Fuzzy Multi-objective Particle Swarm Optimization Solving the Three-Objective Portfolio Optimization Problem

In this paper, the portfolio optimization problem is approached. It is a NP-hard problem that consists in periodically creating an instance of the problem, using the time series of the shares value of a stock exchange. The instance is solved to determine the shares set that maximize the return, minimize the risk and minimize the number of selected shares. As far as we know, only three algorithms of the state-of-the-art of the portfolio selection problem with three objectives have been assessed. In this work, we propose a Fuzzy Multi-objective Particle Swarm Optimization (FOMOPSO) that uses an auto-Tuning Fuzzy Controller. To validate our approach, a series of experiments with the realistic instances and the performance of the proposed algorithm were compared with three state-of-the-art evolutionary algorithms using six commonly used metrics. To support the conclusions, two hypothesis tests were applied. The results show that the Fuzzy Rules auto-configuration contributes to that the proposed algorithm performance clearly outperforms three of the algorithms in comparison, for four of the metrics used.