A multi-population evolutionary algorithm for multi-objective constrained portfolio optimization problem

Due to the rapid development of the financial market, the portfolio selection problem has become of the most complex problem in finance. This paper proposes a new multi-objective evolutionary algorithm based on multi-population, called MP-MOEA, to handle the multi-objective constrained portfolio optimization problem (MOCPOP) in order to achieve an optimal trade-off between return and risk. MP-MOEA uses a multi-population strategy to improve the solution’s quality and considerably accelerate the convergence. Furthermore, two types of archives (local and global) are employed, where the archives local are used to store the non-dominated solutions corresponding to each subpopulation, and the external archive global is used to store the Pareto solutions. The external archive global is controlled using crowding distance to limit the archive size and avoid increasing the complexity of the MP-MOEA algorithm. Several experiments are conducted on two datasets of instances to compare our algorithm with three elevant state-of-art algorithms including AR-MOEA, MOEA/D-AGR, MOEA/D-GR, MOEA/D, MODEwAwL, and MOPSO. The first dataset consists of 5 instances from OR-Library, while other dataset consists 15 instances from NGINX. Statistical analysis of the comparative results obtained using ANOVA and Wilcoxon test demonstrate the merits and the outperformance of our MP-MOEA algorithm.