Abstract
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.
Highlights
With the breakthroughs in both theory and applications of the evolutionary computing (EC), the evolutionary optimization algorithms have attracted a great deal of research interest, and a large amount of research results have been published in the literature [1,31,39,41]
(2) For the proposed proportion-integral-derivative-like particle swarm optimization (PIDLPSO) algorithm, the convergence conditions and the final positions are obtained by means of the Routh stability criterion and the final value theorem of the Z -transformation
The main objective of this paper is to 1) put forward a novel PIDLPSO algorithm; 2) analyze its terminal convergence by means of the Routh stability criterion and the final value theorem of the Z -transformation; and 3) obtain the conditions for convergence and the position of the final particle of the proposed PIDLPSO algorithm
Summary
With the breakthroughs in both theory and applications of the evolutionary computing (EC), the evolutionary optimization algorithms have attracted a great deal of research interest, and a large amount of research results have been published in the literature [1,31,39,41]. The convergence analysis of the PSO algorithm has been studied in [24] from the theoretical aspect, and further insights have been provided in [13,19,29,39] Based on these existing results, we can draw the following conclusions on the performance of the PSO algorithm: 1) the exploration and exploitation ability of the PSO algorithm to control the population diversity are vitally important for its efficiency as an optimizer; and 2) as with the other population-based optimizers, higher population diversity is desirable in the early exploration stage, while lower population diversity is preferable in the later/terminal convergence stage. In [49], the traditional particle swarm optimizer has been interpreted as a proportional-integral controller Following this line, in this paper, we endeavor to develop the PSO algorithm based on the proportional-integral-derivative (PID) strategy and analyze the terminal convergence of this PID-like PSO (PIDLPSO) algorithm. The Z -transform of a vector implies that every element of this vector has taken the Z -transform
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