# Multi-Strategy Improved Flamingo Search Algorithm for Global Optimization
## 4 Experiments and Analysis
### Comparative Analysis of Convergence Curves
\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}{*}{\(F_{13}\)} & Best & \(9.12\times 10^{-2}\) & **0** & **0** & **0** & **0** & **0** & **0** \\  & Std & \(5.27\times 10^{-2}\) & \(8.74\times 10^{-3}\) & \(8.33\times 10^{-3}\) & \(3.46\times 10^{-3}\) & **0** & **0** & **0** \\  & Mean & \(1.85\times 10^{-1}\) & \(5.79\times 10^{-3}\) & \(2.71\times 10^{-3}\) & \(1.10\times 10^{-3}\) & **0** & **0** & **0** \\ \hline \multirow{3}{*}{\(F_{14}\)} & Best & \(3.59\times 10^{-1}\) & \(1.81\times 10^{-1}\) & \(4.59\times 10^{-1}\) & \(9.52\times 10^{-1}\) & \(\mathbf{1.77\times 10^{-4}}\) & \(6.28\times 10^{-4}\) & \(1.01\) \\  & Std & \(1.82\) & \(1.58\times 10^{-1}\) & \(2.28\times 10^{-1}\) & \(2.64\times 10^{-1}\) & \(\mathbf{6.13\times 10^{-2}}\) & \(1.54\times 10^{-1}\) & \(9.13\times 10^{-2}\) \\  & Mean & \(2.08\) & \(4.29\times 10^{-1}\) & \(8.31\times 10^{-1}\) & \(1.48\) & \(\mathbf{2.48\times 10^{-2}}\) & \(3.25\times 10^{-1}\) & \(1.17\) \\ \hline \multirow{3}{*}{\(F_{15}\)} & Best & \(2.59\times 10^{-5}\) & \(2.85\times 10^{-5}\) & \(6.70\times 10^{-5}\) & \(4.19\times 10^{-2}\) & \(\mathbf{2.55\times 10^{-5}}\) & \(\mathbf{2.55\times 10^{-5}}\) & \(\mathbf{2.55\times 10^{-5}}\) \\  & Std & \(7.16\times 10\) & \(5.91\times 10\) & \(9.62\) & \(9.08\times 10\) & \(1.08\times 10^{-6}\) & **0** & \(4.50\times 10^{-5}\) \\  & Mean & \(5.89\times 10\) & \(5.53\times 10\) & \(4.08\) & \(1.12\times 10^{2}\) & \(2.57\times 10^{-5}\) & \(\mathbf{2.55\times 10^{-5}}\) & \(2.71\times 10^{-5}\) \\ \hline \multirow{3}{*}{\(F_{16}\)} & Best & \(9.58\times 10^{-3}\) & \(2.45\times 10^{-3}\) & \(2.45\times 10^{-3}\) & \(2.45\times 10^{-3}\) & **0** & **0** & **0** \\  & Std & \(5.61\times 10^{-3}\) & \(3.36\times 10^{-3}\) & \(1.28\times 10^{-3}\) & \(3.38\times 10^{-6}\) & \(6.11\times 10^{-4}\) & **0** & **0** \\  & Mean & \(1.52\times 10^{-2}\) & \(7.21\times 10^{-3}\) & \(2.69\times 10^{-3}\) & \(2.45\times 10^{-3}\) & \(2.29\times 10^{-3}\) & **0** & **0** \\ \hline \multirow{3}{*}{\(F_{17}\)} & Best & \(1.53\times 10^{-1}\) & **0** & **0** & \(9.83\times 10^{-2}\) & \(1.05\times 10^{-2}\) & \(1.00\times 10^{-1}\) & **0** \\  & Std & \(5.95\times 10^{-1}\) & \(5.14\times 10^{-2}\) & \(1.82\times 10^{-2}\) & \(4.72\times 10^{-2}\) & \(4.66\times 10^{-2}\) & \(\mathbf{2.78\times 10^{-17}}\) & \(2.49\times 10^{-2}\) \\  & Mean & \(9.75\times 10^{-1}\) & \(2.26\times 10^{-2}\) & \(\mathbf{3.37\times 10^{-3}}\) & \(1.34\times 10^{-1}\) & \(8.70\times 10^{-2}\) & \(1.00\times 10^{-1}\) & \(6.67\times 10^{-3}\) \\ \hline \multirow{3}{*}{\(F_{18}\)} & Best & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) \\  & Std & \(9.58\times 10^{-7}\) & \(6.75\times 10^{-9}\) & \(1.47\times 10^{-8}\) & \(1.24\times 10^{-5}\) & \(2.90\times 10^{-10}\) & \(\mathbf{5.40\times 10^{-11}}\) & \(1.14\times 10^{-9}\) \\  & Mean & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) & \(\mathbf{-2.06}\) \\ \hline \multirow{3}{*}{\(F_{19}\)} & Best & \(\mathbf{-1}\) & \(\mathbf{-1}\) & \(\mathbf{-1}\) & \(\mathbf{-1}\) & \(\mathbf{-1}\) & \(\mathbf{-1}\) & \(\mathbf{-1}\) & \(\mathbf{-1}\) & \(\mathbf{-1}\) \\  & Std & \(6.51\times 10^{-4}\) & **0** & **0** & **0** & \(3.12\times 10^{-2}\) & **0** & **0** \\  &Figure 2: _Cont._  
Figure 2: _Cont._  
Figure 2: Comparison of convergence curves. In summary, the IFSA algorithm shows better convergence accuracy and faster search efficiency in most of the tested functions, allowing the optimization process to find the convergence direction quickly.