & **AEFA** & **PSO** & **DE** & **JAYA** & **SCA** & **CS** \\ \hline F1 & **23.990** & 23.874 & 40.696 & 1.801 & 10.423 & 10.757 & 9.059 \\ \hline F2 & 23.468 & **23.744** & 37.481 & 1.889 & 10.821 & 11.391 & 9.719 \\ \hline F3 & **30.354** & 26.628 & 14.308 & 4.643 & 7.535 & 14.579 & 15.415 \\ \hline F4 & **25.580** & 23.877 & 11.405 & 1.593 & 2.984 & 10.922 & 9.229 \\ \hline F5 & **25.433** & 24.087 & 11.716 & 1.926 & 3.235 & 11.538 & 9.476 \\ \hline F6 & **32.218** & 23.863 & 11.717 & 1.811 & 3.135 & 11.492 & 9.388 \\ \hline F7 & **26.256** & 24.369 & 12.371 & 2.109 & 3.374 & 11.440 & 9.427 \\ \hline F8 & **25.878** & 24.007 & 12.553 & 1.805 & 3.158 & 11.541 & 9.496 \\ \hline F9 & **25.843** & 24.081 & 11.327 & 1.857 & 3.075 & 10.961 & 9.703 \\ \hline F10 & **54.693** & 24.279 & 12.558 & 2.208 & 3.476 & 11.874 & 33.917 \\ \hline F11 & **92.284** & 24.405 & 12.796 & 2.244 & 3.545 & 21.765 & 36.307 \\ \hline F12 & **90.376** & 25.107 & 13.412 & 3.071 & 4.267 & 12.985 & 37.827 \\ \hline F13 & **28.186** & 25.230 & 13.675 & 3.263 & 4.528 & 12.889 & 11.843 \\ \hline F14 & **27.039** & 15.286 & 12.312 & 12.026 & 10.989 & 12.206 & 21.921 \\ \hline F15 & **8.413** & 6.382 & 2.331 & 1.406 & 0.968 & 2.211 & 2.726 \\ \hline F16 & **6.080** & 4.495 & 0.983 & 0.740 & 0.312 & 0.911 & 1.224 \\ \hline F17 & **6.240** & 4.504 & 1.017 & 0.762 & 0.331 & 0.947 & 1.290 \\ \hline F18 & **6.562** & 4.608 & 1.084 & 0.856 & 0.414 & 1.027 & 1.444 \\ \hline F19 & **9.443** & 6.186 & 2.421 & 1.785 & 1.328 & 2.296 & 3.366 \\ \hline F20 & **11.910** & 8.449 & 3.723 & 1.913 & 1.719 & 3.529 & 4.399 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Computational time comparison, high values are in bold.  
Figure 5: Diversity plots for GSLEO-AEFA and AEFA for the unimodal functions F1, F2 and the multimodal functions F10, F12.