# A Hybrid Optimization Framework with Dynamic Transition Scheme for Large-Scale Portfolio Management
## 3 Methodology  
### Overall Architecture  
As mentioned in the previous section, the existing hybrid mechanisms between meta-heuristics suffer from two pitfalls. First, the information exchange mechanisms are not carefully considered for the factors including the timing, directions, and information of transition. For instance, frequently exchanging the currently best solution of each meta-heuristic branch to the opposite side may prematurely converge to local minima due to the diversification of populations being reduced. Besides, another major pitfall in some cases is that the hybrid frameworks randomly select one of meta-heuristics for every single individual at each iteration. Clearly, this will adversely affect the continuity of search behaviors, and limit the originally nature-inspired search mechanism of each algorithm for which the advantages of evolution may be revealed after keeping the characteristic search for a few iterations. Therefore, to develop an effective transition mechanism while retaining the advantages of special designs of each meta-heuristic algorithm, a simple yet powerful Dynamic Contribution-based State Transition (DCST) scheme is proposed in this work to connect different meta-heuristic algorithms for enhancing the overall search ability. As shown in Figure 2, the AMPO framework and CSDE approach are linked up by the DCST scheme. In particular, the proposed transition scheme decides when the hybrid framework transmits the information, which direction should be chosen, and what kinds of information should be exchanged. To clearly illustrate the HYPO framework, an example with practical value is how to optimize the capital allocation for different industries as a portfolio usually includes stocks from multiple industries for diversifying the risk. According to the company natures of stocks and the correlation between stocks, the stocks will be allocated to one of the industries (i.e., components). The stocks in the same component have strong correlations while different components may have contrary problems due to different impact factors. However, using a single meta-heuristic mechanism may work on one of the components, and it is difficult to find out the optimal solution for all components at the same time, especially in solving a large-scale portfolio. Thus, integrating different meta-heuristic mechanisms can adapt to more components during the search. For example, a portfolio has several stocks from two industries including real estate and the Internet. The AMPO method may work well on optimizing the capital allocation of stocks in real estate and fail at that of stocks in the Internet, but the CSDE method may fail in real estate and achieve better performance in the Internet. The proposed HYPO framework integrates two meta-heuristic methods and also completely retains their distinctive heuristic mechanism. During the search, those branches obtain some good-performing solutions that implicitly include the locally best allocation schemes of one of the industries, but they trap into local minima as the rest of solutions representing other industries are not optimal. To solve it, the dynamic contribution-based transition scheme in the HYPO framework decides the direction and information of transition by reviewing the contributions of each heuristic branch in the past few generations. Through the dynamic transition scheme, the optimal allocation plan collected by each branch can be shared to help escape from local minima and generate a better solution for the whole portfolio. Algorithm 2 describes the overall process of the hybrid optimization framework. At the beginning of the search, all user-defined parameters are input to the model. Then, all individuals are initialized and assigned to one of populations in two meta-heuristic algorithms. When starting the evolution process, the algorithm decides whether to transmit the good-performing solutions generated by the CSDE approach to the population of the AMPO framework in terms of the current transition direction.