## 3 Numerical Experiment
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **Metric** & **FSS** & **FSSN** & **FSSGD** \\ \hline \multirow{3}{*}{\(f_{1}\)} & Mean & \(-5.9\times 10^{-1}\) & \(\mathbf{-1.3\times 10^{-44}}\) & \(-5.3\times 10^{-39}\) \\  & Best & \(-5.8\times 10^{-2}\) & \(\mathbf{-3.5\times 10^{-46}}\) & \(-1.4\times 10^{-45}\) \\  & Std. dev & \(3.3\times 10^{-1}\) & \(\mathbf{2.9\times 10^{-44}}\) & \(1.6\times 10^{-38}\) \\ \hline \multirow{3}{*}{\(f_{2}\)} & Mean & \(189.65\) & \(\mathbf{190.46}\) & \(\mathbf{190.46}\) \\  & Best & \(195.58\) & \(\mathbf{195.83}\) & \(\mathbf{195.83}\) \\  & Std. dev & \(7.43\) & \(\mathbf{7.42}\) & \(\mathbf{7.42}\) \\ \hline \multirow{3}{*}{\(f_{3}\)} & Mean & \(-82.94\) & \(-17.72\) & \(\mathbf{-5.66}\) \\  & Best & \(-1.0\times 10^{1}\) & \(\mathbf{-4.3\times 10^{-20}}\) & \(-1.7\times 10^{-2}\) \\  & Std. dev & \(52.58\) & \(47.49\) & \(\mathbf{12.29}\) \\ \hline \multirow{3}{*}{\(f_{4}\)} & Mean & \(-7.09\) & \(-2.64\) & \(\mathbf{-2.48}\) \\  & Best & \(-2.20\) & \(0.00\) & \(\mathbf{0.00}\) \\ \cline{1-1}  & Std. dev & \(2.11\) & \(1.64\) & \(\mathbf{1.16}\) \\ \hline \multirow{3}{*}{\(f_{9}\)} & Mean & \(3.41\) & \(3.42\) & \(\mathbf{4.06}\) \\ \cline{1-1}  & Best & \(4.12\) & \(4.65\) & \(\mathbf{4.69}\) \\ \cline{1-1}  & Std. dev & \(\mathbf{0.25}\) & \(0.29\) & \(0.44\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy comparison of the algorithms optimizing 5-dimensional functions from Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **Metric** & **FSS** & **FSSN** & **FSSGD** \\ \hline \multirow{3}{*}{\(f_{5}\)} & Mean & \(-0.18\) & \(-0.18\) & \(\mathbf{-0.04}\) \\  & Best & \(-0.01\) & \(-0.01\) & \(\mathbf{-0.01}\) \\  & Std. dev & \(0.12\) & \(0.12\) & \(\mathbf{0.01}\) \\ \hline \multirow{3}{*}{\(f_{6}\)} & Mean & \(-4.6\times 10^{-4}\) & \(\mathbf{-3.2\times 10^{-44}}\) & \(-2.0\times 10^{-13}\) \\  & Best & \(-7.3\times 10^{-6}\) & \(\mathbf{-1.7\times 10^{-47}}\) & \(-5.8\times 10^{-38}\) \\  & Std. dev & \(4.9\times 10^{-4}\) & \(\mathbf{7.6\times 10^{-44}}\) & \(9.7\times 10^{-13}\) \\ \hline \multirow{3}{*}{\(f_{7}\)} & Mean & \(951.06\) & \(951.57\) & \(\mathbf{959.15}\) \\  & Best & \(959.63\) & \(959.63\) & \(\mathbf{959.64}\) \\ \cline{1-1}  & Std. dev & \(13.14\) & \(11.97\) & \(\mathbf{3.40}\) \\ \hline \multirow{3}{*}{\(f_{8}\)} & Mean & \(-1.6\times 10^{-2}\) & \(\mathbf{-2.3\times 10^{-61}}\) & \(-3.2\times 10^{-22}\) \\ \cline{1-1}  & Best & \(0.00\) & \(\mathbf{0.00}\) & \(\mathbf{0.00}\) \\ \cline{1-1}  & Std. dev & \(1.5\times 10^{-2}\) & \(\mathbf{4.8\times 10^{-31}}\) & \(1.8\times 10^{-11}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Accuracy comparison of the algorithms optimizing 2-dimensional functions from Table 1.  
algorithm can be used in cases, when a function is differentiable inside the study region, by computing the derivative either numerically, by using finite difference approximations, or symbolically. Additionally, we benchmarked the time required for the original and hybrid algorithms to optimize the functions listed in Table 1. The results are shown in Tables 4 and 5, where the best result in each row is highlighted in bold.