Spatially structured evolutionary algorithms (EAs) have shown to be endowed with useful features for global optimization. Distributed EAs (dEA) and cellular EAs (cEA) are two of the most widely known types of structured algorithms. In this paper we deal with cellular EAs. Two important parameters guiding the search in a cEA are the population topology and the neighborhood defined on it. Here we first review some theoretical results which show that a cEA with a 2D grid can be easily tuned to shift from exploration to exploitation. We initially make a study on the relationship between the topology and the neighborhood by defining a ratio measure between they two. Then, we encompass a set of tests aimed at discovering the performance that different ratio values have on different classes of problems. We find out that, with the same neighborhood, rectangular grids have some advantages in multimodal and epistatic problems, while square ones are more efficient for solving deceptive problems and for simple function optimization. Finally, we propose and study a cEA in which the ratio is dynamically changed.