A need for solving more and more complex problems drives the Evolutionary Computation community towards advanced models of Evolutionary Algorithms. One such model is the island model which, although the subject of a variety of studies, still needs additional fundamental research. In my Ph.D. thesis I am aiming at studying the behavior of island models with regard to the amount of cooperation between islands, the level of heterogeneity and the difficulty of the problem being solved. This paper presents the main ideas and gathers preliminary results. Categories and Subject Descriptors: I.2.8 [Artificial Intelligence]: Problem Solving, Control Methods, and Search — heuristic methods; I.2.11 [Artificial Intelligence]: Dis