A Novel Particle Swarm Optimization for Portfolio Optimization Based on Random Population Topology Strategies

Abstract

The problem of portfolio selection in the field of financial engineering has received more attention in recent years and many portfolio selection models has been proposed in succession. To solve a generalized Markowitz mean-variance portfolio selection model, this paper proposed four improved particle swarm optimization algorithms (RTWPSO-AD, RTWPSO-D, DRWTPSO-AD, DRWTPSO-D) based on the strategies of Random Population Topology. We abstract the topology of particle swarm optimization (PSO) into an undirected connected graph which can be generated randomly according to a predetermined degree. The topology changes during the evolution when Dynamic Population Topology strategy is adopted. By setting the degree, we can control the communication mechanisms in the evolutionary period, enhancing the solving performance of PSO algorithms. The generalized portfolio selection model is classified as a quadratic mixed-integer programming model for which no computational efficient algorithms have been proposed. We employ the proposed four algorithms to solve the model and compare the performance of them with the classic PSO variant. The computational results demonstrate that the population topologies of PSO have direct impacts on the information sharing among particles, thus improve the performance of PSO obviously. In particular, the proposed DRTWPSO-D shows an extraordinary performance in most set of test data, providing an effective solution for the portfolio optimization problem.