A novel sequential switching quadratic particle swarm optimization scheme with applications to fast tuning of PID controllers

In this work, a sequential switching quadratic particle swarm optimization (SSQPSO) scheme is investigated, where the velocity update mechanism is improved to enhance the convergence performance. Considering the sequential characteristics (related to evolution factors) of the evolution process, a Markov chain with special probability transition matrix is employed to characterize the switching of evolution state. With the help of the mean distance, the concept of population density is first put forward in the dynamic search region enclosed by all particles. Then, taking into account the change of the population density in different generations, two quadratic acceleration terms are introduced into the velocity update model based on the Hadamard product, where four evolution-state-dependent acceleration coefficients are also adopted. The positivity or negativity of the quadratic acceleration terms is retained by resorting to the matrix sign functions. Several widely utilized benchmark functions (including two unimodal and multimodal functions) are employed to evaluate the search capability of the studied SSQPSO scheme. The experimental consequences illustrate that the performance of the developed SSQPSO scheme is superior to that of some popular particle swarm optimization (PSO) schemes. To further demonstrate the effectiveness in practical engineering, the addressed SSQPSO scheme is successfully applied to achieve the fast parameter tuning of the proportional-integral-derivative controller in a spring-mass-damper system.