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.

This article presents a heuristic Particle Swarm ant colony Optimization algorithm to solve engineering Optimization problems. Although PSO has simple principle and ease to be implemented and can eventually locate the desired solution, however, its practical use in solving engineering Optimization problems is severely limited by the high computational cost of the slow convergence rate. Here, ant colony and harmony search principles are employed to speed up local search and improve precision of the solutions. A modified feasible-based mechanism is described which handles the problem-specific constraints.Benchmark Optimization problems are used to illustrate the reliability of the proposed algorithm.