Artificial bee colony algorithm for portfolio optimization

In the financial investment market, one of the most studied problems is the intractability of portfolios. There are no efficiently solutions using traditionally approaches to solve the non-linear portfolio optimization problem. And the previous models based on expected return-variance cannot meet the needs of the investors. In this paper, firstly, we present a semi-variance model which including cardinality constraints. The return per unit of risk is the key factor to determine an investment decision and the extended model includes two sets of constraints: bounds on holdings, cardinality. 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. Secondly, in order to solve the nonlinear optimization model, an improved artificial bee colony algorithm (IABC) is designed. In addition, several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm.