Differential evolution with proximity-based replacement strategy and elite archive mechanism for global optimization

Abstract

Differential evolution (DE) algorithm is a simple but effective algorithm for numerical optimization. However, the inferior vectors, when compared to the current population, are always abandoned in the selection process. As the previous studies shown, these inferior vectors can provide valuable information in guiding the search of DE. Based on this consideration, this paper proposes a proximity-based replacement strategy (PRS) and an elite archive mechanism (EAM) to further utilize the information of inferior and superior vectors generated during the evolution. In the PRS, the trial vectors that do not defeat their parent vectors will have a chance to replace other parent vectors based on the distance between them. Further, to maintain the diversity of the population, the EAM is adopted by storing the superior vectors both in the selection operator and the PRS to provide the negative direction information. By this way, on the one hand, the search information provided by the inferior vectors can be effectively utilized with PRS to speed up the speed of convergence. On the other hand, the negative direction information derived from the superior vectors can enhance the diversity of population. By incorporating these two novel operators in DE, the novel algorithm, named PREA-DE, is presented. Through an experimental study on the CEC2013 benchmark functions, the effectiveness of PREA-DE is demonstrated when comparing with several original and advanced DE algorithms.