Abstract. This paper presents the Anisotropic selection scheme for cellular Genetic Algorithms (cGA). This new scheme allows to enhance diversity and to control the selective pressure which are two important issues in Genetic Algorithms, especially when trying to solve difficult optimization problems. Varying the anisotropic degree of selection allows swapping from a cellular to an island model of parallel genetic algorithm. Measures of performances and diversity have been performed on one well-known problem: the Quadratic Assignment Problem which is known to be difficult to optimize. Experiences show that, tuning the anisotropic degree, we can find the accurate trade-off between cGA and island models to optimize performances of parallel evolutionary algorithms. This tradeoff can be interpreted as the suitable degree of migration among subpopulations in a parallel Genetic Algorithm.