Adaptive Wave Propagation for Diversity Enhancement in Particle Swarm Optimization

Particle Swarm Optimization (PSO) frequently suffers from premature convergence in complex, multimodal landscapes. While local neighborhood topologies help mitigate stagnation, they typically compromise convergence speed. To resolve this trade-off, this paper introduces Particle Swarm Optimization with Wave Agitation and Covariance Matrix Adaptation (PSO-WA-CMA). Inspired by the collective evasion and wave propagation dynamics observed in biological flocks, the proposed framework injects structured, spatio-temporal perturbations rather than isotropic, random mutations. The main contributions of this work are threefold: (1) a scale-invariant adaptive stagnation detection mechanism that accurately triggers interventions independent of the objective function’s magnitude; (2) a distance-dependent wave propagation model that spatially regulates perturbation intensity; and (3) a covariance-guided directional search that aligns the wave agitation with the swarm’s historically promising search trajectories. The method was rigorously evaluated on 40 benchmarks—23 classical functions, 10 CEC-C06 2019 functions, and 7 engineering design problems—against 18 reference algorithms. PSO-WA-CMA demonstrated robust competitiveness, achieving a higher number of statistically significant wins than losses against all eight evaluated PSO variants. Compared to canonical PSO, the proposed method secured a favorable record of 12 wins and eight losses, maintaining competitive parity in the remaining 20 cases where no significant difference was detected. While excelling particularly on classical and complex real-world engineering problems, the broader evaluations reinforce the problem-dependent nature of metaheuristics. Overall, these findings confirm PSO-WA-CMA as a highly effective extension of PSO that successfully balances exploration and exploitation without permanently disrupting convergence.