Differential Evolution with perturbation mechanism and covariance matrix based stagnation indicator for numerical optimization

Abstract

Differential Evolution (DE), as a promising population-based stochastic optimization algorithm, has drawn attention from researchers of various fields owing to its simple operation, strong robustness and few control parameters. However, classic DE suffers from drawbacks such as premature convergence and stagnation resulted from reduced population diversity when tackling complicated optimization problems with high dimensions. To mitigate these deficiencies, Differential Evolution with Perturbation mechanism and Covariance Matrix based stagnation indicator (PCM-DE) is proposed in this paper. There are three main modifications in the algorithm. First, a two-phase parameter adaptation strategy based on fitness value is proposed to guide the search towards promising direction according to different stages of evolution. Second, a perturbation mechanism for archived population is proposed, where a new weight coefficient is defined by exploiting information of fitness value and position in archived individuals. Third, a stagnation indicator based on covariance matrix is proposed to assess the population diversity and the information of variance is employed to perturb stagnant individuals. To validate the effectiveness of PCM-DE, it is compared with several state-of-the-art DE variants and non-DE based algorithms under a large test suite containing 100 benchmark functions. Besides, three truss optimization problems are also employed to verify the feasibility and scalability of the algorithm. The experiment results confirm its highly competitive performance in terms of solution accuracy and convergence speed.