A Decomposition-Based Hybrid Estimation of Distribution Algorithm for Practical Mean-CVaR Portfolio Optimization

摘要

This paper addresses a practical mean-CVaR portfolio optimization problem, which maximizes mean return and minimizes CVaR. Since the practical constraints are considered, the problem is proved to be NP-hard. To solve this complex problem, we decompose it into an asset selection problem and a proportion allocation problem. For the asset selection problem, an estimation of distribution algorithm (EDA) is developed to determine which assets are included in the portfolio. Once the asset selection is fixed in each generation of the EDA, the proportion of each asset is determined by solving the proportion allocation problem using the linear programming. To guarantee the diversity of the obtained solutions, the probability model (PM) is divided into a set of sub-PMs according to the decomposition of the objective space. A knowledge-based initialization and a cooperation-based local search are designed to improve the solutions obtained in the initialization stage and the search process, respectively. The proposed decomposition-based hybrid EDA (DHEDA) is tested on real-world datasets and compared with an existing algorithm. Numerical results demonstrate the effectiveness and efficiency of the DHEDA.