## 3 Experimental Results and Discussion
### Comparative Analysis of the Optimization Performance of the Parallel EGO Algorithm
#### 3.1.1 Optimization Solution Accuracy
These findings suggest that-filling strategy selection should consider objective function landscape characteristics: more flexible approaches may suit rotation-sensitive functions (e.g., Griewank-class), while rotation-invariant problems (e.g., Rastrigin-class) may benefit from the robust two-point-filling strategy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Systems**} & \multirow{2}{*}{**Test**} & \multirow{2}{*}{**Metrics**} & \multirow{2}{*}{**2 Points**} & \multirow{2}{*}{**4 Points**} & \multirow{2}{*}{**6 Points**} & \multirow{2}{*}{**8 Points**} & \multirow{2}{*}{**10 Points**} \\ \cline{5-8}  & & & Mean & \(4.509\times 10^{-1}\) & \(5.669\times 10^{-1}\) & \(6.046\times 10^{-1}\) & \(6.907\times 10^{-1}\) & \(7.791\times 10^{-1}\) \\ \cline{3-8}  & & Std & \(7.865\times 10^{-1}\) & \(6.880\times 10^{-1}\) & \(4.560\times 10^{-1}\) & \(6.826\times 10^{-1}\) & \(5.662\times 10^{-1}\) \\ \cline{3-8}  & & Rank (\(p=0.0019\)) & \(2.00\) & \(3.03\) & \(3.30\) & \(3.10\) & \(3.57\) \\ \hline \multirow{3}{*}{GEK-based} & \multirow{3}{*}{F1} & Mean & \(4.49\times 10^{-2}\) & \(9.18\times 10^{-2}\) & \(1.220\times 10^{-1}\) & \(1.415\times 10^{-1}\) & \(2.719\times 10^{-1}\) \\ \cline{3-8}  & & Std & \(3.70\times 10^{-2}\) & \(7.06\times 10^{-2}\) & \(1.172\times 10^{-1}\) & \(9.55\times 10^{-2}\) & \(3.565\times 10^{-1}\) \\ \cline{3-8}  & & Rank (\(p<0.0001\)) & \(1.87\) & \(2.57\) & \(3.03\) & \(3.53\) & \(4.00\) \\ \hline \multirow{3}{*}{OK-based} & \multirow{3}{*}{F2} & Mean & \(4.642\times 10^{-1}\) & \(4.967\times 10^{-1}\) & \(4.551\times 10^{-1}\) & \(4.698\times 10^{-1}\) & \(5.096\times 10^{-1}\) \\ \cline{3-8}  & & Std & \(1.153\times 10^{-1}\) & \(1.118\times 10^{-1}\) & \(8.56\times 10^{-2}\) & \(1.151\times 10^{-1}\) & \(1.058\times 10^{-1}\) \\ \cline{3-8}  & & Rank (\(p=0.2998\)) & \(2.97\) & \(3.20\) & \(2.57\) & \(2.87\) & \(3.40\) \\ \cline{3-8}  & & Mean & \(5.479\times 10^{-1}\) & \(5.375\times 10^{-1}\) & \(5.501\times 10^{-1}\) & \(5.312\times 10^{-1}\) & \(5.635\times 10^{-1}\) \\ \cline{3-8}  & & Std & \(1.290\times 10^{-1}\) & \(1.304\times 10^{-1}\) & \(1.107\times 10^{-1}\) & \(1.094\times 10^{-1}\) & \(1.351\times 10^{-1}\) \\ \cline{3-8}  & & Rank (\(p=0.3578\)) & \(3.03\) & \(2.97\) & \(2.90\) & \(2.63\) & \(3.47\) \\ \hline \multirow{3}{*}{OK-based} & \multirow{3}{*}{F3} & Mean & \(-4.9934\times 10^{2}\) & \(-4.9936\times 10^{2}\) & \(-4.9940\times 10^{2}\) & \(-4.9936\times 10^{2}\) & \(-4.9938\times 10^{2}\) \\ \cline{3-8}  & & Std & \(1.858\times 10^{-1}\) & \(1.998\times 10^{-1}\) & \(2.199\times 10^{-1}\) & \(1.658\times 10^{-1}\) & \(1.921\times 10^{-1}\) \\ \cline{3-8}  & & Rank (\(p=0.6387\)) & \(3.27\) & \(3.03\) & \(2.73\) & \(3.17\) & \(2.80\) \\ \cline{3-8}  & & Mean & \(-4.9518\times 10^{2}\) & \(-4.9483\times 10^{2}\) & \(-4.9400\times 10^{2}\) & \(-4.9388\times 10^{2}\) & \(-4.9359\times 10^{2}\) \\ \cline{3-8}  & & Std & \(1.9765\) & \(1.7859\) & \(2.5571\) & \(2.4633\) & \(2.2423\) \\ \cline{3-8}  & & Rank (\(p=0.0316\)) & \(2.43\) & \(2.60\) & \(3.20\) & \(3.20\) & \(3.57\) \\ \hline \multirow{3}{*}{OK-based} & \multirow{3}{*}{F4} & Mean & \(-3.9797\times 10^{2}\) & \(-3.9754\times 10^{2}\) & \(-3.9730\times 10^{2}\) & \(-3.9694\times 10^{2}\) & \(-3.9674\times 10^{2}\) \\ \cline{3-8}  & & Std & \(8.011\times 10^{-1}\) & \(1.3583\) & \(1.6863\) & \(2.0484\) & \(1.8026\) \\ \cline{3-8}  & & Rank (\(p=0.0023\)) & \(2.23\) & \(2.87\) & \(2.83\) & \(3.23\) & \(3.83\) \\ \cline{3-8}  & & Mean & \(-3.9818\times 10^{2}\) & \(-3.9840\times 10^{2}\) & \(-3.9817\times 10^{2}\) & \(-3.9807\times 10^{2}\) & \(-3.9806\times 10^{2}\) \\ \cline{3-8}  & & Std & \(8.714\times 10^{-1}\) & \(8.988\times 10^{-1}\)  
For the case based on the GEK model, the optimization performance advantage of the strategy with two filled points decreased. It only achieved the best convergence accuracy on test functions F1, F3, and F5, while performing relatively poorly on several other test functions.