In this article, the authors investigate the application of genetic algorithms (GAs) with gene dependent mutation probability to the training of artificial neural networks (ANNs) in non-stationary problems (NSPs). In the problems studied, the function mapped by an ANN changes during the search carried out by the GA. In the GA proposed, each gene is associated with an independent mutation probability. The knowledge obtained during the evolution is used to update the mutation probabilities. If the modification of a set of genes is useful when the problem changes its profile, the mutation probabilities of these genes are increased. As a result, the search is concentrated into regions associated with genes presenting higher mutation probabilities.