# 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 c c c} \hline \hline
**Functions** & **ATR** & **PSO** & **GWO** & **WOA** & **TSA** & **ARO** & **AHA** & **IFSA** \\ \hline \multirow{3}{*}{\(F_{1}\)} & Best & \(1.75\times 10^{-1}\) & \(1.71\times 10^{-29}\) & \(3.89\times 10^{-20}\) & \(3.03\times 10^{-71}\) & \(7.46\times 10^{-45}\) & \(2.93\times 10^{-107}\) & **0** \\  & Std & \(3.18\times 10^{-1}\) & \(3.20\times 10^{-27}\) & \(4.21\times 10^{-17}\) & \(2.73\times 10^{-70}\) & \(8.70\times 10^{-32}\) & \(5.95\times 10^{-80}\) & **0** \\  & Mean & \(6.95\times 10^{-1}\) & \(1.82\times 10^{-27}\) & \(1.76\times 10^{-17}\) & \(2.58\times 10^{-70}\) & \(2.62\times 10^{-32}\) & \(1.11\times 10^{-80}\) & **0** \\ \hline \multirow{3}{*}{\(F_{2}\)} & Best & \(1.90\) & \(2.27\times 10^{-17}\) & \(1.84\times 10^{-13}\) & \(2.34\times 10^{-37}\) & \(5.32\times 10^{-23}\) & \(8.67\times 10^{-51}\) & **3.47 \(\times 10^{-225}\)** \\  & Std & \(6.79\times 10^{-1}\) & \(1.09\times 10^{-16}\) & \(3.58\times 10^{-12}\) & \(3.14\times 10^{-37}\) & \(5.05\times 10^{-19}\) & \(6.71\times 10^{-42}\) & **0** \\  & Mean & \(3.36\) & \(1.48\times 10^{-16}\) & \(3.20\times 10^{-12}\) & \(7.29\times 10^{-37}\) & \(2.24\times 10^{-19}\) & \(1.49\times 10^{-42}\) & **1.49 \(\times 10^{-216}\)** \\ \hline \multirow{3}{*}{\(F_{3}\)} & Best & \(3.21\times 10^{2}\) & \(1.48\times 10^{2}\) & \(3.65\) & \(4.32\times 10^{-49}\) & \(2.49\times 10^{-33}\) & \(6.94\times 10^{-84}\) & **0** \\  & Std & \(4.12\times 10^{2}\) & \(8.98\times 10^{2}\) & \(2.37\times 10^{3}\) & \(1.10\times 10^{-34}\) & \(6.95\times 10^{-9}\) & \(3.33\times 10^{-62}\) & **0** \\  & Mean & \(8.94\times 10^{2}\) & \(1.01\times 10^{3}\) & \(6.87\times 10^{2}\) & \(2.06\times 10^{-35}\) & \(1.29\times 10^{-9}\) & \(6.20\times 10^{-63}\) & **0** \\ \hline \multirow{3}{*}{\(F_{4}\)} & Best & \(5.99\times 10^{-1}\) & \(1.47\times 10^{-8}\) & \(1.86\times 10^{-5}\) & \(8.67\times 10^{-33}\) & \(8.88\times 10^{-18}\) & \(1.81\times 10^{-44}\) & **1.45 \(\times 10^{-228}\)** \\  & Std & \(4.19\times 10^{-1}\) & \(1.23\times 10^{-7}\) & \(1.25\times 10^{-3}\) & \(1.39\times 10^{-32}\) & \(1.22\times 10^{-13}\) & \(1.08\times 10^{-38}\) & **0** \\  & Mean & \(1.09\) & \(1.46\times 10^{-7}\) & \(8.65\times 10^{-4}\) & \(2.78\times 10^{-32}\) & \(4.36\times 10^{-14}\) & \(3.25\times 10^{-39}\) & **1.96 \(\times 10^{-215}\)** \\ \hline \multirow{3}{*}{\(F_{5}\)} & Best & \(4.12\times 10\) & \(1.61\times 10\) & \(1.57\times 10\) & \(1.80\times 10\) & **3.65 \(\times 10^{-3}\)** & \(1.60\times 10\) & \(1.69\times 10\) \\  & Std & \(2.47\times 10\) & \(5.18\times 10^{-1}\) & \(7.60\times 10^{-1}\) & **3.77 \(\times 10^{-1}\)** & 4.22 & \(5.69\times 10^{-1}\) & \(4.61\times 10^{-1}\) \\  & Mean & \(8.00\times 10\) & \(1.68\times 10\) & \(1.71\times 10\) & \(1.87\times 10\) & **1.26** & \(1.68\times 10\) & \(1.80\times 10\) \\ \hline \multirow{3}{*}{\(F_{6}\)} & Best & \(3.08\times 10^{-1}\) & \(\textbf{7.66}\times\textbf{10}^{-6}\) & \(5.51\times 10^{-3}\) & \(3.05\) & \(2.02\times 10^{-4}\) & \(7.93\times 10^{-5}\) & 1.86 \\  & Std & \(2.87\times 10^{-1}\) & \(1.25\times 10^{-1}\) & \(3.00\times 10^{-1}\) & \(3.05\times 10^{-1}\) & \(\textbf{3.82}\times 10^{-4}\) & \(3.64\times 10^{-3}\) & \(3.22\times 10^{-1}\) \\  & Mean & \(7.72\times 10^{-1}\) & \(5.90\times 10^{-2}\) & \(4.73\times 10^{-1}\) & 3.86 & \(\textbf{6.41}\times\textbf{10}^{-4}\) & \(2.57\times 10^{-3}\) & 2.70 \\ \hline \multirow{3}{*}{\(F_{7}\)} & Best & \(1.16\times 10^{-1}\) & \(5.81\times 10^{-4}\) & \(2.57\times 10^{-5}\) & \(1.48\times 10^{-6}\) & \(5.69\times 10^{-5}\) & \(2.91\times 10^{-5}\) & \(\textbf{6.40}\times\textbf{10}^{-7}\) \\  & Std & \(1.45\times 10^{-1}\) & \(7.72\times 10^{-4}\) & \(5.21\times 10^{-4}\) & \(\textbf{7.41}\times\textbf{10}^{-5}\) & \(7.52\times 10^{-4}\) & \(2.99\times 10^{-4}\) & \(8.49\times 10^{-5}\) \\  & Mean & \(3.17\times 10^{-1}\) & \(1.44\times 10^{-3}\) & \(5.98\times 10^{-4}\) & \(9.81\times 10^{-5}\) & \(9.16\times 10^{-4}\) & \(3.29\times 10^{-4}\) & \(\textbf{6.43}\times\textbf{10}^{-5}\) \\ \hline \multirow{3}{*}{\(F_{8}\)} & Best & \(1.08\times 10^{-3}\) & \(4.87\times 10^{-67}\) & \(7.09\times 10^{-52}\) & \(1.38\times 10^{-95}\) & \(5.41\times 10^{-48}\) & \(1.34\times 10^{-75}