# Automated Generation of Hybrid Metaheuristics Using Learning-to-Rank
## 5 Experiment Evaluation
### Experimental Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Funes Algorithm**} & \multicolumn{2}{c}{**Dim = 10**} & \multicolumn{2}{c}{**Dim = 30**} & \multicolumn{2}{c}{**Dim = 50**} & \multicolumn{2}{c}{**Dim = 100**} \\ \cline{2-13}  & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Std**} & \multicolumn{2}{c}{**Best**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Std**} & \multicolumn{2}{c}{**Best**} & \multicolumn{2}{c}{**Mean**} & \multicolumn{2}{c}{**Std**} & \multicolumn{2}{c}{**Best**} \\ \hline F3 & WOA & \(2.09\times 10^{4}\) & \(8.40\times 10^{2}\) & \(2.01\times 10^{4}\) & \(3.20\times 10^{11}\) & \(2.99\times 10^{10}\) & \(2.94\times 10^{11}\) & \(3.82\times 10^{5}\) & \(2.79\times 10^{3}\) & \(3.79\times 10^{5}\) & \(7.64\times 10^{5}\) & \(1.66\times 10^{5}\) & \(5.98\times 10^{5}\) \\  & HHO & \(1.45\times 10^{4}\) & \(2.45\times 10^{3}\) & \(1.20\times 10^{4}\) & \(4.74\times 10^{11}\) & \(1.36\times 10^{11}\) & \(3.38\times 10^{11}\) & \(1.97\times 10^{5}\) & \(2.48\times 10^{3}\) & \(1.95\times 10^{5}\) & \(3.73\times 10^{5}\) & \(6.72\times 10^{3}\) & \(3.66\times 10^{5}\) \\  & GA & \(2.63\times 10^{4}\) & \(1.17\times 10^{4}\) & \(1.46\times 10^{4}\) & \(4.50\times 10^{10}\) & \(1.20\times 10^{3}\) & \(3.00\times 10^{40}\) & \(1.40\times 10^{5}\) & \(7.47\times 10^{4}\) & \(3.35\times 10^{5}\) & \(3.80\times 10^{5}\) & \(4.82\times 10^{4}\) & \(7.82\times 10^{5}\) \\  & ISGA & \(2.20\times 10^{4}\) & \(9.50\times 10^{5}\) & \(1.50\times 10^{4}\) & \(2.80\times 10^{9}\) & \(8.10\times 10^{9}\) & \(1.90\times 10^{3}\) & \(4.30\times 10^{7}\) & \(8.70\times 10^{4}\) & \(3.50\times 10^{5}\) & \(8.50\times 10^{5}\) & \(8.00\times 10^{4}\) & \(8.00\times 10^{5}\) \\  & RLWOA & \(1.35\times 10^{4}\) & \(3.80\times 10^{3}\) & \(1.25\times 10^{4}\) & \(**2.37\times 10^{4}\)** & \(7.23\times 10^{4}\) & \(1.64\times 10^{9}\) & \(1.90\times 10^{7}\) & \(1.70\times 10^{4}\) & \(1.70\times 10^{5}\) & \(3.70\times 10^{5}\) & \(6.00\times 10^{4}\) & \(3.60\times 10^{5}\) \\  & Rand-MHA & \(1.30\times 10^{4}\) & \(3.60\times 10^{3}\) & \(1.24\times 10^{5}\) & \(5.63\times 10^{3}\) & \(6.23\times 10^{4}\) & \(1.06\times 10^{9}\) & \(1.97\times 10^{5}\) & \(2.36\times 10^{4}\) & \(1.85\times 10^{5}\) & \(8.00\times 10^{5}\) & \(5.97\times 10^{5}\) & \(3.55\times 10^{5}\) \\  & LIR-MHA & \(\mathbf{5.89\times 10^{3}}\) & \(2.17\times 10^{2}\) & \(5.67\times 10^{3}\) & \(0.44\times 10^{10}\) & \(1.19\times 10^{9}\) & \(2.85\times 10^{5}\) & \(\mathbf{1.85\times 10^{5}}\) & \(1.62\times 10^{4}\) & \(1.62\times 10^{5}\) & \(8.90\times 10^{5}\) & \(8.80\times 10^{5}\) & \(8.89\times 10^{5}\) & \(8.90\times 10^{5}\) \\ \hline F5 & WOA & \(5.67\times 10^{2}\) & \(1.47\times 10^{5}\) & \(5.66\times 10^{2}\) & \(9.28\times 10^{2}\) & \(2.99\times 10^{1}\) & \(8.98\times 10^{2}\) & \(1.18\times 10^{3}\) & \(1.03\times 10^{1}\) & \(1.17\times 10^{3}\) & \(2.08\times 10^{3}\) & \(9.71\times 10^{2}\) & \(2.07\times 10^{5}\) \\  & HHO & \(5.59\times 10^{2}\) & \(2.67\times 10^{1}\) & \(5.56\times 10^{2}\) & \(8.67\times 10^{2}\) & \(8.78\times 10^{1}\) & \(8.66\times 10^{2}\) & \(1.16\times 10^{3}\) & \(3.72\times 10^{1}\) & \(1.12\times 10^{3}\) & \(2.02\times 10^{3}\) & \(1.33\times 10^{1}\) & \(2.01\times 10^{3}\) \\  & GA & \(5.32\times 10^{2}\) & \(1.82\times 10^{1}\) & \(5.14\times 10^{1}\) & \(6.94\times 10^{2}\) & \(4.28\times 10^{4}\) & \(6.52\times 10^{2}\) & \(1.03\times 10^{3}\) & \(5.21\times 10^{4}\) & \(9.76\times 10^{5}\) & \(1.95\times 10^{5}\) & \(1.55\times 10^{5}\) & \(1.79\times 10^{5}\) \\  & ISGA & \(5.30\times 10^{2}\) & \(1.80\times 10^{1}\) & \(8.01\times 10^{1}\) & \(5.12\times 10^{2}\) & \(7.00\times 10^{4}\) & \(4.30\times 10^{10}\) & \(6.60\times 10^{2}\) & \(1.04\times 10^{10}\) & \(1.04\times 10^{5}\) & \(5.20\times 10^{10}\) & \(9.80\times 10^{2}\) & \(1.96\times 10^{5}\) & \(1.50\times 10^{10}\) & \(1.80\times 10^{5}\) \\  & RLWOA & \(5.35\times 10^{2}\) & \(8.50\times 10^{2}\) & \(5.27\times 10^{2}\) & \(7.30\times 10^{2}\) & \(2.50\times 10^{4}\) & \(6.90\times 10^{2}\) & \(9.00\times 10^{2}\) & \(4.30\times 10^{1}\) & \(8.80\times 10^{2}\) & \(1.66\times 10^{3}\) & \(1.80\times 10^{1}\) & \(1.64\times 10^{9}\) \\  & Rand-MHA & \(\mathbf{5.36\times 10^{2}}\) & \(8.46\times 10^{10}\) & \Figure 3 shows the average fitness convergence curves of five algorithms on nine typical functions (F3, F6, F9, F12, F14, F19, F22, F24, and F30) from the CEC2017 benchmark, with a dimensional setting of \(D=30\).