Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms

Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only few theoretical studies are focused the working principle DE algorithms. To make first attempt to reveal function binomial crossover, this paper aims answer whether it can reduce approximation error evolutionary By investigating expected and probability not finding optimum, we conduct case study comparing two with without crossover classical benchmark problems: OneMax Deceptive. It is proven that using leads dominance transition matrices. As result, algorithm asymptotically outperforms both Deceptive, OneMax, however, Furthermore, an adaptive parameter strategy proposed which strengthen superiority