# 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 c} \hline \hline
**Dim.** & **Metric** & **GA** & **PSO** & **WOA** & **DE** & **AMPO** & **CSDE** & **SADE** & **HYPO** \\ \hline
100 & SR Mean & 1.1219 & 0.9771 & 1.1765 & 1.4051 & 1.5137 & 1.5152 & **1.5207** & 1.5207 \\  & SR Std. & 4.61\(\times 10^{-3}\) & 1.99\(\times 10^{-2}\) & 1.30\(\times 10^{-1}\) & 2.42\(\times 10^{-2}\) & 1.13\(\times 10^{-2}\) & 8.84\(\times 10^{-3}\) & 1.03\(\times 10^{-6}\) & 2.76\(\times 10^{-6}\) \\  & +/=/- & + & + & + & + & + & + & - & - \\
200 & SR Mean & 1.0583 & 0.9085 & 1.0793 & 1.3004 & 1.6618 & 1.6137 & 1.6749 & **1.6840** \\  & SR Std. & 3.87\(\times 10^{-3}\) & 1.70\(\times 10^{-2}\) & 1.13\(\times 10^{-1}\) & 2.13\(\times 10^{-2}\) & 3.18\(\times 10^{-2}\) & 3.12\(\times 10^{-2}\) & 1.29\(\times 10^{-2}\) & 1.72\(\times 10^{-5}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\
300 & SR Mean & 1.0456 & 0.8916 & 1.2593 & 1.3125 & 2.0323 & 1.8549 & 2.0074 & **2.0893** \\  & SR Std. & 2.75\(\times 10^{-3}\) & 1.43\(\times 10^{-2}\) & 2.90\(\times 10^{-1}\) & 2.99\(\times 10^{-2}\) & 4.78\(\times 10^{-2}\) & 6.61\(\times 10^{-2}\) & 6.36\(\times 10^{-2}\) & 1.47\(\times 10^{-5}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\
400 & SR Mean & 0.9977 & 0.8495 & 1.2334 & 1.2127 & 1.9398 & 1.6984 & 1.8334 & **2.0894** \\  & SR Std. & 2.50\(\times 10^{-3}\) & 9.26\(\times 10^{-3}\) & 3.12\(\times 10^{-1}\) & 1.94\(\times 10^{-2}\) & 4.69\(\times 10^{-2}\) & 4.35\(\times 10^{-2}\) & 5.27\(\times 10^{-2}\) & 5.00\(\times 10^{-5}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\
490 & SR Mean & 0.9035 & 0.7631 & 1.1391 & 1.0988 & 1.8371 & 1.5822 & 1.7065 & **2.0891** \\  & SR Std. & 2.87\(\times 10^{-3}\) & 1.12\(\times 10^{-2}\) & 3.53\(\times 10^{-1}\) & 2.21\(\times 10^{-2}\) & 4.63\(\times 10^{-2}\) & 3.66\(\times 10^{-2}\) & 5.65\(\times 10^{-2}\) & 1.82\(\times 10^{-3}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparative Results on the SP500 Set. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dim.** & **Metric** & **GA** & **PSO** & **WOA** & **DE** & **AMPO** & **CSDE** & **SADE** & **HYPO** \\ \hline
50 & SR Mean & 1.6756 & 1.5327 & 1.6692 & 1.8461 & 1.8480 & 1.8482 & **1.8482** & 1.8482 \\  & SR Std. & 4.23\(\times 10^{-3}\) & 5.11\(\times 10^{-2}\) & 7.74\(\times 10^{-2}\) & 6.31\(\times 10^{-3}\) & 6.60\(\times 10^{-4}\) & 2.68\(\times 10^{-6}\) & 7.22\(\times 10^{-9}\) & 3.30\(\times 10^{-7}\) \\  & +/=/- & + & + & + & + & + & + & - & - \\
100 & SR Mean & 1.6503 & 1.4299 & 1.6125 & 1.8956 & 1.9854 & 1.9867 & 1.9881 & **1.9881** \\  & SR Std. & 4.74\(\times 10^{-3}\) & 3.69\(\times 10^{-2}\) & 1.03\(\times 10^{-1}\) & 1.81\(\times 10^{-2}\) & 3.58\(\times 10^{-3}\) & 1.67\(\times 10^{-3}\) & 1.53\(\times 10^{-5}\) & 5.20\(\times 10^{-5}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\
150 & SR Mean & 1.5761 & 1.3180 & 1.5289 & 1.8526 & 2.0222 & 2.0199 & 2.0314 & **2.0317** \\  & SR Std. & 5.03\(\times 10^{-3}\) & 3.56\(\times 10^{-2}\) & 1.13\(\times 10^{-1}\) & 2.20\(\times 10^{-2}\) & 1.22\(\times 10^{-2}\) & 1.08\(\times 10^{-2}\) & 1.94\(\times 10^{-4}\) & 2.55\(\times 10^{-5}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\
200 & SR Mean & 1.4810 & 1.2271 & 1.4671 & 1.7743 & 2.0370 & 2.0226 & 2.0599 & **2.0682** \\  & SR Std. & 6.26\(\times 10^{-3}\) & 2.71\(\times 10^{-2}\) & 1.34\(\times 10^{-1}\) & 2.17\(\times 10^{-2}\) & 2.40\(\times 10^{-2}\) & 1.26\(\times 10^{-2}\) & 9.82\(\times 10^{-3}\) & 7.41\(\times 10^{-5}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\
239 & SR Mean & 1.4129 & 1.1602 & 1.4284 & 1.7086 & 2.0248 & 1.9703 & 2.0316 & **2.0703** \\  & SR Std. & 4.94\(\times 10^{-3}\) & 2.28\(\times 10^{-2}\) & 1.40\(\times 10^{-1}\) & 2.83\(\times 10^{-2}\) & 2.02\(\times 10^{-2}\) & 2.36\(\times 10^{-2}\) & 1.95\(\times 10^{-2}\) & 1.48\(\times 10^{-4}\) \\  & +/=/- & + & + & + & + & + & + & + & + \\  & +/=/- & + & + & + & + & + & + & + & + \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparative Results on the CSI300 Set.