Portfolio Optimization According to Variance and Value at Risk Using MOACO, NSGA II and MOABC Algorithms

the portfolio optimization problem is one of the important issues in the field of investment, which has led to the presentation of various models to solve them. These problems are nonlinear and NP-Hard and they are very difficult and time-consuming to solve accurately. Since meta-heuristic methods have a high ability to solve the portfolio optimization problem, this study examines the value criterion at risk from another perspective and presents a new type of mean-value at Risk model. To solve the portfolio optimization problem in Tehran Stock Exchange, we use NSGA II, MOACO, and MOABC algorithms by mean- the percentage of Value at Risk model and the mean-variance model and then compare MOABC algorithms whit both other algorithms AND also compare two models to each other. We show that, at low iterations, the performance of the NSGA II algorithm is better than the MOABC and MOACO algorithms in solving the portfolio optimization problem. As the iteration increases, the performance of the algorithms improves, but the rate of improvement is not the same, in a way, the performance of the MOABC algorithm is better than that of the NSGA II and MOACO algorithms. Then, to compare the mean-percentage of the Value at Risk model and the mean-variance model, we examine both models in the standard mean-variance model and show the mean- the percentage of Value at Risk model compared to the mean-variance model, Has better performance in portfolio optimization.