In some practical classification problems in which the number of instances of a particular class is much lower/higher than the instances of the other classes, one commonly adopted strategy is to train the classifier over a small, balanced portion of the training data set. Although straightforward, this procedure may discard instances that could be important for the better discrimination of the classes, affecting the performance of the resulting classifier. To address this problem more properly, in this paper we present MOGASamp (after Multiobjective Genetic Sampling) as an adaptive approach that evolves a set of samples of the training data set to induce classifiers with optimized predictive performance. More specifically, MOGASamp evolves balanced portions of the data set as individuals of a multiobjective genetic algorithm aiming at achieving a set of induced classifiers with high levels of diversity and accuracy. Through experiments involving eight binary classification problems with varying levels of class imbalancement, the performance of MOGASamp is compared against the performance of six traditional methods. The overall results show that the proposed method have achieved a noticeable performance in terms of accuracy measures.