## 4 Numerical Validation and Performance of Hybrid HCGA Algorithm
### Parameter Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \(\mathbf{F}\) & \(\mathbf{D}\) & \(\mathbf{P_{c}}\) & \(\mathbf{P_{m}}\) & \(\boldsymbol{\alpha}\) & \(\boldsymbol{\gamma}\) & \(\boldsymbol{\mu}\) & \(\boldsymbol{K}\) & \(\boldsymbol{p}\) \\ \hline \multirow{4}{*}{\(F_{1}\)} & 10 & \(2.71\times 10^{-96}\) & \(2.71\times 10^{-96}\) & \(2.71\times 10^{-96}\) & \(2.71\times 10^{-96}\) & \(2.71\times 10^{-96}\) & \(2.71\times 10^{-96}\) & \(2.71\times 10^{-96}\) \\  & 30 & \(1.74\times 10^{-95}\) & \(1.73\times 10^{-95}\) & \(1.73\times 10^{-95}\) & \(1.82\times 10^{-95}\) & \(1.73\times 10^{-95}\) & \(1.73\times 10^{-95}\) & \(1.73\times 10^{-95}\) \\  & 100 & \(7.17\times 10^{-20}\) & \(6.78\times 10^{-20}\) & \(6.83\times 10^{-20}\) & \(6.79\times 10^{-20}\) & \(6.78\times 10^{-20}\) & \(6.78\times 10^{-20}\) & \(7.81\times 10^{-20}\) \\  & 10 & \(3.25\times 10^{-64}\) & \(3.25\times 10^{-64}\) & \(3.25\times 10^{-64}\) & \(3.25\times 10^{-64}\) & \(3.25\times 10^{-64}\) & \(3.25\times 10^{-64}\) & \(3.25\times 10^{-64}\) \\ \multirow{4}{*}{\(F_{2}\)} & 30 & \(3.98\times 10^{-54}\) & \(2.62\times 10^{-54}\) & \(2.62\times 10^{-54}\) & \(6.26\times 10^{-54}\) & \(2.62\times 10^{-54}\) & \(2.62\times 10^{-54}\) & \(6.26\times 10^{-54}\) \\  & 100 & \(8.53\times 10^{-14}\) & \(5.98\times 10^{-14}\) & \(6.25\times 10^{-14}\) & \(6.08\times 10^{-14}\) & \(5.98\times 10^{-14}\) & \(5.98\times 10^{-14}\) & \(6.01\times 10^{-14}\) \\  & 10 & \(2.96\times 10^{-99}\) & \(2.96\times 10^{-99}\) & \(2.96\times 10^{-99}\) & \(2.96\times 10^{-99}\) & \(2.96\times 10^{-99}\) & \(2.96\times 10^{-99}\) & \(3.02\times 10^{-99}\) \\ \multirow{4}{*}{\(F_{3}\)} & 30 & \(3.66\times 10^{-90}\) & \(3.63\times 10^{-90}\) & \(3.63\times 10^{-90}\) & \(3.68\times 10^{-90}\) & \(3.63\times 10^{-90}\) & \(3.63\times 10^{-90}\) & \(3.63\times 10^{-90}\) \\  & 100 & \(4.76\times 10^{-17}\) & \(4.63\times 10^{-17}\) & \(4.67\times 10^{-17}\) & \(4.64\times 10^{-17}\) & \(4.63\times 10^{-17}\) & \(5.02\times 10^{-17}\) \\  & 10 & \(2.91\times 10^{-6}\) & \(1.35\times 10^{-6}\) & \(1.96\times 10^{-6}\) & \(9.89\times 10^{-7}\) & \(1.14\times 10^{-6}\) & \(1.04\times 10^{-6}\) & \(4.52\times 10^{-6}\) \\ \multirow{4}{*}{\(F_{4}\)} & 30 & \(6.01\times 10^{-7}\) & \(2.30\times 10^{-7}\) & \(1.23\times 10^{-6}\) & \(2.07\times 10^{-7}\) & \(2.33\times 10^{-7}\) & \(2.81\times 10^{-7}\) & \(1.86\times 10^{-7}\) \\  & 100 & \(5.77\times 10^{-5}\) & \(6.78\times 10^{-5}\) & \(3.01\times 10^{-4}\) & \(5.91\times 10^{-5}\) & \(8.77\times 10^{-5}\) & \(7.14\times 10^{-5}\) & \(6.37\times 10^{-5}\) \\ \multirow{4}{*}{\(F_{5}\)} & 10 & \(1.23\times 10^{-15}\) & \(1.23\times 10^{-15}\) & \(1.23\times 10^{-15}\) & \(1.23\times 10^{-15}\) & \(1.23\times 10^{-15}\) & \(1.23\times 10^{-15}\) & \(1.23\times 10^{-15}\) \\  & 100 & \(4.32\times 10^{-2}\) & \(2.24\times 10^{-1}\) & \(4.47\times 10^{-2}\) & \(3.91\times 10^{-2}\) & \(3.73\times 10^{-2}\) & \(3.91\times 10^{-2}\) & \(4.32\times 10^{-2}\) \\  & 100 & \(1.47\times 10^{-1}\) & \(6.41\times 10^{-1}\) & \(1.47\times 10^{-1}\) & \(1.58\times 10^{-1}\) & \(1.29\times 10^{-1}\) & \(1.58\times 10^{-1}\) & \(1.63\times 10^{-1}\) \\  & 10 & \(4.75\times 10^{-3}\) & \(6.52\times 10^{-3}\) & \(3.47\times 10^{-3}\) & \(5.71\times 10^{-3}\) & \(5.10\times 10^{-3}\) & \(3.48\times 10^{-3}\) & \(3.47\times 10^{-3}\) \\ \multirow{4}{*}{\(F_{6}\)} & 30 & \(1.54\times 10^{-3}\) & \(1.38\times 10^{-3}\) & \(1.11\times 10^{-3}\) & \(2.00\times 10^{-3}\) & \(2.11\times 10^{-3}\) & \(2.77\times 10^{-3}\) & \(2.10\times 10^{-3}\) \\  & 100 & \(1.81\times 10^{-3}\) & \(2.23\times 10^{-3}\) & \(2.56\times 10^{-3}\) & \(2.63\times 10^{-3}\) & \(3.73\times 10^{-3}\) & \(3.24\times 10^{-3}\) & \(2.36\times 10^{-3}\) \\ \multirow{4}{*}{\(F_{7}\)} & 10 & \(1.21\times 10^{-13}\) & \(1.21\times 10^{-13}\) & \(1.21\times 10^{-13}\) & \(1.21\times 10^{-13}\) & \(1.21\times 10^{-13}\) & \(1.21\times 10^{-13}\) & \(1.21\times 10^{-13}\) \\  & 100 & \(4.43\times 10^{-11}\) & \(2.83\times 10^{-11}\) & \(3.16\times 10^{-11}\) & \(2.84\times 10^{-11}\) & \(2.82\times 10^{-11}\) & \(9.93\times 10^{-11}\) & \(3.02\times 10^{-11}\) \\ \multirow{4}{*}{\(F_{8}\)} & 2 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{1-1} \cline{3-12}  & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \cline{1-1} \cline{3-12}  & & & & & & &From Table 4, it can be seen that for low-dimensional functions with unimodal functions, \(P_{c}\) has a greater influence on the algorithm performance, while for high-dimensional complex functions, it is \(p\), \(\alpha\) and \(K\) that have a greater influence.