Improved differential evolution algorithm based on the sawtooth-linear population size adaptive method

Abstract

The main parameters that affect the performance of a differential evolution algorithm are the scaling factor, crossover rate, and population size. To adaptively adjust the population diversity and balance the exploration and exploitation abilities of a differential evolution algorithm during the evolution process, this study proposes a sawtooth-linear population size adaptive (SLPSA) method and an improved scaling factor and crossover rate control method. Subsequently, an improved differential evolution algorithm called SLDE is proposed. The SLPSA method constructs an external archive for storing the abandoned trial vectors and periodically adds vectors from external archive to the population during the iterative process, thereby periodically increasing the diversity of the population, which enhances the algorithm’s ability to jump out of locally optimal values. Based on a distance-based parameter adaptation method, the update formulas for the scaling factor weight and crossover rate weight are improved. By using 84 benchmark functions from CEC 2011, CEC 2014, CEC 2015, and CEC 2017, the SLDE performance was verified experimentally by analyzing and comparing the proposed SLDE to six state-of-the-art differential evolution algorithms. The experimental results demonstrated that the SLDE performance was significantly better than that of the six state-of-the-art differential evolution algorithms.