On epistasis for measure of genetic algorithm hardness

Aiming at the essence of epistasis and its significance in measuring genetic algorithm hardness, a theoretical analysis and a practical research are processed. Based on the analysis of the Euclidean normalization of epistasis variance and the extent of epistasis coefficient, which reflect the extent of epistasis or genetic algorithms, two theorems are formulated and proved. Then the experiments using some elementary functions and NK-models are carried out to verify the method. The obtained results show that the method can determine the difficult genetic algorithm hardness problems, but may misdetermine some easy ones, some times.