# 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} \hline \hline
**Functions** & **ATR** & **FSA** & **FSA1** & **FSA2** & **FSA3** & **IFSA** \\ \hline \multirow{4}{*}{\(F_{13}\)} & Best & **0** & **0** & **0** & **0** & **0** \\  & Std & **0** & **0** & **0** & **0** & **0** \\  & Mean & **0** & **0** & **0** & **0** & **0** \\ \hline \multirow{4}{*}{\(F_{14}\)} & Best & 1.04 & 1.08 & **9.72 \(\times\) 10\(-\)1** & 1.03 & 1.01 \\  & Std & 8.47 \(\times\) 10\({}^{-2}\) & **7.49 \(\times\) 10\({}^{-2}\)** & 9.90 \(\times\) 10\({}^{-2}\) & 9.04 \(\times\) 10\({}^{-2}\) & 9.13 \(\times\) 10\({}^{-2}\) \\  & Mean & 1.22 & 1.23 & 1.23 & 1.22 & **1.17** \\ \hline \multirow{4}{*}{\(F_{15}\)} & Best & **2.55 \(\times\) 10\({}^{-5}\)** & **2.55 \(\times\) 10\({}^{-5}\)** & **2.55 \(\times\) 10\({}^{-5}\)** & **2.55 \(\times\) 10\({}^{-5}\)** \\  & Std & 1.61 \(\times\) 10\({}^{-6}\) & 6.21 \(\times\) 10\({}^{-5}\) & **7.74 \(\times\) 10\({}^{-7}\)** & 3.73 \(\times\) 10\({}^{-5}\) & 4.50 \(\times\) 10\({}^{-5}\) \\  & Mean & 2.60 \(\times\) 10\({}^{-5}\) & 3.77 \(\times\) 10\({}^{-5}\) & **2.57 \(\times\) 10\({}^{-5}\)** & 3.27 \(\times\) 10\({}^{-5}\) & 2.71 \(\times\) 10\({}^{-5}\) \\ \hline \multirow{4}{*}{\(F_{16}\)} & Best & **0** & **0** & **0** & **0** & **0** \\  & Std & 8.32 \(\times\) 10\({}^{-4}\) & 8.33 \(\times\) 10\({}^{-4}\) & **0** & 1.08 \(\times\) 10\({}^{-3}\) & **0** \\  & Mean & 2.12 \(\times\) 10\({}^{-3}\) & 2.12 \(\times\) 10\({}^{-3}\) & **0** & 1.80 \(\times\) 10\({}^{-3}\) & **0** \\ \hline \multirow{4}{*}{\(F_{17}\)} & Best & **0** & **0** & **0** & **0** & **0** \\  & Std & 3.00 \(\times\) 10\({}^{-2}\) & 3.00 \(\times\) 10\({}^{-2}\) & 3.00 \(\times\) 10\({}^{-2}\) & **2.49 \(\times\) 10\({}^{-2}\)** & **2.49 \(\times\) 10\({}^{-2}\)** \\  & Mean & 1.00 \(\times\) 10\({}^{-2}\) & 1.00 \(\times\) 10\({}^{-2}\) & 1.00 \(\times\) 10\({}^{-2}\) & **6.67 \(\times\) 10\({}^{-3}\)** & **6.67 \(\times\) 10\({}^{-3}\)** \\ \hline \multirow{4}{*}{\(F_{18}\)} & Best & **-2.06** & **-2.06** & **-2.06** & **-2.06** & **-2.06** \\  & Std & 7.11 \(\times\) 10\({}^{-11}\) & **4.34 \(\times\) 10\({}^{-12}\)** & 1.89 \(\times\) 10\({}^{-10}\) & 4.29 \(\times\) 10\({}^{-9}\) & 1.14 \(\times\) 10\({}^{-9}\) \\  & Mean & **-2.06** & **-2.06** & **-2.06** & **-2.06** & **-2.06** \\ \hline \multirow{4}{*}{\(F_{19}\)} & Best & **-1** & **-1** & **-1** & **-1** & **-1** \\  & Std & **0** & **0** & **0** & **0** & **0** \\  & Mean & **-1** & **-1** & **-1** & **-1** & **-1** \\ \hline \multirow{4}{*}{\(F_{20}\)} & Best & **0** & **0** & **0** & **0** & **0** \\  & Std & **0** & **0** & **0** & **0** & **0** \\  & Mean & **0** & **0** & **0** & **0** & **0** \\ \hline \multirow{4}{*}{\(F_{21}\)} & Best & **0** & **0** & **0** & **0** & **0** \\  & Mean & 5.30 \(\times\) 10\({}^{-304}\) & 1.05 \(\times\) 10\({}^{-302}\) & **0** & **0** & **0** \\ \hline \multirow{4}{*}{\(F_{22}\)} & Best & **0** & **0** & **0** & **0** & **0** \\  & Std & **0** & **0** & **0** & **0** & **0** \\ \cline{1-1}  & Mean & **0** & 1.51 \(\times\) 10\({}^{-305}\) & **0** & **0** & **0** \\ \hline \multirow{4}{*}{\(F_{23}\)} & Best & **6.05 \(\times\) 10\({}^{-2}\)** & 2.24 \(\times\) 10\({}^{-1}\) & 1.97 \(\times\) 10\({}^{-1}\) & 1.88 \(\times\) 10\({}^{-1}\) & 2.24 \(\times\) 10\({}^{-1}\) \\ \cline{1-1}  & Std & **7.73 \(\times\) 10\({}^{-1}\)** & 1.27 & 1.40 & 1.17 & 9.20 \(\times\) 10\({}^{-1}\) \\ \cline{1-1}  & Mean & **6.70 \(\times\) 10\({}^{-1}\)** & 9.41 \(\times\) 10\({}^{-1}\) & 1.08 & 1.06 & 7.60 \(\times\) 10\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._optimization. For the fixed-size test functions F18-F22, with fixed dimensions, IFSA has the optimal results for all of them. In addition, for F19-F22, the standard deviations of IFSA are all zero, indicating that IFSA has good stability and search accuracy in solving these functions. For F17, WOA performs the best, and IFSA has the least difference from the WOA algorithm in terms of standard deviation and mean value.