A dual-time dual-population multi-objective evolutionary algorithm with application to the portfolio optimization problem

Abstract

The article proposes a dual-time dual-population multi-objective evolutionary algorithm, DTDP-EAMO, to address the challenges faced by multi-objective differential evolution algorithms in solving complex optimization problems, such as weakened late-stage search capability, susceptibility to local optima, and insufficient diversity. Firstly, DTDP-EAMO divides the population into three sub-populations using fast nondominated sorting. Then, it introduces a dual-stage and multi-population adaptive mutation strategy to maintain the convergence and diversity of each sub-population. Meanwhile, a dual external archive mechanism is introduced to enable the population to escape local optima and facilitate information exchange between sub-populations through archiving high-quality solutions from both stages. Finally, the individuals in the external archive are sorted, and high-quality solutions are selected and recombined to generate a new population. To demonstrate the effectiveness of DTDP-EAMO, fourteen test functions and a portfolio optimization problem are selected. Experimental results show that the algorithm's overall performance is superior to three comparative algorithms. Furthermore, practical application results demonstrate DTDP-EAMO's ability to reduce risk and increase returns in portfolio optimization problems, further confirming its effectiveness and feasibility. DTDP-EAMO outperforms comparative algorithms in convergence and distribution, indicating higher accuracy and superiority in solving portfolio models.