The electroencephalographic (EEG) signals provide highly informative data on brain activities and functions. However, their heterogeneity and high dimensionality may represent an obstacle for their interpretation. The introduction of a priori knowledge seems the best option to mitigate high dimensionality problems, but could lose some information and patterns present in the data, while data heterogeneity remains an open issue that often makes generalization difficult. In this study, we propose a genetic algorithm (GA) for feature selection that can be used with a supervised or unsupervised approach. Our proposal considers three different fitness functions without relying on expert knowledge. Starting from two publicly available datasets on cognitive workload and motor movement/imagery, the EEG signals are processed, normalized and their features computed in the time, frequency and time-frequency domains. The feature vector selection is performed by applying our GA proposal and compared with two benchmarking techniques. The results show that different combinations of our proposal achieve better results in respect to the benchmark in terms of overall performance and feature reduction. Moreover, the proposed GA, based on a novel fitness function here presented, outperforms the benchmark when the two different datasets considered are merged together, showing the effectiveness of our proposal on heterogeneous data.