A hybrid particle swarm optimization approach to mixed integer quadratic programming for portfolio selection problems

Portfolio selection problems in investments are most studied in modern finance because of their computational intractability. The basic topic of modern portfolio theory is the way in which investors can construct a diversified portfolio of financial securities so as to achieve improved tradeoffs between risk and return. In this paper, a heuristic algorithm using particle swarm optimization (PSO) is applied to the problem. PSO realizes the search algorithm by combining a local search method through self-experience with global search method through neighboring experience, attempting to balance the exploration trade-off which achieves the efficiency and accuracy of an optimization. A newly obtained effect is proposed in this paper by adding the mutation operator of genetic algorithms (GA) to unravel the stagnation and control the velocity. We applied our adaptation and implementation of the PSO search strategy to the portfolio selection problem. Results on typical applications demonstrate that the velocity information and mutation operator play pivotal roles in searching for the best solution, and that our method is a viable approach for the portfolio selection problem.