Heuristic Methods Solving Markowitz Mean-Variance Portfolio Optimization Problem

Abstract

In this paper, we introduce two heuristic methods for solving Markowitz mean-variance portfolio optimization problem with cardinality constraints and bounding on variables: genetic algorithm (GA) and heuristic branching (HB) with some proposed improvements. There are exact methods for solving the problem: outer approximation, branch-and-bound, etc. They are efficient for small-size problems, which is under five hundred stocks. However, they are not applicable for larger size problems. We implement the algorithms on Vietnam and the United States stock market data. Numerical experiments show that GA and HB give good results and have some advantages, especially in computation times.