The velocity updating rule according to an oblique coordinate system with mutation and dynamic scaling for particle swarm optimization

Particle swarm optimization (PSO) has been showing powerful search performance especially in separable and unimodal problems. However, the performance is deteriorated in non-separable problems such as rotated problems. In this study, a new velocity updating rule according to an oblique coordinate system, instead of an orthogonal coordinate system, is proposed to solve non-separable problems. Two mutation operations for the best particle and the worst particle are proposed to improve the diversity of particles and to decrease the degradation of moving speed of particles. In addition, the vectors generated according to the oblique coordinate system are dynamically scaled to improve the robustness and efficiency of the search. The advantage of the proposed method is shown by solving various problems including separable, non-separable, unimodal, and multimodal problems, and their rotated problems and by comparing the results of the proposed method with those of standard PSO.