MDLPSO-DE: a memory-driven distribution learning hybrid swarm optimizer with application to humanistic learning path optimization

Abstract

Particle swarm optimization (PSO) tends to suffer from premature convergence and limited adaptability when addressing high-dimensional and complex multimodal optimization problems. To alleviate these issues, a hybrid framework termed MDLPSO-DE is proposed by integrating memory-driven distribution learning with differential evolution and adaptive operator selection. An archive mechanism is employed to retain high-quality historical solutions and provide stable evolutionary guidance. A rank-weighted distribution model constructed from elite individuals is used to enhance exploitation while maintaining population diversity. A differential evolution mutation operator is incorporated into the velocity–position update process to improve global search capability. Furthermore, operator activation probabilities are dynamically adjusted according to their historical contribution, enabling adaptive coordination between exploration and exploitation during different search stages. The proposed method is evaluated on the CEC2017 benchmark suite under multiple dimensional settings. Comparative results indicate that MDLPSO-DE achieves improved optimization accuracy and convergence behavior relative to several representative swarm and evolutionary algorithms. Statistical analysis based on the Friedman test and Holm-corrected Wilcoxon signed-rank tests confirms that the performance advantage of MDLPSO-DE is statistically significant across the majority of benchmark functions and baseline algorithms. Ablation experiments are conducted to examine the contribution of each module. An application-inspired learning path optimization case study is further used to demonstrate the applicability of the proposed method under structured and constrained optimization settings.