A cooperative particle swarm optimization with difference learning

Particle swarm optimization (PSO) is applied in complex model solving problems due to its fast convergence rate and concise algorithm structure. However, the balancing ability of PSO between exploration and exploitation still faces significant challenges. Therefore, a cooperative-based difference learning particle swarm optimization (CDLPSO) is proposed. In CDLPSO, dual swarm time-varying adjustment (DST) based on the subswarm division method is introduced on different periods, while using an appropriate subswarm division method to promote the cooperative learning of particles. Furthermore, a pros-cons coevolution mechanism (PCC) is designed in cooperative learning based on swarms. The elite subswarm can adaptively select a group of proper particles as the swarm updates, thereby obtaining a better exploration performance. Meanwhile, a stage-based cross-learning strategy (SBC) which is adopted to utilize common subswarm rationally adjusts different learning strategies on different stages. To further enhance the convergence accuracy, the common subswarm is added in more superior particles for learning. Ultimately, CDLPSO is used to solve the complex function problems on the CEC2013, CEC2022 test suite and a practical application. The experimental results demonstrate that CDLPSO can significantly balance exploitation and exploration abilities.