## 5 Experiment for Benchmark Functions
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**F** & **dim** & **Metric** & **MVO** & **ALO** & **SCA** & **GWO** & **CSCO** & **MSCSO** & **HSCSO** \\ \hline \multirow{4}{*}{F\({}_{1}\)} & min & 2.6327 & 4.1823 & 8.0045 \(\times 10^{3}\) & 1.0344 \(\times 10^{-17}\) & 2.2536 \(\times 10^{-248}\) & 0 & **0** \\  & 30 & mean & 5.6327 & 258.3733 & 136.4308 & 1.3223 \(\times 10^{-15}\) & 1.8527 \(\times 10^{-183}\) & 0 & **0** \\  & std & 1.9329 & 294.5664 & 230.9609 & 2.0616 \(\times 10^{-15}\) & 0 & 0 & **0** \\ \cline{2-8}  & \multirow{2}{*}{100} & min & 460.4557 & \(1.7996\times 10^{4}\) & 893.2494 & 3.5353 \(\times 10^{-8}\) & 8.1391 \(\times 10^{-252}\) & 0 & **0** \\  & & mean & 797.0433 & \(3.8002\times 10^{4}\) & 1.6369 \(\times 10^{4}\) & 6.3857 \(\times 10^{-7}\) & 2.4626 \(\times 10^{-186}\) & 0 & **0** \\  & & std & 178.2052 & \(1.0709\times 10^{4}\) & 1.1242 \(\times 10^{4}\) & 8.0299 \(\times 10^{-7}\) & 0 & 0 & **0** \\ \hline \multirow{4}{*}{F\({}_{2}\)} & min & 0.8037 & 12.2256 & 5.4967 \(\times 10^{-4}\) & 3.5132 \(\times 10^{-11}\) & 7.0641 \(\times 10^{-128}\) & 0 & **0** \\  & mean & 21.5927 & 87.17768 & 0.1127 & 5.3524 \(\times 10^{-10}\) & 2.6198 \(\times 10^{-101}\) & 0 & **0** \\  & std & 35.4733 & 46.8098 & 0.18727 & 4.1349 \(\times 10^{-10}\) & 2.6112 \(\times 10^{-100}\) & 0 & **0** \\ \cline{2-8}  & \multirow{2}{*}{100} & min & \(2.1626\times 10^{4}\) & 99.8106 & 0.5031 & 2.2138 \(\times 10^{-5}\) & 9.3442 \(\times 10^{-133}\) & 0 & **0** \\  & mean & \(9.8551\times 10^{33}\) & \(1.0053\times 10^{39}\) & 11.8113 & 7.0761 \(\times 10^{-5}\) & 7.7748 \(\times 10^{-101}\) & 0 & **0** \\  & std & \(9.8550\times 10^{34}\) & \(1.005\times 10^{40}\) & 9.0156 & 2.8239 \(\times 10^{-5}\) & 5.9144 \(\times 10^{-100}\) & 0 & **0** \\ \hline \multirow{4}{*}{F\({}_{3}\)} & min & 505.6024 & 6.5421 \(\times 10^{3}\) & 2.9688 \(\times 10^{3}\) & 1.1846 \(\times 10^{-4}\) & 4.9008 \(\times 10^{-218}\) & 0 & **0** \\  & mean & \(1.6749\times 10^{3}\) & \(2.1478\times 10^{4}\) & 1.6678 \(\times 10^{4}\) & 0.31494 & 1.4011 \(\times 10^{-113}\) & 0 & **0** \\  & std & \(627.0235\) & \(7.1650\times 10^{3}\) & 9.2015 \(\times 10^{3}\) & 0.70297 & 1.3405 \(\times 10^{-112}\) & 0 & **0** \\ \cline{2-8}  & \multirow{2}{*}{100} & min & \(8.0640\times 10^{4}\) & \(1.2447\times 10^{5}\) & 1.4818 \(\times 10^{5}\) & 486.0576 & 1.544 \(\times 10^{-217}\) & 0 & **0** \\  & & mean & \(1.0594\times 10^{5}\) & \(2.5221\times 10^{5}\) & 3.1412 \(\times 10^{5}\) & 5.8055 \(\times 10^{3}\) & 2.2715 \(\times 10^{-101}\) & 0 & **0** \\  & std & \(1.2983\times 10^{4}\) & \(8.6313\times 10^{4}\) & 1.0087 \(\times 10^{4}\) & 4.2713 \(\times 10^{3}\) & 2.2592 \(\times 10^{-100}\) & 0 & **0** \\ \hline \multirow{4}{*}{F\({}_{4}\)} & min & 63.4226 & 702.8128 & 276.6508 & 26.4809 & 28.7114 & 25.4941 & 28.7128 \\  & mean & \(823.1095\) & \(5.3803\times 10^{4}\) & 6.6770 \(\times 10^{5}\) & 28.1834 & 28.7411 & 27.956 & 28.7388 \\  & std & \(868.9818\) & \(7.2946\times 10^{4}\) & 8.0540 \(\times 10^{5}\) & 0.6845 & 0.0201 & 1.1103 & **0.0191** \\ \cline{2-8}  & \multirow{2}{*}{100} & min & \(3.5548\times 10^{4}\) & \(4.9803\times 10^{5}\) & 5.2962 \(\times 10^{7}\) & 97.5900 & 98.0808 & 98.0642 & **97.0305** \\  & mean & \(7.6548\times 10^{4}\) & \(2.5937\times 10^{7}\) & 1.5968 \(\times 10^{8}\) & 98.4024 & 98.1361 & 98.2444 & **98.1313** \\  & std & \(3.9204\times 10^{4}\) & \(1.9097\times 10^{7}\) & 5.0095 \(\times 10^{7}\) & 0.3076 & 0.0588 & 0.4850 & **0.0308** \\ \hline \multirow{4}{*}{F\({}_{5}\)} & min & 1.4699 & 3.1114 & 5.2411 & 1.0104 & 0.066901 & 0.75081 & 0.40856 \\  & mean & 5.1007 & 319.13956 & 113.9063 & 2.1401 & 0.79039 & 2.0531 & 0.93118 \\  & std & \(1.9181\) & 394.3906 & 188.4741 & 0.67296 & 0.42361 & 0.64171 & **0.41159** \\ \cline{2-8}  & \multirow{2}{*}{100} & min & 472.9413 & 2.6769 \(\times 10^{4}\) & 956.6184 & 13.0826 & 0.35754 & 10.2747 & 1.4734 \\  & mean & \(791.0462\) & \(3.9654\times 10^{4}\) & \(1.4741\times 10^{4}\) & 14.7925 & 2.9234 & 12.7907 & 3.6416 \\  & std & \(151.679\) & \(1.1052\times 10^{4}\) & \(1.0678\times 10^{4}\) & 1.0674 & 1.9161 & 1.6529 & 1.6461 \\ \hline \multirow{4}{*}{F\({}_{6}\)} & min & 88.88812 & 69.1000 & 2.6361 & 1.1369 \(\times 10^{-12}\) &As can be seen from Figure 5 and Table 3, compared with other algorithms, the HSCSO algorithm has a very superior convergence accuracy without significantly affecting the convergence speed.