Elite-guided Resampling and Multi-mutation based Differential Evolution with exponential crossover for numerical optimization

Abstract

In the existing Differential Evolution (DE) research, there are two main crossover schemes: exponential crossover and binomial crossover. Most researchers believe that binomial crossover is skilled in handling numerical optimization problems while exponential crossover has the advantage in handling optimization problems with certain correlation between adjacent variables. However, we discover that DE variants with exponential crossover can achieve performance comparable to advanced ones utilizing binomial crossover in optimization applications, provided that an appropriate crossover rate CR and associated parameter control are established. In this paper, an Elite-guided Resampling and Multi-mutation based DE with exponential crossover (ERM-DE) is raised to fill the blank in this field, and its main highlights are as follows: First, a novel structure with two stages is raised in our ERM-DE algorithm. The first stage is elite-guided global opposition learning based resampling, and the other is novel exponential crossover DE evolution stage. Second, a Novel Parameter Control (NPC) technique involving scale factor F and crossover rate CR is raised. Different from applying the fitness-based parameter control, the adaptation schemes of the parameters F and CR in our ERM-DE algorithm are fitness-independent. In addition, this NPC technique will also be selectively applied to the trial vector generation strategy DE/target-to-pbest/1/exp with or without optional archive. Third, a novel population Diversity Enhancement Mechanism (DEM) is proposed, which can enhance population diversity by recalculating individuals in a stagnant state. Finally, a time stamp mechanism is posed to deal with outdated inferior and historical solutions in the external archive. A Large test suite with 88 benchmark functions from CEC2013, CEC2014, and CEC2017 test suites is used for algorithm validation and the experimental results indicate that our ERM-DE demonstrates competitiveness with several state-of-the-art DE variants.