A study on scale factor/crossover interaction in distributed differential evolution

This paper studies the use of multiple scale factor values within distributed Differential Evolution structures employing the so-called exponential crossover. Four different scale factor schemes are proposed, tested, compared and analyzed. Two schemes simply employ multiple scale factor values and two also include an update logic during the evolution. The four schemes have been integrated for comparison within three recently proposed distributed Differential Evolution structures and tested on several various test problems. The results are then compared to those of a previous study where the so-called binomial crossover was employed. Numerical results show that, when associated to the exponential crossover, the employment of multiple scale factors is not systematically beneficial and in some cases even detrimental to the performance of the algorithm. The exponential crossover accentuates the exploitative character of the Differential Evolution, which cannot always be counterbalanced by the increase in the explorative aspect of the algorithm introduced by the employment of multiple scale factor values.