Portfolio Optimization Based on Principal Component Analysis and Second-Order Surrogate-Assisted Memetic Differential Evolution Algorithm

Portfolio optimization involves applying the concept of diversification across asset classes, which entails investing in a diverse range of asset types to mitigate risk. It aims to maximize net gains in a portfolio while simultaneously minimizing risk. In this paper, principal component analysis and k-means algorithm are employed for stock screening, and an enhanced differential evolution algorithm is proposed to solve the portfolio optimization model. Through a comprehensive analysis of stock data using principal component analysis and the k-means clustering algorithm, it was discovered that certain factors have a significant impact on stock price movement. Subsequently, 10 stocks with investment value were selected. Additionally, a Mean-Value at Risk (VaR) model is constructed, considering both the cost function and the diversification constraint. Finally, a second-order surrogate-assisted memetic differential evolution (SOSMDE) algorithm is introduced to solve the proposed model. The experiments demonstrate that the proposed SOSMDE algorithm is effective in solving the Mean-VaR model and that principal component analysis is a valuable tool for addressing the problem of portfolio optimization.