## 3 Proposal Methodology
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Sphere Function**} \\ \hline \multirow{2}{*}{**Decades**} & \multirow{2}{*}{**ICA**} & \(\beta\)**Inc** & \(\xi\)**Inc** & \(\beta\)**Inc-\(\xi\)**Dec** \\ \cline{3-6}  & & & **1-2** & **0-1** & **1-2 and 0-1** \\ \hline \multirow{3}{*}{**1000**} & **Best** & \(3.11\times 10^{-31}\) & \(7.70\times 10^{-28}\) & \(4.59\times 10^{-31}\) & \(3.35\times 10^{-27}\) \\  & **Worst** & \(7.51\times 10^{-20}\) & \(1.71\times 10^{-24}\) & \(6.39\times 10^{-18}\) & \(7.98\times 10^{-22}\) \\  & **Mean** & \(2.51\times 10^{-21}\) & \(2.28\times 10^{-25}\) & \(2.50\times 10^{-19}\) & \(6.37\times 10^{-23}\) \\ \hline \multirow{3}{*}{**2000**} & **Best** & \(1.68\times 10^{-61}\) & \(1.94\times 10^{-57}\) & \(5.05\times 10^{-62}\) & \(1.26\times 10^{-56}\) \\  & **Worst** & \(3.55\times 10^{-48}\) & \(9.63\times 10^{-51}\) & \(3.62\times 10^{-27}\) & \(3.91\times 10^{-90}\) \\  & **Mean** & \(1.76\times 10^{-49}\) & \(5.08\times 10^{-52}\) & \(1.21\times 10^{-28}\) & \(2.59\times 10^{50}\) \\ \hline \multirow{3}{*}{**3000**} & **Best** & \(6.42\times 10^{-90}\) & \(3.66\times 10^{-87}\) & \(3.56\times 10^{-90}\) & \(2.14\times 10^{-85}\) \\  & **Worst** & \(1.33\times 10^{-52}\) & \(4.04\times 10^{-76}\) & \(7.56\times 10^{-25}\) & \(7.24\times 10^{-75}\) \\  & **Mean** & \(4.43\times 10^{-54}\) & \(1.53\times 10^{-77}\) & \(2.52\times 10^{-26}\) & \(2.86\times 10^{-76}\) \\ \hline \multirow{3}{*}{**4000**} & **Best** & \(1.66\times 10^{-123}\) & \(3.27\times 10^{-110}\) & \(1.19\times 10^{-122}\) & \(3.05\times 10^{-110}\) \\  & **Worst** & \(1.67\times 10^{-71}\) & \(2.21\times 10^{-97}\) & \(1.15\times 10^{-47}\) & \(9.98\times 10^{-97}\) \\ \cline{1-1}  & **Mean** & \(5.56\times 10^{-73}\) & \(9.51\times 10^{-99}\) & \(3.84\times 10^{-49}\) & \(3.34\times 10^{-98}\) \\ \hline \multirow{3}{*}{**5000**} & **Best** & \(3.25\times 10^{-154}\) & \(7.20\times 10^{-138}\) & \(8.53\times 10^{-154}\) & \(7.05\times 10^{-133}\) \\ \cline{1-1}  & **Worst** & \(4.50\times 10^{-121}\) & \(4.24\times 10^{-20}\) & \(9.90\times 10^{-16}\) & \(2.55\times 10^{-116}\) \\ \cline{1-1}  & **Mean** & \(1.50\times 10^{-122}\) & \(1.42\times 10^{-21}\) & \(3.30\times 10^{-17}\) & \(1.68\times 10^{-117}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sphere function. Table 3 shows the results of executing 30 times the proposed ICA algorithm with dynamic adaptation the \(\beta\) and \(\xi\), parameters, where we find the average, best and worst results obtained for the Rosenbrock function. Table 4 summarizes the results of running 30 times the proposed ICA algorithm with dynamic adaptation the \(\beta\) and \(\xi\), parameters, where we find the average, best and worst results obtained for the Rastrigin function. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{6}{c}{**Rastrigin Function**} \\ \hline \multirow{2}{*}{Decades} & \multirow{2}{*}{**ICA**} & \(\beta\)**Inc** & \(\xi\)**Inc** & \(\beta\)**Inc**-\(\xi\)**Dec** \\ \cline{3-6}  & & **1–2** & **0–1** & **1–2 and 0–1** \\ \hline \multirow{3}{*}{**1000**} & **Best** & 77.60654371 & 33.89704822 & 101.485221 & 61.40540354 \\  & **Worst** & 165.3705786 & 157.4160653 & 174.25906 & 151.2330801 \\  & **Mean** & 131.0164965 & 95.8100497 & 125.297209 & 108.721887 \\ \hline \multirow{3}{*}{**2000**} & **Best** & 66.66206493 & 3.542874325 & 46.762995 & 4.320732599 \\  & **Worst** & 156.421085 & 1154.4147346 & 153.222524 & 117.6886745 \\ \cline{1-1}  & **Mean** & 116.4624694 & 59.5472621 & 115.942776 & 52.6112894 \\ \hline \multirow{3}{*}{**3000**} & **Best** & 38.8033477 & 4.01886266 & 51.737346 & 0.065497359 \\ \cline{1-1}  & **Worst** & 149.3852153 & 98.57159506 & 159.192274 & 134.3184949 \\ \cline{1-1}  & **Mean** & 100.2171148 & 103.0026754 & 97.9436946 & 61.0832188 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Rastrigin function.