A self-adaptive gradient-based particle swarm optimization algorithm with dynamic population topology

Abstract

The aggregation of individuals facilitates local information exchange, and the migration of individuals from one population to another leads to a dynamic community structure. In addition, the negative feedback regulation mechanism of organisms helps them in good living conditions. Based on the above knowledge, a novel particle swarm optimization algorithm with a self-organizing topology structure and self-adaptive adjustable parameters is proposed (KGPSO). During the optimization process, the K-Means clustering method periodically divides the particle swarm into multiple distance-based sub-swarms, and the optimal number of sub-swarms is determined by maximizing the Calinski-Harabasz index. This strategy helps maintain the population diversity and gives particles the ability to perceive the surrounding environment. The parameters used to update the particle velocity are adjusted based on the gradient descent of its fitness error, ensuring a dynamic balance between exploration and exploitation. The hyperparameters of KGPSO are tuned by Bayesian optimization method to improve the algorithm performance further. Two benchmark suites are used to evaluate the performance of KGPSO. Both ranking results and Wilcoxon signed-rank tests show that KGPSO performs best among the PSO algorithms tested. Moreover, the excellent optimization capability of KGPSO are proven in the process of X-ray CT image enhancement, making it possible to analyze the structure and motion of heterogeneous granular materials efficiently and robustly. In conclusion, the proposed KGPSO can provide a stable and powerful support for the frontier experimental research of granular materials and expand the research scope.