## 3 Experimental Results and Discussion
### Comparative Analysis of the Optimization Performance of the Parallel EGO Algorithm
#### 3.1.1 Optimization Solution Accuracy
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Systems**} & \multirow{2}{*}{\begin{tabular}{c} **Test** \\ **Problems** \\ \end{tabular} } & \multirow{2}{*}{**Metrics**} & \multirow{2}{*}{**2 Points**} & \multirow{2}{*}{**4 Points**} & \multirow{2}{*}{**6 Points**} & \multirow{2}{*}{**8 Points**} & \multirow{2}{*}{**10 Points**} \\ \hline \multirow{4}{*}{\begin{tabular}{c} OK- \\ based \\ \end{tabular} } & \multirow{2}{*}{F6} & Mean & \(-6.444\times 10^{1}\) & \(-1.817\times 10^{1}\) & \(-4.460\times 10^{1}\) & \(-2.078\times 10^{1}\) & \(-1.944\times 10^{1}\) \\ \cline{3-8}  & & Std & \(6.382\times 10^{1}\) & \(1.0328\times 10^{2}\) & \(1.3318\times 10^{2}\) & \(9.513\times 10^{1}\) & \(1.1667\times 10^{2}\) \\ \cline{3-8}  & & Rank (\(p=0.0086\)) & 2.50 & 3.40 & 2.37 & 3.53 & 3.20 \\ \hline \multirow{4}{*}{\begin{tabular}{c} GEK- \\ based \\ \end{tabular} } & \multirow{2}{*}{F7} & Mean & \(-8.770\times 10^{1}\) & \(-9.324\times 10^{1}\) & \(-8.852\times 10^{1}\) & \(-8.099\times 10^{1}\) & \(-9.426\times 10^{1}\) \\ \cline{3-8}  & & Std & \(3.885\times 10^{1}\) & \(2.106\times 10^{1}\) & \(2.939\times 10^{1}\) & \(4.975\times 10^{1}\) & \(8.0437\) \\ \cline{3-8}  & & Rank (\(p=0.6868\)) & 3.30 & 2.80 & 3.13 & 2.80 & 2.97 \\ \hline \multirow{4}{*}{\begin{tabular}{c} OK- \\ based \\ \end{tabular} } & \multirow{2}{*}{F7} & Mean & \(2.0104\times 10^{2}\) & \(1.7902\times 10^{2}\) & \(1.8019\times 10^{2}\) & \(1.7962\times 10^{2}\) & \(1.7694\times 10^{2}\) \\ \cline{3-8}  & & Std & \(1.4379\times 10^{2}\) & \(1.0624\times 10^{2}\) & \(1.0799\times 10^{2}\) & \(1.0126\times 10^{2}\) & \(1.0803\times 10^{2}\) \\ \cline{3-8}  & & Rank (\(p=0.8136\)) & 3.13 & 2.73 & 2.97 & 2.97 & 3.20 \\ \cline{3-8}  & & Mean & \(1.3460\times 10^{2}\) & \(1.4083\times 10^{2}\) & \(1.3083\times 10^{2}\) & \(1.3919\times 10^{2}\) & \(1.3518\times 10^{2}\) \\ \cline{3-8}  & & Std & \(6.349\times 10^{1}\) & \(6.999\times 10^{1}\) & \(5.526\times 10^{1}\) & \(6.968\times 10^{1}\) & \(6.090\times 10^{1}\) \\ \cline{3-8}  & & Rank (\(p=0.9197\)) & 3.23 & 2.93 & 2.97 & 2.87 & 3.00 \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} OK- \\ based \\ \end{tabular} } & \multirow{2}{*}{F8} & Mean & \(5.0284\times 10^{2}\) & \(5.0311\times 10^{2}\) & \(5.0334\times 10^{2}\) & \(5.0351\times 10^{2}\) & \(5.0351\times 10^{2}\) \\ \cline{3-8}  & & Std & \(6.669\times 10^{-1}\) & \(8.299\times 10^{-1}\) & \(9.720\times 10^{-1}\) & \(9.606\times 10^{-1}\) & \(1.3396\) \\ \cline{3-8}  & & Rank (\(p=0.0047\)) & 2.17 & 2.57 & 3.40 & 3.37 & 3.50 \\ \cline{3-8}  & & Mean & \(5.0500\times 10^{2}\) & \(5.0480\times 10^{2}\) & \(5.0476\times 10^{2}\) & \(5.0566\times 10^{2}\) & \(5.0515\times 10^{2}\) \\ \cline{3-8}  & & Std & \(1.7700\) & 1.3614 & 1.3429 & 2.0348 & 1.3429 \\ \cline{3-8}  & & Rank (\(p=0.6828\)) & 2.90 & 2.63 & 2.83 & 3.33 & 3.20 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} OK- \\ based \\ \end{tabular} } & \multirow{2}{*}{F9} & Mean & \(9.7651\times 10^{2}\) & \(1.0291\times 10^{3}\) & \(1.0683\times 10^{3}\) & \(1.0344\times 10^{3}\) & \(1.0929\times 10^{3}\) \\ \cline{3-8}  & & Std & \(1.6718\times 10^{2}\) & \(1.3887\times 10^{2}\) & \(1.3285\times 10^{2}\) & \(1.5219\times 10^{2}\) & \(1.5950\times 10^{2}\) \\ \cline{3-8}  & & Rank (\(p=0.0071\)) & 2.20 & 2.83 & 3.47 & 2.97 & 3.53 \\ \cline{3-8}  & & Mean & \(9.5022\times 10^{2}\) & \(9.5390\times 10^{2}\) & \(9.6924\times 10^{2}\) & \(9.3789\times 10^{2}\) & \(9.4671\times 10^{2}\) \\ \cline{3-8}  & & Std & \(8.041\times 10^{1}\) & \(8.716\times 10^{1}\) & \(1.0428\times 10^{2}\) & \(7.287\times 10^{1}\) & \(8.207\times 10^{1}\) \\ \cline{3-8}  & & Rank (\(p=0.8088\)) & 2.97 & 3.17 & 3.20 & 2.90 & 2.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 6: Three-dimensional maps for two-dimensional Griewank and rotated Griewank functions. functions. Particularly, the convergence accuracy obtained on F2, F6, and F7 was the worst.