A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems

•We solve several variants of the portfolio selection problem with a unified approach.•A novel adaptive ranking procedure based on three mechanisms is introduced.•Extensive computational experiments show the efficiency and robustness of the method. The portfolio selection problem (PSP) concerns the resource allocation to a finite number of assets. In its classic approach, the problem aims at overcoming a trade-off between the risk and expected return of the portfolio. In recent years, additional constraints identified in financial markets have been incorporated into the literature, as an attempt to close the gap between theory and practice. In view of this, this paper introduces a unified multi-objective particle swarm optimization approach capable of solving a class of mean-variance PSPs. An adaptive ranking procedure is also developed, which is based on three mechanisms, including a new one. Extensive computational experiments were carried out in five PSP variants and the results obtained were compared with those found by problem-specific methods from the literature. The proposed approach was capable of finding highly competitive results in all problems and in most of the multi-objective metrics considered.