# A Hybrid Optimization Framework with Dynamic Transition Scheme for Large-Scale Portfolio Management
## 3 Methodology
### Dynamic Information Transition
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Func.** & **Metric** & **GA** & **PSO** & **WOA** & **DE** & **AMPO** & **CSDE** & **SADE** & **HYPO** \\ \hline F9 & Mean & 8.03\(\times\)10\({}^{8}\) & 2.66\(\times\)10\({}^{9}\) & 2.65\(\times\)10\({}^{9}\) & 6.62\(\times\)10\({}^{8}\) & 4.87\(\times\)10\({}^{8}\) & **1.75\(\times\)10\({}^{8}\)** & 4.07\(\times\)10\({}^{8}\) & 9.13\(\times\)10\({}^{8}\) \\  & Std. & 1.61\(\times\)10\({}^{7}\) & 4.47\(\times\)10\({}^{8}\) & 4.05\(\times\)10\({}^{8}\) & 3.81\(\times\)10\({}^{7}\) & 8.08\(\times\)10\({}^{7}\) & 1.70\(\times\)10\({}^{7}\) & 6.23\(\times\)10\({}^{7}\) & 1.95\(\times\)10\({}^{8}\) \\  & +/=/- & - & + & + & - & - & - & - \\ F10 & Mean & 9.40\(\times\)10\({}^{7}\) & 9.32\(\times\)10\({}^{7}\) & 9.34\(\times\)10\({}^{7}\) & 9.40\(\times\)10\({}^{7}\) & 9.27\(\times\)10\({}^{7}\) & 9.30\(\times\)10\({}^{7}\) & 9.30\(\times\)10\({}^{7}\) & **9.20\(\times\)10\({}^{7}\)** \\  & Std. & 2.83\(\times\)10\({}^{5}\) & 3.96\(\times\)10\({}^{5}\) & 4.32\(\times\)10\({}^{5}\) & 2.22\(\times\)10\({}^{5}\) & 5.10\(\times\)10\({}^{5}\) & 4.21\(\times\)10\({}^{5}\) & 6.59\(\times\)10\({}^{5}\) & 9.27\(\times\)10\({}^{5}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\ F11 & Mean & 1.20\(\times\)10\({}^{12}\) & 1.79\(\times\)10\({}^{15}\) & 6.56\(\times\)10\({}^{11}\) & 3.64\(\times\)10\({}^{11}\) & 3.75\(\times\)10\({}^{9}\) & 2.30\(\times\)10\({}^{9}\) & 2.09\(\times\)10\({}^{9}\) & **3.85\(\times\)10\({}^{8}\)** \\  & Std. & 1.05\(\times\)10\({}^{11}\) & 1.10\(\times\)10\({}^{15}\) & 8.70\(\times\)10\({}^{11}\) & 1.43\(\times\)10\({}^{11}\) & 5.07\(\times\)10\({}^{8}\) & 1.89\(\times\)10\({}^{9}\) & 3.97\(\times\)10\({}^{9}\) & 9.14\(\times\)10\({}^{7}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\ F12 & Mean & 5.07\(\times\)10\({}^{11}\) & 3.74\(\times\)10\({}^{12}\) & 4.54\(\times\)10\({}^{9}\) & 9.05\(\times\)10\({}^{11}\) & 4.00\(\times\)10\({}^{4}\) & 7.97\(\times\)10\({}^{3}\) & 1.23\(\times\)10\({}^{7}\) & **1.52\(\times\)10\({}^{3}\)** \\  & Std. & 1.06\(\times\)10\({}^{10}\) & 2.43\(\times\)10\({}^{11}\) & 4.94\(\times\)10\({}^{8}\) & 6.62\(\times\)10\({}^{10}\) & 5.29\(\times\)10\({}^{4}\) & 4.39\(\times\)10\({}^{3}\) & 3.42\(\times\)10\({}^{7}\) & 1.88\(\times\)10\({}^{2}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\ F13 & Mean & 3.85\(\times\)10\({}^{11}\) & 1.56\(\times\)10\({}^{15}\) & 9.15\(\times\)10\({}^{10}\) & 1.44\(\times\)10\({}^{11}\) & 5.06\(\times\)10\({}^{9}\) & 7.15\(\times\)10\({}^{9}\) & 1.19\(\times\)10\({}^{9}\) & **1.63\(\times\)10\({}^{8}\)** \\  & Std. & 2.69\(\times\)10\({}^{10}\) & 1.37\(\times\)10\({}^{15}\) & 3.68\(\times\)10\({}^{10}\) & 7.71\(\times\)10\({}^{10}\) & 8.88\(\times\)10\({}^{8}\) & 2.72\(\times\)10\({}^{9}\) & 3.58\(\times\)10\({}^{8}\) & 7.63\(\times\)10\({}^{7}\) \\  & +/=/- & + & + & + & + & + & + & + & \\ F14 & Mean & 3.32\(\times\)10\({}^{12}\) & 3.97\(\times\)10\({}^{15}\) & 1.45\(\times\)10\({}^{12}\) & 6.65\(\times\)10\({}^{11}\) & 2.07\(\times\)10\({}^{10}\) & 3.34\(\times\)10\({}^{10}\) & 8.85\(\times\)10\({}^{9}\) & **1.17\(\times\)10\({}^{8}\)** \\  & Std. & 2.31\(\times\)10\({}^{11}\) & 3.29\(\times\)10\({}^{15}\) & 6.61\(\times\)10\({}^{11}\) & 1.59\(\times\)10\({}^{11}\) & 1.09\(\times\)10\({}^{10}\) & 2.32\(\times\)10\({}^{10}\) & 6.63\(\times\)10\({}^{9}\) & 2.07\(\times\)10\({}^{7}\) \\  & +/=/- & + & + & + & + & + & + & + \\ F15 & Mean & 6.22\(\times\)10\({}^{9}\) & 1.28\(\times\)10\({}^{16}\) & 3.29\(\times\)10\({}^{10}\) & 3.27\(\times\)10\({}^{13}\) & 9.79\(\times\)10\({}^{7}\) & 1.99\(\times\)10\({}^{7}\) & 1.34\(\times\)10\({}^{7}\) & **6.23\(\times\)10\({}^{6}\)** \\  & Std. & 2.94\(\times\)10\({}^{9}\) & 1.37\(\times\)10\({}^{16}\) & 1.14\(\times\)10\({}^{10}\) & 1.21\(\times\)10\({}^{13}\) & 2.79\(\times\)10\({}^{7}\) & 5.68\(\times\)10\({}^{6}\) & 4.82\(\times\)10\({}^{6}\) & 3.96\(\times\)10\({}^{5}\) \\  & +/=/- & + & + & + & + & + & + & + \\ \hline \end{tabular}
\end{table}