Optimized pid controller using adaptive differential evolution with mean-of-pbest mutation strategy

Abstract

On the basis of JADE (adaptive differential evolution with optional external archive) and the modified differential evolution with p-best crossover (MDE_pBX), this study attempts to propose a modified mutation strategy termed “DE/( pbest̅̅̅̅̅̅̅ ) ̅/1” for the differential evolution (DE) algorithm, where (formula presented) represents the mean of p top-best vectors. Two modified parameter adaptation mechanisms are also proposed to update the crossover rate and the scale factor, respectively, in an adaptive manner. The DE variant with the proposed mutation strategy and two modified adaptation mechanisms is termed adaptive differential evolution with mean-of-pbest mutation strategy, denoted by ADE_p̅BM. In this study, the proposed two schemes are used not only to preserve the diversity of the population and prevent the premature convergence but also improve the search performance. The results of global optimization problems and the PID controller designs show that ADE_p̅BM is comparable to or better than the four state-of-the-art adaptive DE variants in terms of accuracy, reliability and efficiency.