ERG-DE: An elites regeneration framework for differential evolution

Abstract

Differential evolution (DE) is one of the most popular paradigms of evolutionary algorithms. Numerous variants of basic DE have been developed in the past two decades after it was first proposed. However, very few works focused on re-exploring the neighborhood area of the elite solutions, which is definitely a promising area according to the proximate optimality principle. Here, a simple yet efficient elites regeneration (ERG) framework was designed to fill this gap. The elite population in this framework is defined as a group of individuals with better fitness values and they are regenerated after the selection procedure in DE. Specifically, a new individual is produced from the search space around each elite individual (i.e. the parent individual) by sampling Gaussian or Cauchy probability models and replaces the parent if it has better fitness value. The implementation of this procedure only introduces two parameters that need to be tuned, i.e. the standard deviation for Gaussian distribution and the scale parameter for the Cauchy distribution. In the proposed framework, the elite individuals serve as the mean or location parameters of the probability models and the standard deviation and scale parameters are tuned by experiments as a small constant value. Thus, offspring individuals are generated in areas close to their corresponding elite parents. The framework allows thorough exploitation of search neighborhoods around elite individuals and ultimately helps the elite individuals escaping from local optima. Experiments results on CEC2014 benchmark revealed that ERG framework significantly increased the optimization capacity for four original DE algorithms, four classical DE variants, and two state-of-the-art DE variants. In addition, it also demonstrated competitive performance when compared with another DE framework.