Chaotic Multi-swarm Particle Swarm Optimization Using Combined Quartic Functions

In this paper, we focus on the PSO using a chaotic system, PSO-SDPC, which was proposed in [11]. The method uses a perturbation-based chaotic system to update a particle's position, which is derived from the steepest descent method for a quartic function having global minima at the pbest and the gbest. It was shown that the parameter selection is easy for the chaotic system, numerical experiments demonstrated the good performance of the PSO-SDPC. However, since the used chaotic system is based on only the pbest and gbest, the search of a particle is restricted around the the two points despite the chaoticity of its searching trajectories. Therefore, we extend the PSO-SDPC by introducing a multi-swarm structure, where each particle can search for solutions more extensively by exploiting not only the gbest and pbest, but also the sbest, the best solution found by particles in each swarm. In addition, we derive a perturbation-based chaotic system from a combined quartic function having global minima at three points to which the gbest, pbest and sbest are mapped by the proposed affine mapping for each particle. We show that it is easy to select appropriate parameter values of the chaotic system for the effective search, and evaluate the advantage of the proposed PSO through numerical experiments.