Constrained Portfolio Selection using Particle Swarm Optimization

This paper presents a novel heuristic method for solving an extended Markowitz mean–variance portfolio selection model. The extended model includes four sets of constraints: bounds on holdings, cardinality, minimum transaction lots and sector (or market/class) capitalization constraints. The first set of constraints guarantee that the amount invested (if any) in each asset is between its predetermined upper and lower bounds. The cardinality constraint ensures that the total number of assets selected in the portfolio is equal to a predefined number. The sector capitalization constraints reflect the investors’ tendency to invest in sectors with higher market capitalization value to reduce their risk of investment.The extended model is classified as a quadratic mixed-integer programming model necessitating the use of efficient heuristics to find the solution. In this paper, we propose a heuristic based on Particle Swarm Optimization (PSO) method. The proposed approach is compared with the Genetic Algorithm (GA). The computational results show that the proposed PSO effectively outperforms GA especially in large-scale problems.