portfolio optimization using particle swarm optimization method

the markowitz’s optimization problem is considered as a standard quadratic programming problem that has exact mathematical solutions. considering real world limits and conditions, the portfolio optimization problem is a mixed quadratic and integer programming problem for which efficient algorithms do not exist. therefore, the use of meta-heuristic methods such as neural networks and evolutionary algorithms has been an important issue in the literature of portfolio optimization. this study considers the problem of finding the efficient frontier associated with the standard mean-variance portfolio optimization model and presents a heuristic algorithm based upon particle swarm optimization for finding the cardinality constrained efficient frontier. the test data set is the daily prices of 20 companies from march 2006 to september 2008 from the tepix in iran. the results show that pso is successful in constrained portfolio optimization to find the optimum solutions in all levels of risk and return.