An adaptive integral separated proportional–integral controller based strategy for particle swarm optimization

Abstract

Particle swarm optimization algorithm (PSO), which updates the particle by the linear summation of the particle’s past momentum and current search direction, has demonstrated its power in many optimization applications. However, few researches have focused on the overshoot problem of PSO caused by past momentum, which may result in an oscillation search and slow convergence speed on complex optimization problems. Based on the connection between the PSO optimization process and the PID controller based control system, we first analyze the effect of the momentum in PSO, then we find that the oscillation problem relates to the gathering of the momentum term and the current search direction. Inspired by the conditional integration in automatic control, we propose an adaptive search direction learning approach for PSO, namely ISPSO (Integral Separated PI controller-based PSO). The ISPSO separates momentum term adaptively when the current search direction is consistent with historical momentum direction, and then the IS strategy will guide particles to fly to better and steady directions by eliminating the integral gathering of historical momentum. We select seven main-stream approaches as control group, and conduct experiments on benchmark CEC2013 test suite. The experimental results of ISPSO, providing the faster steady global convergence and higher solution accuracy, show a significant improvement on PSO algorithm. Compared with the results of the seven methods, the performance of ISPSO is also promising in general, especially for unimodal and composition functions. Furthermore, our results validate the generalization and effectiveness of IS strategy by the designed experiments of PSO variants with and without IS strategy, which also indicates that the IS strategy can be applied to PSO variants with any topological structures.