Chaotic particle swarm optimization using a rotation transformation based on two best solutions

In this paper, we discuss the particle swarm optimization method (PSO) for global optimization, especially, a PSO using a perturbation-based chaotic updating system called PSO-SDPC. In this method, it is easy to select appropriate parameter values for effective search, and numerical experiments showed its good search ability. However, the search of the PSO-SDPC is not rotation-invariant because the perturbation terms of the chaotic updating system are added along the coordinate system of the standard basis, and the component-wise selection from the chaotic and the standard PSO updating systems for a particle's position deeply depends on the coordinate system. Therefore, in this paper, we improve the PSO-SDPC: the perturbations are added along a new coordinate system that is selected according to two best solutions, and all components of each particle's position are updated by the same system, which is selected from the two updating systems. Moreover, we show that the proposed method can be regarded as the rotation-invariant and keeps a high search ability for many problems through numerical experiments.