A novel PID-like particle swarm optimizer: on terminal convergence analysis

Abstract

Copyright © 2021 The Author(s). In this paper, a novel proportion-integral-derivative-like particle swarm optimization (PIDLPSO) algorithm is presented with improved terminal convergence of the particle dynamics. A derivative control term is introduced into the traditional particle swarm optimization (PSO) algorithm so as to alleviate the overshoot problem during the stage of the terminal convergence. The velocity of the particle is updated according to the past momentum, the present positions (including the personal best position and the global best position), and the future trend of the positions, thereby accelerating the terminal convergence and adjusting the search direction to jump out of the area around the local optima. By using a combination of the Routh stability criterion and the final value theorem of the Z-transformation, the convergence conditions are obtained for the developed PIDLPSO algorithm. Finally, the experiment results reveal the superiority of the designed PIDLPSO algorithm over several other state-of-the-art PSO variants in terms of the population diversity, searching ability and convergence rate.