## 10 Experimental Analysis
### Statistical Comparisons on CEC2014 Problems
#### 10.1.2 Analyzing the Effectiveness of the Proposed Hybridization
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ICDEBOA**} & \multicolumn{2}{c}{**HFSODOA**} & \multicolumn{2}{c}{**JIDE**} & \multicolumn{2}{c}{**BOA**} & \multicolumn{2}{c}{**SHADE**} \\ \hline  & & & & **Mean STD Sign** & & \\ \hline \multirow{3}{*}{\(f_{1}\)} & 10 & \(7.80\times 10^{-25}\) (\(8.67\times 10^{-15}\)) & \(2.51\times 10^{6}\) (\(1.22\times 10^{68}\))- & \(2.24\times 10^{6}\) (\(2.59\times 10^{6}\))- & \(2.76\times 10^{6}\) (\(2.10\times 10^{6}\))- & \(2.02\times 10^{6}\) (\(1.15\times 10^{6}\))- \\  & 30 & \(1.28\times 10^{4}\) (\(1.04\times 10^{4}\)) & \(1.28\times 10^{4}\) (\(1.03\times 10^{4}\))- & \(5.80\times 10^{7}\) (\(3.57\times 10^{7}\))- & \(1.62\times 10^{6}\) (\(5.33\times 10^{6}\))- & \(2.32\times 10^{6}\) (\(6.41\times 10^{7}\))- \\  & 50 & \(1.28\times 10^{4}\) (\(1.04\times 10^{4}\)) & \(1.24\times 10^{4}\) (\(3.15\times 10^{4}\))- & \(5.80\times 10^{7}\) (\(3.57\times 10^{7}\))- & \(1.62\times 10^{6}\) (\(5.33\times 10^{7}\))- & \(2.32\times 10^{6}\) (\(6.41\times 10^{7}\))- \\  & 50 & \(1.28\times 10^{4}\) (\(1.04\times 10^{4}\)) & \(1.24\times 10^{4}\) (\(3.15\times 10^{4}\))- & \(5.80\times 10^{7}\) (\(3.57\times 10^{7}\))- & \(1.62\times 10^{6}\) (\(5.33\times 10^{7}\))- & \(2.32\times 10^{6}\) (\(6.41\times 10^{7}\))- \\  & 100 & \(4.74\times 10^{4}\) (\(5.91\times 10^{4}\)) & \(4.74\times 10^{4}\) (\(5.19\times 10^{4}\))- & \(3.13\times 10^{4}\) (\(1.25\times 10^{7}\))- & \(4.47\times 10^{4}\) (\(6.49\times 10^{4}\))- & \(8.87\times 10^{4}\) (\(6.11\times 10^{7}\))- \\ \hline \multirow{3}{*}{\(f_{2}\)} & 10 & \(0.00\times 10^{0}\) (\(0.00\times 10^{5}\)) & \(1.22\times 10^{4}\) (\(2.28\times 10^{7}\))- & \(2.69\times 10^{3}\) (\(8.31\times 10^{7}\))- & \(2.78\times 10^{6}\) (\(2.42\times 10^{6}\))- & \(3.04\times 10^{5}\) (\(1.60\times 10^{7}\))- \\  & 30 & \(2.46\times 10^{-3}\) (\(1.01\times 10^{-3}\)) & \(9.79\times 10^{4}\) (\(1.49\times 10^{4}\))- & \(5.20\times 10^{6}\) (\(3.36\times 10^{7}\))- & \(9.79\times 10^{4}\) (\(1.49\times 10^{4}\))- & \(2.74\times 10^{4}\) (\(9.07\times 10^{7}\))- \\  & 50 & \(2.46\times 10^{-3}\) (\(1.01\times 10^{-3}\)) & \(1.90\times 10^{4}\) (\(2.41\times 10^{4}\))- & \(5.20\times 10^{6}\) (\(3.36\times 10^{7}\))- & \(9.79\times 10^{4}\) (\(1.49\times 10^{4}\  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{2}{c}{**ICDEBOA**} & **HPSOBOA** & **jDE** & **BOA** & **SHADE** \\ \hline \multirow{3}{*}{\(f_{5}\)} & 10 & \(4.16\times 10^{-1}(1.04\times 10^{-1})\) & \(4.86\times 10^{9}(2.37\times 10^{9})\)- & \(1.00\times 10^{9}(2.82\times 10^{9})\)- & \(2.01\times 10^{9}(2.15\times 10^{9})\)- & \(5.65\times 10^{9}(9.89\times 10^{-1})\)- \\  & 30 & \(1.97\times 10^{1}(5.86\times 10^{9})\) & \(1.48\times 10^{9}(3.72\times 10^{9})\)- & \(4.91\times 10^{9}(8.53\times 10^{9})\)- & \(8.49\times 10^{9}(3.97\times 10^{9})\)- & \(5.92\times 10^{10}(8.10\times 10^{9})\)- \\  & 50 & \(1.97\times 10^{1}(5.86\times 10^{9})\) & \(1.48\times 10^{9}(3.72\times 10^{9})\)- & \(4.91\times 10^{9}(8.53\times 10^{9})\)- & \(8.49\times 10^{9}(3.97\times 10^{9})\)- & \(5.92\times 10^{10}(8.10\times 10^{9})\)- \\  & 100 & \(1.28\times 10^{9}(3.03\times 10^{9})\) & \(4.46\times 10^{9}(5.50\times 10^{9})\)- & \(1.38\times 10^{9}(9.85\times 10^{9})\)- & \(7.84\times 10^{9}(2.81\times 10^{9})\)- & \(2.12\times 10^{9}(15.85\times 10^{9})\)- \\ \hline \multirow{3}{*}{\(f_{76}\)} & 10 & \(3.87\times 10^{-1}(2.67\times 10^{-1})\) & \(3.70\times 10^{9}(6.83\times 10^{-2})\)- & \(6.83\times 10^{9}(5.79\times 10^{-1})\)- & \(2.80\times 10^{9}(2.03\times 10^{-1})\)- & \(4.15\times 10^{9}(2.00\times 10^{-1})\)- \\  & 30 & \(1.72\times 10^{9}(4.31\times 10^{-1})\) & \(2.32\times 10^{1}(5.31\times 10^{-2})\)- & \(1.95\times 10^{9}(9.41\times 10^{-1})\)- & \(2.22\times 10^{9}(1.81\times 10^{-1})\)- & \(2.39\times 10^{9}(2.54\times 10^{-1})\)- \\  & 50 & \(1.72\times 10^{9}(4.31\times 10^{-1})\) & \(2.32\times 10^{1}(5.31\times 10^{-2})\)- & \(1.95\times 10^{9}(4.10\times 10^{-1})\)- & \(2.22\times 10^{1}(1.81\times 10^{-1})\)- & \(2.39\times 10^{9}(2.54\times 10^{-1})\)- \\  & 100 & \(4.02\times 10^{1}(5.16\times 10^{-1})\) & \(4.76\times 10^{1}(1.65\times 10^{-1})\)- & \(4.35\times 10^{1}(1.27\times 10^{9})\)- & \(4.46\times 10^{1}(2.31\times 10^{-1})\)- & \(4.85\times 10^{9}(3.34\times 10^{-1})\)- \\ \hline \multirow{3}{*}{\(f_{77}\)} & 10 & \(9.66\times 10^{1}(7.45\times 10^{1})\) & \(6.57\times 10^{9}(2.29\times 10^{9})\)- & \(4.25\times 10^{9}(3.01\times 10^{9})\)- & \(1.28\times 10^{9}(3.00\times 10^{9})\)- & \(4.78\times 10^{9}(5.45\times 10^{9})\)- \\  & 30 & \(2.12\times 10^{9}(3.03\times 10^{9})\) & \(8.49\times 10^{9}(2.51\times 10^{9})\)- & \(2.93\times 10^{9}(2.81\times 10^{9})\)- & \(7.92\times 10^{9}(5.10\times 10^{9})\)- & \(4.56\times 10^{9}(1.86\times 10^{9})\)- \\  & 50 & \(2.12\times 10^{9}(3.35\times 10^{9})\) & \(8.89\times 10^{9}(2.51\times 10^{9})\)- & \(2.93\times 10^{9}(2.81\times 10^{9})\)- & \(7.92\times 10^{9}(5.10\times 10^{9})\)- & \(4.56\times 10^{9}(1.86\times 10^{9})\)- \\  & 100 & \(6.85\times 10^{9}(3.36\times 10^{9})\) & \(2.86\times 10^{9}(4.30\times 10^{9})\)- & \(2.38\times 10^{9}(1.17\times 10^{9})\)- & \(6.68\times 10^{9}(2.88\times 10^{9})\)- & \(1.89\times 10^{9}(6.03\times 10^{9})\)- \\ \hline \multirow{3}{*}{\(f_{8}\)} & 10 & \(4.65\times 10^{9}(4.33\times 10^{9})\) & \(1.96\times 10^{9}(2.80\times 10^{9})\)- & \(4.40\times 10^{9}(5.30\times 10^{9})\)- & \(4.14\times 10^{9}(1.99\times 10^{9})\)- & \(1.92\times 10^{9}(2.70\times 10^{9})\)- \\  & 30 & \(6.75\times 10^{9}(7.08\times 10^{9})\) & \(2.98\times 10^{9}(1.08\times 10^{9})\)-  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ICDEBOA**} & \multicolumn{2}{c}{**HPSOBOA**} & \multicolumn{2}{c}{**JDE**} & \multicolumn{2}{c}{**BOOA**} & \multicolumn{2}{c}{**SHADE**} \\ \hline \multicolumn{6}{c}{**Mean (STD) Sign**} \\ \hline \multirow{3}{*}{\(f_{22}\)} & 10 & \(2.17\times 10^{-1}\) (\(1.85\times 10^{-1}\)) & \(6.45\times 10^{2}\) (\(1.99\times 10^{5}\)) & \(6.11\times 10^{1}\) (\(5.32\times 10^{1}\)) & \(5.66\times 10^{1}\) (\(1.51\times 10^{1}\)) & \(-1.43\times 10^{2}\) (\(1.07\times 10^{1}\)) \\  & 30 & \(3.97\times 10^{2}\) (\(1.05\times 10^{2}\)) & \(2.87\times 10^{2}\) (\(2.2\times 10^{2}\)) & \(7.20\times 10^{2}\) (\(3.24\times 10^{2}\)) & \(6.27\times 10^{2}\) (\(4.31\times 10^{2}\)) & \(2.76\times 10^{2}\) (\(3.29\times 10^{2}\)) \\  & 50 & \(3.97\times 10^{2}\) (\(1.50\times 10^{2}\)) & \(2.87\times 10^{2}\) (\(1.22\times 10^{2}\)) & \(7.20\times 10^{2}\) (\(3.24\times 10^{2}\)) & \(6.27\times 10^{2}\) (\(4.31\times 10^{2}\)) & \(2.76\times 10^{2}\) (\(3.29\times 10^{2}\)) \\  & 100 & \(1.47\times 10^{2}\) (\(3.58\times 10^{2}\)) & \(5.47\times 10^{2}\) (\(7.45\times 10^{2}\)) & \(1.80\times 10^{3}\) (\(6.15\times 10^{2}\)) & \(2.57\times 10^{2}\) (\(2.61\times 10^{2}\)) & \(6.24\times 10^{2}\) (\(5.61\times 10^{2}\)) \\ \hline \multirow{3}{*}{\(f_{23}\)} & 10 & \(-4.03\times 10^{2}\) (\(1.00\times 10^{2}\)) & \(-5.33\times 10^{2}\) (\(2.91\times 10^{-4}\)) & \(-4.02\times 10^{2}\) (\(2.83\times 10^{2}\)) & \(-5.33\times 10^{2}\) (\(4.51\times 10^{2}\)) & \(-4.03\times 10^{2}\) (\(5.60\times 10^{2}\)) \\  & 50 & \(-5.07\times 10^{2}\) (\(4.98\times 10^{-12}\)) & \(-5.21\times 10^{2}\) (\(1.39\times 10^{-3}\)) & \(-5.00\times 10^{2}\) (\(3.20\times 10^{2}\)) & \(-5.21\times 10^{2}\) (\(2.76\times 10^{2}\)) & \(-5.06\times 10^{2}\) (\(1.48\times 10^{2}\)) \\  & 100 & \(-7.19\times 10^{2}\) (\(2.71\times 10^{-4}\)) & \(-7.34\times 10^{2}\) (\(1.73\times 10^{-3}\)) & \(-6.95\times 10^{2}\) (\(6.80\times 10^{2}\)) & \(-7.34\times 10^{2}\) (\(9.19\times 10^{-2}\)) & \(-7.10\times 10^{2}\) (\(1.43\times 10^{2}\)) \\ \hline \multirow{3}{*}{\(f_{23}\)} & 10 & \(-1.95\times 10^{2}\) (\(4.25\times 10^{2}\)) & \(-1.01\times 10^{2}\) (\(6.83\times 10^{2}\)) & \(-1.81\times 10^{2}\) (\(1.32\times 10^{2}\)) & \(-1.68\times 10^{2}\) (\(6.91\times 10^{2}\)) & \(-1.40\times 10^{2}\) (\(8.36\times 10^{2}\)) (\(1.68\times 10^{2}\)) \\  & 30 & \(-8.87\times 10^{2}\) (\(1.05\times 10^{2}\)) & \(-9.60\times 10^{2}\) (\(2.03\times 10^{-3}\)) & \(-9.60\times 10^{2}\) (\(2.51\times 10^{2}\)) & \(-9.60\times 10^{2}\) (\(8.04\times 10^{2}\)) (\(8.65\times 10^{2}\)) & \(-8.65\times 10^{2}\) (\(5.95\times 10^{2}\)) \\  & 50 & \(-7.17\times 10^{2}\) (\(9.79\times 10^{2}\)) & \(-1.95\times 10^{2}\) (\(9.30\times 10^{-3}\)) & \(-1.95\times 10^{2}\) (\(5.76\times 10^{2}\)) & \(-1.55\times 10^{2}\) (\(6.89\times 10^{2}\)) (\(8.04\times 10^{2}\)) & \(-1.69\times 10^{2}\) (\(6.99\times 10^{2}\)) \\ \hline \multirow{3}{*}{\(f_{23}\)} & 10 & \(-1.86\times 10^{2}\) (\(3.33\times 10^{2}\)) & \(-1.22\times 10^{2}\) (\(2.78\times 10^{2}\)) & \(-1.32\times 10^{2}\) (\(2.51\times 10^{2}\)) & \(-1.42\times 10^{2}\) (\(1.50\times 10^{2}\)) & \(-1.23\times 10^{2}\) (\(8.76\times 10^{2}\)) (\(6.76\times 10^{2}\)) \\  & 80 & \(-8.46\times 10^{2}\) (\(6.8  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**ICDEBOA**} & \multicolumn{2}{c}{**HYSOBOA**} & \multicolumn{2}{c}{**jDE**} & \multicolumn{2}{c}{**BOA**} & \multicolumn{2}{c}{**SHADE**} \\ \hline \multicolumn{6}{c}{**Mean (STD) Sign**} \\ \hline \multirow{3}{*}{\(f_{25}\)} & 10 & \(-6.04\times 10^{5}\)(\(5.49\times 10^{5}\)) & \(-6.26\times 10^{5}\)(\(3.34\times 10^{-2}\)) & \(-6.04\times 10^{5}\)(\(7.17\times 10^{5}\))\(\approx\) & \(-6.03\times 10^{5}\)(\(6.97\times 10^{5}\))\(-6.03\times 10^{5}\)(\(8.59\times 10^{5}\))\(-6.03\times 10^{5}\)(\(8.59\times 10^{5}\))\(-2.28\times 10^{4}\)(\(9.38\times 10^{5}\)) \(-2.43\times 10^{4}\)(\(9.75\times 10^{-2}\)) \(+2.26\times 10^{4}\)(\(4.68\times 10^{5}\))\(-2.24\times 10^{4}\)(\(5.24\times 10^{5}\))\(-2.20\times 10^{4}\)(\(10.00\times 10^{5}\))\(-2.28\times 10^{4}\)(\(4.08\times 10^{5}\))\(-2.26\times 10^{4}\)(\(4.68\times 10^{5}\))\(-2.24\times 10^{4}\)(\(4.28\times 10^{5}\))\(-2.20\times 10^{4}\)(\(10.00\times 10^{5}\))\(-5.38\times 10^{5}\)(\(9.93\times 10^{5}\)) \(-5.82\times 10^{4}\)(\(1.43\times 10^{5}\))\(-5.21\times 10^{4}\)(\(9.93\times 10^{5}\))\(+4.84\times 10^{5}\)(\(6.2\times 10^{5}\))\(-5.80\times 10^{4}\)(\(2.77\times 10^{5}\))\(-5.80\times 10^{4}\)(\(2.87\times 10^{5}\))\(-5.80\times 10^{4}\)(\(2.87\times 10^{5}\))\(-5.80\times 10^{4}\)(\(2.87\times 10^{5}\))\(-5.80\times 10^{4}\)(\(2.87\times 10^{5}\))\(-5.80\times 10^{5}\)(\(2.87\times 10^{5}\))\(-5.80\times 10^{5}\)(\(2.