# A Selection Process for Genetic Algorithm Using Clustering Analysis
## 3 Problem Definition
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Problem**} & \multicolumn{2}{c}{**KGA\({}_{\mathbf{o}}\)**} & \multicolumn{2}{c}{**KGA\({}_{\mathbf{o}}\)**} & \multicolumn{2}{c}{**Genetic**} & \multicolumn{2}{c}{**KGA\({}_{\mathbf{f}}\)**} & \multicolumn{1}{c}{**GCO**} \\ \cline{3-8} \multicolumn{1}{c}{} & Best & \(1.67\times 10^{-3}\) & \(2.36\times 10^{-3}\) & \(1.05\) & \(4.51\times 10^{-3}\) & \(3.60\times 10^{1}\) \\ \cline{3-8} \multicolumn{1}{c}{} & Mean & \(1.22\times 10^{-2}\) & \(1.53\times 10^{-2}\) & \(1.63\) & \(1.16\times 10^{-1}\) & \(1.19\times 10^{1}\) \\ \multicolumn{1}{c}{} & Worst & \(6.32\times 10^{-2}\) & \(9.89\times 10^{-2}\) & \(2.43\) & \(6.42\times 10^{-1}\) & \(2.17\times 10^{1}\) \\ \multicolumn{1}{c}{} & SD & \(1.45\times 10^{-2}\) & \(1.87\times 10^{-2}\) & \(3.13\times 10^{-1}\) & \(1.40\times 10^{-1}\) & \(5.88\) \\ \hline \multirow{3}{*}{2} & Best & \(3.76\times 10^{-3}\) & \(5.68\times 10^{-3}\) & \(8.99\) & \(5.01\times 10^{-2}\) & \(7.79\times 10^{1}\) \\ \cline{3-8} \multicolumn{1}{c}{} & Mean & \(1.17\times 10^{-1}\) & \(1.19\times 10^{-1}\) & \(1.02\times 10^{1}\) & \(4.10\) & \(9.34\times 10^{1}\) \\ \cline{3-8} \multicolumn{1}{c}{} & Worst & \(1.16\) & \(2.05\) & \(1.33\times 10^{1}\) & \(2.75\times 10^{1}\) & \(1.79\times 10^{2}\) \\ \multicolumn{1}{c}{} & SD & \(2.17\times 10^{-1}\) & \(2.94\times 10^{-1}\) & \(1.48\) & \(6.05\) & \(4.75\times 10^{1}\) \\ \hline \multirow{3}{*}{3} & Best & \(1.96\times 10^{-1}\) & \(5.50\times 10^{-3}\) & \(1.49\times 10^{1}\) & \(2.27\times 10^{-2}\) & \(3.33\) \\ \cline{3-8} \multicolumn{1}{c}{} & Mean & \(9.16\times 10^{-1}\) & \(3.34\times 10^{-1}\) & \(2.45\times 10^{1}\) & \(2.04\) & \(1.44\times 10^{2}\) \\ \cline{3-8} \multicolumn{1}{c}{} & Worst & \(3.19\) & \(4.59\) & \(3.53\times 10^{1}\) & \(1.27\times 10^{1}\) & \(2.62\times 10^{2}\) \\ \multicolumn{1}{c}{} & SD & \(4.29\times 10^{-1}\) & \(6.85\times 10^{-1}\) & \(4.19\) & \(2.55\) & \(4.76\times 10^{1}\) \\ \hline \multirow{3}{*}{4} & Best & \(7.00\) & \(7.00\) & \(3.19\times 10^{2}\) & \(1.70\times 10^{1}\) & \(3.00\) \\ \cline{3-8} \multicolumn{1}{c}{} & Mean & \(7.91\times 10^{1}\) & \(7.52\times 10^{1}\) & \(4.89\times 10^{2}\) & \(8.83\times 10^{1}\) & \(8.48\) \\ \cline{3-8} \multicolumn{1}{c}{} & Worst & \(5.37\times 10^{2}\) & \(3.32\times 10^{2}\) & \(7.23\times 10^{2}\) & \(3.17\times 10^{2}\) & \(1.40\times 10^{1}\) \\ \multicolumn{1}{c}{} & SD & \(9.23\times 10^{1}\) & \(7.44\times 10^{1}\) & \(9.99\times 10^{1}\) & \(6.41\times 10^{1}\) & \(3.01\) \\ \hline \multirow{3}{*}{5} & Best & \(1.46\) & \(1.32\times 10^{-1}\) & \(9.83\) & \(1.55\) & \(1.28\) \\ \cline{3-8} \multicolumn{1}{c}{} & Mean & \(6.75\) & \(5.59\) & \(1.16\) & \(5.18\) & \(4.58\) \\ \cline{3-8} \multicolumn{1}{c}{} & Worst & \(1.26\times 10^{1}\) & \(1.28\times 10^{1}\) & \(1.25\times 10^{1}\) & \(1.20\times 10^{1}\) & \(8.94\) \\ \multicolumn{1}{c}{} & SD & \(3.69\) & \(3.58\) & \(7.38\times 10^{-1}\) & \(2.47\) & \(1.16\) \\ \hline \multirow{3}{*}{6} & Best & \(1.46\) & \(1.32\times 10^{-1}\) & \(9.83\) & \(1.55\) & \(1.28\) \\ \cline{3-8} \multicolumn{1}{c}{} & Mean & \(6.75\) & \(5.59\) & \(1.16\) & \(5.18\) & \(4.58\) \\ \cline{3-8} \multicolumn{1}{c}{} & Worst & \(1.26\times 10^{1}\) & \(1.28\times 10^{1}\) & \(1.25\times 10^{1}\) & \(1.20\times 10^{1}\) & \(8.94\) \\ \cline{3-8} \multicolumn{1}{c}{} & SD & \(3.69\) & \(3.58\) & \(7.38\times 10^{-1}\) & \(2.47\) & \(1.16\) \\ \hline \multirow{3}{*}{7} & Best & \(1.65\times 10^{-2}\) & \(1.02\times 10^{-2}\) & \(7.99\) & \(5.04\times 10^{-2}\) & \(3.10\times 10^{1}\) \\ \cline{3-8} \multicolumn{1}{c}{} & Mean & \(1.87\times 10^{1}\) & \(1.59\times 10^{1}\) & \(2.63\times 10^{1}\) & \(1.96\times 10^{1}\) & \(1.13\times 10^{2}\) \\ \cline{3-8} \multicolumn{1}{c}{} & Worst & \(7.54\times 10^{1}\) & \(7.21\times 10^{1}\) & \(6.15\times 10^{1}\) & \(7.85\times 10^{1}\) & \(1.72\times 10^{2}\) \\ \multicolumn{1}{c}{} & SD & \(2.82\times 10^{1}\) & \(2.75\times 10^{1}\) & \(1.34\times 10^{1}\) & \(2.97\times 10^{1}\) & \(2.67\times 10^{1}\) \\ \hline \hline \end{tabular}
\end{table}