Particle Swarm Optimization Based on Cubic Chaotic Mapping and Random Differential Mutation

Particle swarm optimization is a metaheuristic optimization algorithm that boasts advantages such as fast convergence speed, fewer tunable parameters, and a simple search mechanism. However, it suffers from premature convergence and insufficient later-stage exploitation, limiting its performance on multimodal and high-dimensional problems. In light of this, this paper proposes a Chaos-based Differential Mutation Particle Swarm Optimization (CDMPSO) algorithm to address these limitations. The algorithm employs four synergistic strategies: cubic chaotic mapping with inverse learning for population initialization; adaptive inertia weight to balance exploration and exploitation; convex lens imaging inverse learning to escape local optima; and random differential mutation to maintain population diversity. Ablation experiments validate the contribution of each strategy, with adaptive weight being the most significant. Comparative experiments demonstrate that CDMPSO achieves an average ranking of 1.00, outperforming standard PSO, CPSO (Constriction Particle Swarm Optimization), ACPSO (Adaptive Chaotic Particle Swarm Optimization), and HPSOALS (Hybrid Particle Swarm Optimization with Adaptive Learning Strategy). On the unimodal function f1, it attains ultra-high precision of 7.07 × 10−248, and on the multimodal function f9, it uniquely converges to the theoretical optimum of zero. The results demonstrate that CDMPSO possesses excellent convergence precision, global search capability, and robustness, providing an effective solution for complex engineering optimization problems.