## 4 Analysis of Experimental Results
### Simulation Experiment
#### 4.1.3 Statistical Significance Testing
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fun No.**} & \multicolumn{2}{c}{**BOA**} & \multicolumn{2}{c}{**GWO**} & \multicolumn{2}{c}{**PSO**} & \multicolumn{2}{c}{**SCA**} \\ \cline{2-10}  & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** \\ \hline F1 & \(1.80\times 10^{-14}\) & \(7.59\times 10^{-16}\) & \(2.55\times 10^{-34}\) & \(5.00\times 10^{-34}\) & \(9.66\times 10^{-1}\) & \(9.73\times 10^{-1}\) & \(4.16\times 10^{3}\) & \(2.98\times 10^{3}\) \\ F2 & \(2.52\times 10^{99}\) & \(1.08\times 10^{90}\) & \(7.94\times 10^{-21}\) & \(4.65\times 10^{-21}\) & \(6.07\times 10^{-2}\) & \(2.53\times 10^{9}\) & \(1.42\times 10^{9}\) & \(1.98\times 10^{9}\) \\ F3 & \(1.11\times 10^{-14}\) & \(5.64\times 10^{-15}\) & \(1.32\times 10^{-3}\) & \(5.92\times 10^{-3}\) & \(1.31\times 10^{-2}\) & \(7.07\times 10^{-3}\) & \(3.78\times 10^{1}\) & \(2.83\times 10^{1}\) \\ F4 & \(1.14\times 10^{-11}\) & \(3.99\times 10^{-13}\) & \(7.01\times 10^{-14}\) & \(5.09\times 10^{-15}\) & \(2.29\times 10^{9}\) & \(3.26\times 10^{-1}\) & \(1.90\times 10^{1}\) & \(4.51\times 10^{9}\) \\ F5 & \(3.32\times 10^{1}\) & \(2.45\times 10^{0}\) & \(3.00\times 10^{1}\) & \(6.44\times 10^{0}\) & \(1.16\times 10^{0}\) & \(9.13\times 10^{-2}\) & \(1.87\times 10^{1}\) & \(1.13\times 10^{9}\) \\ F6 & \(2.36\times 10^{-8}\) & \(1.67\times 10^{-7}\) & \(3.66\times 10^{-1}\) & \(1.88\times 10^{0}\) & \(4.02\times 10^{2}\) & \(5.38\times 10^{1}\) & \(2.22\times 10^{2}\) & \(1.15\times 10^{2}\) \\ F7 & \(3.29\times 10^{-1}\) & \(2.96\times 10^{-2}\) & \(2.60\times 10^{-1}\) & \(4.95\times 10^{-2}\) & \(1.30\times 10^{9}\) & \(8.69\times 10^{-2}\) & \(8.08\times 10^{9}\) & \(2.86\times 10^{9}\) \\ F8 & \(1.06\times 10^{-29}\) & \(2.55\times 10^{-30}\) & \(2.87\times 10^{-41}\) & \(6.96\times 10^{-41}\) & \(1.19\times 10^{-42}\) & \(8.93\times 10^{-44}\) & \(9.62\times 10^{-29}\) & \(3.19\times 10^{-28}\) \\ \hline \multicolumn{10}{c}{**SSA**} & \multicolumn{2}{c}{**WOA**} & \multicolumn{2}{c}{**GEO**} & \multicolumn{2}{c}{**IGEO**} \\ \cline{2-10}  & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** \\ \hline F1 & \(9.86\times 10^{-3}\) & \(7.53\times 10^{-3}\) & \(5.55\times 10^{-170}\) & 0 & \(6.94\times 10^{-1}\) & \(1.47\times 10^{-1}\) & 0 & 0 \\ F2 & \(1.38\times 10^{1}\) & \(4.25\times 10^{0}\) & \(8.93\times 10^{-108}\) & \(4.34\times 10^{-107}\) & \(7.88\times 10^{9}\) & \(1.77\times 10^{9}\) & 0 & 0 \\ F3 & \(1.18\times 10^{-1}\) & \(2.42\times 10^{-2}\) & \(4.34\times 10^{-3}\) & \(2.17\times 10^{-2}\) & \(4.14\times 10^{-1}\) & \(6.60\times 10^{-2}\) & 0 & 0 \\ F4 & \(5.25\times 10^{0}\) & \(1.42\times 10^{0}\) & \(4.01\times 10^{-15}\) & \(2.55\times 10^{-15}\) & \(3.95\times 10^{9}\) & \(4.67\times 10^{-1}\) & \(8.88\times 10^{-16}\) & 0 \\ F5 & \(1.06\times 10^{1}\) & \(3.70\times 10^{9}\) & \(9.50\times 10^{-1}\) & \(9.03\times 10^{-2}\) & \(7.14\times 10^{9}\) & \(1.13\times 10^{9}\) & \(9.00\times 10^{-1}\) & \(2.24\times 10^{-16}\) \\ F6 & \(1.34\times 10^{2}\) & \(3.27\times 10^{1}\) & 0 & 0 & \(4.01\times 10^{1}\) & \(5.67\times 10^{9}\) & 0 & 0 \\ F7 & \(5.92\times 10^{0}\) & \(6.35\times 10^{-1}\) & \(1.38\times 10^{-1}\) & \(7.79\times 10^{-2}\) & \(2.41\times 10^{9}\) & \(2.26\times 10^{-1}\) & 0 & 0 \\ F8 & \(1.82\times 10^{-42}\) & \(1.54\times 10^{-42}\) & \(-3.60\times 10^{-1}\) & \(4.85\times 10^{-1}\) & \(1.18\times 10^{-42}\) & \(1.42\times 10^{-44}\) & \(-1.00\times 10^{9}\) & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of the test results of IGEO and other advanced algorithms (dim = 100). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Fun No. **} & \multirow{2}{*}{**Items**} & \multirow{2}{*}{**Min**} & \multirow{2}{*}{**Max**} & \multirow{2}{*}{**Std**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**Non.