A Synergistic Multi-Objective Evolutionary Algorithm with Diffusion Population Generation for Portfolio Problems

Abstract

When constructing an investment portfolio, it is important to maximize returns while minimizing risks. This portfolio optimization can be considered as a multi-objective optimization problem that is solved by means of multi-objective evolutionary algorithms. The use of multi-objective evolutionary algorithms (MOEAs) provides an effective approach for dealing with the complex data involved in multi-objective optimization problems. However, current MOEAs often rely on a single strategy to obtain optimal solutions, leading to premature convergence and an insufficient population diversity. In this paper, a new MOEA called the Synergistic MOEA with Diffusion Population Generation (DPG-SMOEA) is proposed to address these limitations by integrating MOEAs with diffusion models. To train the diffusion model, a mixed memory pool strategy is optimized, which collects improved solutions from the MOEA/D-AEE, an optimized MOEA, as training samples. The trained model is then used to generate offspring. Considering the cold-start mechanism of the diffusion model, particularly during the training phase where it is not suitable for generating initial offspring, this paper adjusts and optimizes the collaborative strategy to enhance the synergy between the diffusion model and MOEA/D-AEE. Experimental validation of the DPG-SMOEA demonstrates the advantages of using diffusion models in low-dimensional and relatively continuous data analysis. The results show that the DPG-SMOEA performs well on the low-dimensional Hang Seng Index test dataset, while achieving average performance on other high-dimensional datasets, consistent with theoretical predictions. Overall, the DPG-SMOEA achieves better results compared to MOEA/D-AEE and other multi-objective optimization algorithms.

A Novel Improved Genetic Algorithm for Multi-Period Fractional Programming Portfolio Optimization Model in Fuzzy Environment

“…Zhao, Chen, Zhan, et al [17] presented MoCCPOP and MPCoPSO algorithms based on the MPMO framework, established a BLS strategy based on particle update and a HEC strategy based on archive update, and effectively addressed the multi-objective issue in the MoCCPOP model. Yang, Qian,Yang, et al [18] propose a new collaborative MOEA with diffused population generation (DPG-SMOEA), which addresses premature convergence and insufficient population diversity by integrating MOEA with a diffusion model. Deliktas and Ustun [19] propose a fuzzy MULTIMOORA method based on correlation coefficient and standard deviation (CCSD) and an integrated method based on mean-variance-ranking cardinal-constrained portfolio optimization (MVRCCPO) to extend the classical mean-variance cardinal-constrained portfolio optimization model.…”