# 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} \hline \hline
**Func.** & **Metric** & \begin{tabular}{c} **Uni-AMPO-** \\ **CSDE** \\ \end{tabular} & \begin{tabular}{c} **Uni-CSDE-** \\ **AMPO** \\ **CSDE** \\ \end{tabular} & \begin{tabular}{c} **Bi-AMPO-** \\ **CSDE** \\ \end{tabular} & \
\begin{tabular}{c} **No-Exchange** \\ \end{tabular} &
\begin{tabular}{c} **HYPO** \\ **HYPO** \\ \end{tabular} \\ \hline F3 & Fit Mean & 2.08\(\times\)10\({}^{1}\) & 2.08\(\times\)10\({}^{1}\) & 2.06\(\times\)10\({}^{1}\) & 2.08\(\times\)10\({}^{1}\) & **2.05\(\times\)10\({}^{1}\)** \\  & Std. & 1.97\(\times\)10\({}^{-2}\) & 2.33\(\times\)10\({}^{-2}\) & 1.29\(\times\)10\({}^{-1}\) & 2.28\(\times\)10\({}^{-2}\) & 7.74\(\times\)10\({}^{-2}\) \\ F7 & Fit Mean & 1.69\(\times\)10\({}^{8}\) & 2.16\(\times\)10\({}^{8}\) & 4.70\(\times\)10\({}^{6}\) & 2.27\(\times\)10\({}^{8}\) & 3.79\(\times\)10\({}^{6}\) \\  & Std. & 4.44\(\times\)10\({}^{7}\) & 4.62\(\times\)10\({}^{7}\) & 1.17\(\times\)10\({}^{6}\) & 6.74\(\times\)10\({}^{7}\) & 1.40\(\times\)10\({}^{6}\) \\ F12 & Fit Mean & 1.99\(\times\)10\({}^{4}\) & 3.35\(\times\)10\({}^{4}\) & **1.38\(\times\)10\({}^{3}\)** & 6.56\(\times\)10\({}^{4}\) & 1.52\(\times\)10\({}^{3}\) \\  & Std. & 1.30\(\times\)10\({}^{4}\) & 3.96\(\times\)10\({}^{4}\) & 2.04\(\times\)10\({}^{2}\) & 6.28\(\times\)10\({}^{4}\) & 1.88\(\times\)10\({}^{2}\) \\ F15 & Fit Mean & 2.18\(\times\)10\({}^{7}\) & 4.95\(\times\)10\({}^{7}\) & **5.72\(\times\)10\({}^{6}\)** & 6.03\(\times\)10\({}^{7}\) & 6.23\(\times\)10\({}^{6}\) \\  & Std. & 5.71\(\times\)10\({}^{6}\) & 2.62\(\times\)10\({}^{7}\) & 4.86\(\times\)10\({}^{5}\) & 3.93\(\times\)10\({}^{7}\) & 3.96\(\times\)10\({}^{5}\) \\ SP500-490 Dim & SR Mean & 1.7040 & 1.2715 & 2.0791 & 1.4377 & **2.0891** \\  & Std. & 3.16\(\times\)10\({}^{-1}\) & 2.47\(\times\)10\({}^{-2}\) & 1.16\(\times\)10\({}^{-2}\) & 2.06\(\times\)10\({}^{-1}\) & 1.82\(\times\)10\({}^{-3}\) \\ CSI300-239 Dim & SR Mean & 1.8843 & 1.8082 & 2.0700 & 1.8010 & **2.0703** \\  & Std. & 2.54\(\times\)10\({}^{-2}\) & 2.61\(\times\)10\({}^{-2}\) & 2.86\(\times\)10\({}^{-3}\) & 2.74\(\times\)10\({}^{-2}\) & 1.48\(\times\)10\({}^{-4}\) \\ Mix-788 Dim & SR Mean & 2.0952 & 1.8916 & 2.8521 & 1.9239 & **2.8804** \\  & Std. & 1.24\(\times\)10\({}^{-1}\) & 4.10\(\times\)10\({}^{-2}\) & 2.04\(\times\)10\({}^{-2}\) & 8.09\(\times\)10\({}^{-2}\) & 7.80\(\times\)10\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparative Results on Different Settings of Transition Directions. united framework may help to strengthen the adaptability of the underlying algorithms and potentially solve more optimization problems while speeding up the convergence at different search stages. This is especially the case when solving large-scale optimization problems for which different meta-heuristic approaches can be good at optimizing various subcomponents of the problem at hand. More importantly, the hybrid mechanism is the key to success in developing a cooperative framework in which an intelligent guiding mechanism is included to determine the direction, information, and frequency of exchanges between the key search methods. However, the existing approaches do not carefully consider such a guiding mechanism of a hybrid search framework in a systematic manner, for which the resulting hybrid search framework will prematurely converge to local minima at an early search stage. Therefore, an efficient Hybrid Population-based Optimization (HYPO) framework is proposed in this work in which a systematic guiding scheme named the Dynamic Contribution-based State Transition (DCST) is considered to integrate two prominent meta-heuristic algorithms into the HYPO framework through constantly reviewing their individual contributions to decide the timing and direction of an information exchange between the two concerned search algorithms.