A Hierarchical Hybrid PSO for Single-Objective Numerical Optimization

This paper presents a hierarchical hybrid particle swarm optimization (HH-PSO) variant featuring a hierarchical hybrid search behavior framework that tailors distinct search strategies for individual particles across evolutionary stages. The proposed framework systematically coordinates exploration and exploitation capabilities through two core innovations: a hybrid search architecture integrating global topology with local refinement mechanisms, and an adaptive fitness-regulated balance factor dynamically adjusting particle velocity coefficients. Experimental evaluations on the CEC2019 and CEC2022 benchmark suites demonstrate that HH-PSO achieves improvement in solution accuracy compared with five state-of-the-art PSO variants. Statistical analysis using the Wilcoxon signed-rank test confirms the algorithm's superior performance ranking across 80% of comparions, establishing its effectiveness in balancing search intensification and diversification.