This work concerns some heuristic concepts that can be used to improve the search capabilities and speed of convergence of Genetic Algorithms (GA) in terms of finding global solutions for problems of function optimization. The main idea is to group the members of the population into clusters using a local criterion to distinguish them. Pairing of individuals belonging to distinct clusters is then promoted in order to generate descendants with improved fitness conditions. Moreover, severely unfavorable regions are made to become an Exclusion Zone (EZ). The descendants that are generated close to an EZ have a reduced survival probability. The search for outlying clusters is based on a continuously adjusted mutation rate to increase the probability of finding the global minima.