Epistatic arithmetic crossover based on Cartesian graph product in ensemble differential evolution

Epistasis in genetics denotes an impact of one gene on the expression of the another genes. This means that so called epistatic gene influences the characteristics of the so called hypostatic genes. As a matter of fact, there is no one-to-one correspondence between genes and traits in nature. On the other hand, values of offspring genes are inherited from the parents genes. In this paper, the impact of epistatic genes in evolutionary computation is studied, where each epistatic gene in offspring depends on the corresponding hypostatic genes of its parents by an epistatic arithmetic crossover used in differential evolution. Thus, epistatic genes are determined by the Cartesian graph product of both parents presented as linear graphs. The epistatic arithmetic crossover is applied as a mutation strategy to the ensemble differential evolution. The results of extensive experiments conducted on CEC-14 function benchmark suite showed a great potential of the proposed algorithm and encouraged us to start to experiment with other graph products as well.