Global Opposition Learning and Diversity ENhancement based Differential Evolution with exponential crossover for numerical optimization

Abstract

Since the inception of Differential Evolution (DE), the vast majority of studies on it indicate that exponential crossover does not solve the real-parameter optimization in continuous spaces very well. However, we find that once the appropriate crossover rate CR and its corresponding parameter control are found, the DE variants with exponential crossover can achieve comparable performance with the ones employing binomial crossover. In this paper, a new DE algorithm, called Global Opposition Learning and Diversity ENhancement based DE with exponential crossover (GOLDEN-DE), is proposed to fill the gap in this field. The GOLDEN-DE algorithm has the following highlights: First, a novel global opposition learning mechanism is proposed in our GOLDEN-DE algorithm; Second, a Novel Parameter Control, namely NPC technique, with fitness-independent characteristic is incorporated in the GOLDEN-DE algorithm. Third, a novel population Diversity ENhancement (DEN) mechanism is proposed, and individuals in the stagnation status can be re-calculated in order to enhance population diversity. Fourth, a time stamp mechanism for handling too old inferior solutions in the external archive is also put forward. We evaluate the GOLDEN-DE algorithm for real-parameter single-objective global optimization on 88 benchmarks from the three universal test sets, including CEC2013, CEC2014, and CEC2017 test suites, and experiment results show that our GOLDEN-DE algorithm is competitive with several state-of-the-art DE variants.