# 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 \hline
**Func. ** & **Metric** & **GA** & **PSO** & **WOA** & **DE** & **AMPO** & **CSDE** & **SADE** & **HYPO** \\ \hline F1 & Mean & 3.95\(\times 10^{10}\) & 1.85\(\times 10^{11}\) & 7.88\(\times 10^{9}\) & 2.74\(\times 10^{10}\) & 8.47\(\times 10^{7}\) & **7.72\(\times 10^{2}\)** & 2.20\(\times 10^{5}\) & 1.23\(\times 10^{5}\) \\  & Std. & 8.21\(\times 10^{8}\) & 1.93\(\times 10^{10}\) & 4.82\(\times 10^{8}\) & 3.00\(\times 10^{9}\) & 1.15\(\times 10^{8}\) & 1.94\(\times 10^{3}\) & 4.62\(\times 10^{5}\) & 8.02\(\times 10^{4}\) \\  & +/=/- & + & + & + & + & + & - & - & \\ F2 & Mean & 2.45\(\times 10^{4}\) & 6.82\(\times 10^{4}\) & 3.74\(\times 10^{4}\) & 2.44\(\times 10^{4}\) & 1.13\(\times 10^{4}\) & **2.66\(\times 10^{3}\)** & 1.87\(\times 10^{4}\) & 2.01\(\times 10^{4}\) \\  & Std. & 2.49\(\times 10^{2}\) & 5.84\(\times 10^{5}\) & 5.57\(\times 10^{2}\) & 8.94\(\times 10^{2}\) & 6.05\(\times 10^{2}\) & 2.26\(\times 10^{2}\) & 3.02\(\times 10^{3}\) & 1.01\(\times 10^{3}\) \\  & +/=/- & + & + & + & + & + & - & - & - \\ F3 & Mean & 2.16\(\times 10^{1}\) & 2.15\(\times 10^{1}\) & 2.16\(\times 10^{1}\) & 2.15\(\times 10^{1}\) & 2.07\(\times 10^{1}\) & 2.08\(\times 10^{1}\) & 2.07\(\times 10^{1}\) & **2.05\(\times 10^{1}\)** \\  & Std. & 4.52\(\times 10^{-3}\) & 2.28\(\times 10^{-2}\) & 1.56\(\times 10^{-2}\) & 4.41\(\times 10^{-3}\) & 3.07\(\times 10^{-2}\) & 2.22\(\times 10^{-2}\) & 8.69\(\times 10^{-3}\) & 7.74\(\times 10^{-2}\) \\  & +/=/- & + & + & + & + & + & + & + & \\ F4 & Mean & 1.16\(\times 10^{12}\) & 3.67\(\times 10^{12}\) & 7.03\(\times 10^{11}\) & 3.15\(\times 10^{11}\) & 1.65\(\times 10^{11}\) & 4.05\(\times 10^{10}\) & 7.59\(\times 10^{9}\) & **2.48\(\times 10^{9}\)** \\  & Std. & 6.91\(\times 10^{10}\) & 1.38\(\times 10^{12}\) & 6.80\(\times 10^{10}\) & 6.06\(\times 10^{10}\) & 1.33\(\times 10^{10}\) & 1.96\(\times 10^{10}\) & 2.89\(\times 10^{9}\) & 7.59\(\times 10^{8}\) \\  & +/=/- & + & + & + & + & + & + & + & \\ F5 & Mean & 1.02\(\times 10^{7}\) & 3.17\(\times 10^{7}\) & 3.16\(\times 10^{7}\) & 8.18\(\times 10^{6}\) & 4.24\(\times 10^{6}\) & **1.70\(\times 10^{6}\)** & 4.59\(\times 10^{6}\) & 1.18\(\times 10^{7}\) \\  & Std. & 2.34\(\times 10^{5}\) & 3.91\(\times 10^{6}\) & 3.45\(\times 10^{6}\) & 7.37\(\times 10^{5}\) & 9.02\(\times 10^{5}\) & 4.17\(\times 10^{5}\) & 8.43\(\times 10^{5}\) & 3.82\(\times 10^{6}\) \\  & +/=/- & - & + & + & + & - & - & - & - \\ F6 & Mean & 1.06\(\times 10^{6}\) & 1.05\(\times 10^{6}\) & 1.06\(\times 10^{6}\) & 1.06\(\times 10^{6}\) & 1.05\(\times 10^{6}\) & 1.05\(\times 10^{6}\) & 1.05\(\times 10^{6}\) & **1.03\(\times 10^{6}\)** \\  & Std. & 8.65\(\times 10^{2}\) & 3.16\(\times 10^{5}\) & 2.75\(\times 10^{3}\) & 9.49\(\times 10^{2}\) & 6.65\(\times 10^{3}\) & 3.51\(\times 10^{3}\) & 7.50\(\times 10^{3}\) & 1.43\(\times 10^{4}\) \\  & +/=/- & + & + & + & + & + & + & + & \\ F7 & Mean & 6.15\(\times 10^{9}\) & 1.02\(\times 10^{13}\) & 7.15\(\times 10^{9}\) & 1.57\(\times 10^{9}\) & 2.00\(\times 10^{8}\) & 1.96\(\times 10^{8}\) & 1.72\(\times 10^{7}\) & **3.79\(\times 10^{6}\)** \\  & Std. & 5.88\(\times 10^{8}\) & 9.79\(\times 10^{12}\) & 3.76\(\times 10^{9}\) & 6.68\(\times 10^{8}\) & 5.37\(\times 10^{7}\) & 1.68\(\times 10^{8}\) & 9.20\(\times 10^{6}\) & 1.40\(\times 10^{6}\) \\  & +/=/- & + & + & + & + & + & + & + & \\ F8 & Mean & 1.24\(\times 10^{16}\) & 9.40\(\times 10^{16}\) & 4.71\(\times 10^{15}\) & 2.57\(\times 10^{15}\) & 3.90\(\times 10^{14}\) & 2.42\(\times 10^{14}\) & 8.43\(\times 10^{13}\) & **4.66\(\times 10^{13}\)** \\  & Std. & 2.36\(\times 10^{15}\) & 5.92\(\times 10^{16}\) & 2.04\(\times 10^{15}\) & 7.94\(\times 10^{14}\) & 1.78\(\times 10^{14}\) & 1.30\(\times 10^{14}\) & 3.45\(\times 1

#### 4.1.2 The Analysis of the Convergence

Besides being evaluated the quality of solutions at the end of the search, the speed of convergence is concerned in this work in which the average currently best fitness values at each generation on 25 runs are recorded to plot the convergence curve.