A dimensional difference-based population size adjustment framework for differential evolution

Aiming at the problems of premature convergence and evolutionary stagnation faced by differential evolution (DE), a dimensional difference-based population size adjustment framework (DDPSA) is proposed in this work. The framework monitors the speed of convergence based on the dimensional difference between the parent and the offspring, to judge the problem faced by the current population. An adaptive mechanism of population size is designed at the population level to adjust the convergence speed and avoid the above two issues timely. Besides, For the two types of stagnant individuals caused by premature convergence and evolutionary stagnation, two replacement techniques based on the history and elite are proposed at the individual level, respectively, to assist them in restoring normal evolution, cooperating with the mechanism of population size adjustment. The DDPSA framework is introduced into ten DE algorithms and tested in the CEC 2014 and CEC 2017 benchmark suites, as well as four practical problems. The experimental results show that the DDPSA framework can effectively enhance the competitiveness of DEs, which is particularly obvious in some complex multimodal scenarios, achieving significant improvement in terms of DEs' performance on 71.4% and 60.5% of multimodal functions in CEC 2014 and CEC 2017, respectively.