# A Hybrid Optimization Framework with Dynamic Transition Scheme for Large-Scale Portfolio Management
###### Abstract  
Meta-heuristic algorithms have successfully solved many real-world problems in recent years. Inspired by different natural phenomena, the algorithms with special search mechanisms can be good at tackling certain problems. However, they may fail to solve other problems. Among the various approaches, hybridizing meta-heuristic algorithms may possibly help to enrich their search behaviors while promoting the search adaptability. Accordingly, an efficient hybrid population-based optimization framework, namely the HYPO, is proposed in this study in which two meta-heuristic algorithms with different search ideas are connected by a dynamic contribution-based state transition scheme. Specifically, the dynamic transition scheme determines the directions of information transitions after considering the current contribution and system state at each iteration so that useful information can be shared and learnt between the concerned meta-heuristic algorithms throughout the search process. To carefully examine the effectiveness of the dynamic transition scheme, the proposed HYPO framework is compared against various well-known meta-heuristic algorithms on a set of large-scale benchmark functions and portfolio management problems of different scales in which the HYPO attains outstanding performances on the problems with complex features. Last but not least, the hybrid framework sheds lights on many possible directions for further improvements and investigations. meta-heuristic; hybridized algorithm; portfolio optimization; large-scale optimization; information transition +
Footnote †: journal: _Algorithms_  
definition  
attracted by population-based approaches in recent years. A population consisting of several individuals can be used to concurrently explore feasible solutions in promising regions. Meanwhile, the useful information is spread to all individuals of the population in which other individuals can learn from it. However, most population-based approaches depend on a single search manner with the same update mechanism during the whole search process, for which the diversity of search strategies is limited and may not adapt to more fields. To cooperate with multiple meta-heuristics, it cannot merely merge different algorithms without an effective cooperation mechanism. Thus, a carefully designed cooperative framework to integrate different meta-heuristics is critical to enhance the quality of solutions and speed up the convergence. Computational finance [6; 7] is a modern discipline that applies mathematical tools to optimize financial problems including stock price prediction [8], asset pricing [9], portfolio allocation [10] and risk measurement [11]. Among them, portfolio optimization is a fundamental financial problem, having been studied for few decades. Given a set of assets like stock, futures, and bond, investors allocate the initial capital to each asset of the portfolio for maximizing the returns and controlling the risk at a certain level. Modern Portfolio Theory (MPT) [12] was introduced by [PERSON] and has become one of the foundation theories in computation finance. Within this theory, a pioneering concept named the mean-variance model was presented to describe the relationship between the expected returns and volatilities of a portfolio through calculating the mean and standard deviation of weighted daily returns. To further study the forming of equilibrium price for discovering arbitrage opportunities, there are some theories [13; 14] that extend the MPT by introducing practical market constraints and reducing the sensitivity of impact factors. However, those MPT-based models mainly focus on the allocation in a single period, but lack prediction abilities to adjust portfolios during multiple trading periods. Thus, originating from the Capital Growth Theory (CGT) [15], more portfolio strategies [16] in the past few years have tried to dynamically adjust wealth allocation at any timepoint of the trading period at which fund managers can maintain efficient portfolios all the time.