# A Hybrid Optimization Framework with Dynamic Transition Scheme for Large-Scale Portfolio Management
## 3 Methodology
### Dynamic Information Transition  
As inspired by the dynamic branch prediction in the computer architecture filed, the decision process of information exchange in the proposed hybrid framework should be quickly responded to with less computing delay according to the historical contributions of meta-heuristics. As aforementioned, the information should not be unconditionally exchanged at each iteration. Accordingly, there are three essential components in the DCST scheme, namely contribution identification, state transition mechanism, and direction update mechanism. Before discussing the details, two new concepts, namely the system state and transition direction, are introduced into the DCST scheme for constructing the branch  
Figure 2: The Architecture of the Proposed HYPO Framework. predictor. Specifically, the system states including the stable state and intermediate state indicate the current position of the transition system. Besides, three transition directions are defined in this work. The bi-directional information transition enables the two meta-heuristic algorithms to share their best solutions with each other, whereas the other two situations are unidirectional transition for two algorithms such that that only one side can send the information to the opposite side. For convenience, the symbol of bi-directional transition is represented by 0 while that of unidirectional transitions are described by 1 or 2 for the transition flow from the AMPO framework to the CSDE approach only or vice versa. In recent studies, most adaptive mechanisms or cooperative mechanisms in meta-heuristic algorithms adjust search strategies by reviewing the historical contributions of each component. However, in tackling time-sensitive tasks such as online trading and path planning of unmanned driving, calculating the contributions of individuals or populations by using complicated rules is computationally intensive and requires larger memory space for storing historical data. Hence, to trade off the time requirement and contribution calculation on solving large-scale optimization problems, a simple update scheme is presented to identify the current contribution so that it can drive the state transition in the following step. As clearly depicted in Algorithm 3, the scheme will check if any information is being transmitted from the AMPO framework to the CSDE approach at the current iteration. It returns false if no information is being exchanged, otherwise it will further verify if there is an enhancement that is driven by the exchanging information just now. Finally, the value of the contribution signal is assigned true when the transmitted information from the AMPO approach can promote the CSDE search. The intent of the positive signal is to encourage the information transition from the AMPO algorithm to the CSDE approach in the following iterations. ```
Input:\(currentDirection\),\(isEnhance\). Output:\(contribSignal\). if(\(currentDirection=0\)) or (\(currentDirection=1\))then if(\(isEnhance=True\))then \(contribSignal\gets True\). else \(contribSignal\gets False\). end if else \(contribSignal\gets False\). end return\(contribSignal\). ```  
**Algorithm 3**The Update of Contribution Signal  
Furthermore, instead of using memory to store the historical performance of each meta-heuristic algorithm, a state-based transition system is applied in this work in which the system states are utilized to implicitly indicate the current environment of the system with the consideration of historical impacts. As depicted in Figure 3, \(S_{A}\) and \(M_{A}\) are the stable state and intermediate state that indicate the information transition direction from the AMPO to the CSDE. Conversely, \(S_{C}\) and \(M_{C}\) are the stable state and intermediate state that show the direction from the CSDE to the AMPO. \(stateCount\) records the current position of the system in which the \(stateCount\) will increase by 1 when the \(contribSignal\) is true, otherwise it will decrease by 1 when the \(contribSignal\) turns false.