Freezing Mechanism and Topology Dependence of Information Flow Structure in Small-Scale Particle Swarm Optimization

Abstract

The neighborhood topology of particle swarm optimization (PSO) determines information propagation and regulates the exploration-exploitation balance. However, existing evaluation methods based on fitness and spatial diversity fail to characterize the dynamic evolution internal interaction structure of the population. To address this gap, this paper focuses on small-scale PSO (20-50 particles) with regular topologies and models the iterative process as a dynamic weighted influence graph. We construct a multi-scale information-flow evaluation framework covering micro-, meso-, and macro-level metrics, and propose a freeze-point detection method based on effective nodes, a macro-level distributional metric. Experiments on CEC2017 benchmark functions show that the information flow structure freezes early in the search (3 percent - 22 percent for representative configurations and 15 percent-49 percent for global medians) and remains unchanged thereafter. The freeze time follows the order Gbest$<$ Von Neumann $<$Ring, consistent across standard, LDIW, and TVAC variants. Parameter-adaptive variants delay freezing without altering the topological order, and the freeze point is significantly negatively correlated with final solution quality. Intervention experiments under Gbest show that weakening hub nodes delays freezing and improves performance on multimodal functions, while strengthening hubs produces no additional deterioration due to saturation, revealing a decoupling between structural and performance effects. Among the three metric levels, only macro-level distributional metrics effectively capture freezing under regular topologies, because micro- and meso-level structures are predetermined by the topology. These findings reveal the freezing mechanism of information flow in small-scale PSO and provide structural prior signals for adaptive topology control.