# Multi-Strategy Improved Flamingo Search Algorithm for Global Optimization
## 4 Experiments and Analysis
### Results and Analysis of Comparison Experiments between Two Groups
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Functions** & **ATR** & **FSA** & **FSA1** & **FSA2** & **FSA3** & **IFSA** \\ \hline \multirow{3}{*}{\(F_{1}\)} & Best & \(1.98\times 10^{-261}\) & \(1.45\times 10^{-262}\) & **0** & **0** & **0** \\  & Std & **0** & **0** & **0** & **0** & **0** \\  & Mean & \(1.40\times 10^{-238}\) & \(8.60\times 10^{-238}\) & \(1.75\times 10^{-291}\) & **0** & **0** \\ \hline \multirow{3}{*}{\(F_{2}\)} & Best & \(3.44\times 10^{-131}\) & \(2.73\times 10^{-132}\) & \(6.97\times 10^{-161}\) & \(1.17\times 10^{-201}\) & \(3.47\times 10^{-225}\) \\  & Std & \(1.12\times 10^{-120}\) & \(7.25\times 10^{-122}\) & \(1.82\times 10^{-146}\) & **0** & **0** \\  & Mean & \(3.07\times 10^{-121}\) & \(2.71\times 10^{-122}\) & \(4.89\times 10^{-147}\) & \(2.04\times 10^{-168}\) & \(1.49\times 10^{-216}\) \\ \hline \multirow{3}{*}{\(F_{3}\)} & Best & \(2.92\times 10^{-244}\) & \(2.47\times 10^{-242}\) & **0** & **0** & **0** \\  & Std & **0** & **0** & **0** & **0** & **0** \\  & Mean & \(1.96\times 10^{-218}\) & \(1.61\times 10^{-218}\) & \(6.80\times 10^{-284}\) & **0** & **0** \\ \hline \multirow{3}{*}{\(F_{4}\)} & Best & \(2.92\times 10^{-131}\) & \(2.57\times 10^{-130}\) & \(2.55\times 10^{-158}\) & \(8.73\times 10^{-197}\) & \(1.45\times 10^{-228}\) \\  & Std & \(3.77\times 10^{-112}\) & \(2.22\times 10^{-116}\) & \(2.38\times 10^{-143}\) & **0** & **0** \\  & Mean & \(7.00\times 10^{-113}\) & \(4.20\times 10^{-117}\) & \(5.39\times 10^{-144}\) & \(3.73\times 10^{-192}\) & \(1.96\times 10^{-215}\) \\ \hline \multirow{3}{*}{\(F_{5}\)} & Best & \(1.74\times 10\) & \(1.74\times 10\) & \(1.73\times 10\) & \(1.73\times 10\) & \(1.69\times 10\) \\  & Std & \(4.39\times 10^{-1}\) & \(4.86\times 10^{-1}\) & \(4.17\times 10^{-1}\) & \(4.63\times 10^{-1}\) & \(4.61\times 10^{-1}\) \\  & Mean & \(1.81\times 10\) & \(1.81\times 10\) & \(1.81\times 10\) & \(1.81\times 10\) & \(1.80\times 10\) \\ \hline \multirow{3}{*}{\(F_{6}\)} & Best & \(2.04\) & **1.72** & 1.98 & 2.11 & 1.86 \\  & Std & \(\textbf{2.41}\times\textbf{10}^{-1}\) & \(3.26\times 10^{-1}\) & \(2.44\times 10^{-1}\) & \(2.80\times 10^{-1}\) & \(3.22\times 10^{-1}\) \\  & Mean & \(2.56\) & \(2.49\) & **2.46** & 2.77 & 2.70 \\ \hline \multirow{3}{*}{\(F_{7}\)} & Best & \(4.24\times 10^{-6}\) & \(9.63\times 10^{-7}\) & \(8.43\times 10^{-6}\) & \(1.36\times 10^{-6}\) & \(6.40\times 10^{-7}\) \\  & Std & \(7.04\times 10^{-5}\) & \(\textbf{5.93}\times\textbf{10}^{-5}\) & \(6.06\times 10^{-5}\) & \(7.60\times 10^{-5}\) & \(8.49\times 10^{-5}\) \\  & Mean & \(7.47\times 10^{-5}\) & \(7.07\times 10^{-5}\) & \(7.56\times 10^{-5}\) & \(7.50\times 10^{-5}\) & \(6.43\times 10^{-5}\) \\ \hline \multirow{3}{*}{\(F_{8}\)} & Best & \(2.78\times 10^{-183}\) & \(1.51\times 10^{-185}\) & \(1.82\times 10^{-195}\) & **0** & \(8.38\times 10^{-302}\) \\  & Std & **0** & **0** & **0** & **0** & **0** \\  & Mean & \(1.57\times 10^{-173}\) & \(2.02\times 10^{-171}\) & \(1.28\times 10^{-180}\) & \(7.80\times 10^{-263}\) & \(\textbf{4.63}\times 10^{-283}\) \\ \hline \multirow{3}{*}{\(F_{9}\)} & Best & \(1.53\times 10^{-265}\) & \(7.02\times 10^{-258}\) & **0** & **0** & **0** \\  & Std & **0** & **0** & **0** & **0** & **0** \\  & Mean & \(2.85\times 10^{-238}\) & \(4.51\times 10^{-237}\) & \(2.53\times 10^{-287}\) & **0** & **0** \\ \hline \multirow{3}{*}{\(F_{10}\)} & Best & \(-5.48\times 10^{3}\) & \(-5.87\times 10^{3}\) & \(-6.47\times 10^{3}\) & \(-6.14\times 10^{3}\) & \(-6.43\times 10^{3}\) \\  & Std & \(\textbf{2.99}\times\textbf{10}^{2}\) & \(3.42\times 10^{2}\) & \(5.23\times 10^{2}\) & \(5.81\times 10^{2}\) & \(5.83\times 10^{2}\) \\  & Mean & \(-4.87\times 10^{3}\) & \(-4.98\times 10^{3}\) & \(-5.36\times 10^{3}\) & \(-5.06\times 10^{3}\) & \(-5.67\times 10^{3}\) \\ \hline \multirow{3}{*}{\(F_{11}\)} & Best & **0** & **0** & **0** & **0** & **0** \\  & Std & **0** & **0** & **0** & **0** & **0** \\ \hline \multirow{3}{*}{\(F_{12}\)} & Best & \(4.73\) & \(4.76\) & **4.72** & 4.76 & 4.75 \\ \cline{1-1}  & Std & \(4.77\times 10^{-2}\) & \(4.35\times 10^{-2}\) & \(4.09\times 10^{-2}\) & \(4.15\times 10^{-2}\) & \(\textbf{3.61}\times 10^{-2}\) \\ \cline{1-1}  & Mean & \(4.86\) & \(4.87\) & **4.84** & 4.88 & **4.84** \\ \hline \hline \end{tabular}
\end{table}