A new differential evolution algorithm for solving multimodal optimization problems with high dimensionality

Differential evolution (DE) is an efficient intelligent optimization algorithm which has been widely applied to real-world problems, however poor in solution quality and convergence performance for complex multimodal optimization problems. To tackle this problem, a new improving strategy for DE algorithm is presented, in which crossover operator, mutation operator and a new local variables adjustment strategy are integrated together to make the DE more efficient and effective. An improved dynamic crossover rate is adopted to manage the three operators, so to decrease the computational cost of DE. To investigate the performance of the proposed DE algorithm, some frequently referred mutation operators, i.e., DE/rand/1, DE/Best/1, DE/current-to-best/1, DE/Best/2, DE/rand/2, are employed, respectively, in proposed method for comparing with standard DE algorithm which also uses the same mutation operators as our method. Three state-of-the-art evolutionary algorithms (SaDE, CoDE and CMAES) and seven large-scale optimization algorithms on seven high-dimensional optimization problems of CEC2008 are compared with the proposed algorithm. We employ Wilcoxon Signed-Rank Test to further test the difference significance of performance between our algorithm and other compared algorithms. Experimental results demonstrate that the proposed algorithm is more effective in solution quality but with less CPU time (e.g., when dimensionality equals 1000, its mean optimal fitness is less than 1e-9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1\hbox {e}{-}9$$\end{document} and the CPU time reduces by about 19.3% for function Schwefel 2.26), even with a very small population size, no matter which mutation operator is adopted.