# A Hybrid Optimization Framework with Dynamic Transition Scheme for Large-Scale Portfolio Management
###### Abstract
Furthermore, more intelligent algorithms have been introduced to deal with online portfolio optimization problems with the consideration of real market factors such as transaction cost, slippage, and turnover rate. Yet for the simplicity of the analysis of large-scale portfolio management problems, it is our intent to consider returns and risks only in the following sections. As aforementioned, cooperating two or more meta-heuristic algorithms may benefit from adapting more scenarios by introducing various search mechanisms. However, when hybridizing different algorithms, unconditionally exchanging all information between meta-heuristic algorithms may reduce the diversification of populations because the populations in all meta-heuristic branches are synchronized to the same individuals after exchanging at each generation. In particular, in the early search stage, all branches will search on the same local areas so that the abilities to explore more promising areas will be limited, eventually leading to premature convergence. Accordingly, a simple yet efficient Hybrid Population-based Optimization (HYPO) framework is presented in this paper to flexibly control the directions of information flow between two meta-heuristic algorithms so as to appropriately transmit the useful information to another side while both sides can keep their characteristic search paradigms. First, an Adaptive Multi-Population Optimization (AMPO) algorithm and a self-adaptive Differential Evolution (DE) algorithm are selected and assigned to two algorithmic branches. Then, a Dynamic Contribution-based State Transition (DCST) scheme is proposed to decide the directions of information transition through reviewing the current contribution and system state. Lastly, according to the updated directions of information flow, useful information is shared from one side to another side from which the individuals can learn. The useful information can be defined as the currently best solution or all good-performing solutions of each meta-heuristic. The main contributions of this paper are described as follows:  
1. Both swarm intelligence techniques and evolutionary computation algorithms are integrated into a united optimization framework. The advanced concepts of search in each algorithm are retained and complement each other so that the proposed framework can adapt to more scenarios. 2. The proposed dynamic transition scheme can conditionally control the directions of information flow by introducing a contribution-based mechanism in which the findings of each algorithm can be shared at the appropriate time to enhance the search efficiency and avoid trapping into local minima. 3. For large-scale optimization problems, different meta-heuristic algorithms are good at optimizing different subcomponents with a set of non-separable decision variables. The proposed hybrid framework can help to integrate locally optimal solutions of subcomponents so as to enhance the quality of the whole solution and speed up the convergence. 4. Compared with other meta-heuristic algorithms, the presented framework clearly demonstrates outstanding improvements on different scales of problems with various difficult aspects both on well-known benchmark functions and portfolio management problems. The rest of this paper is organized as follows. Section 2 reviews the past studies on meta-heuristics and portfolio management. Then, Section 3 introduces a dynamic transition scheme to control the directions of information transition. The experimental settings and results both on well-known benchmark functions and portfolio optimization problems are described and analyzed in Section 4. Lastly, Section 5 concludes the proposed framework, and sheds light on improving large-scale portfolio management for future investigation.