In this study a class of Multi-Objective Genetic Algorithms (MOGAs) is proposed to select the most relevant features for the problem of speech-based emotion recognition. The employed evolutionary algorithms are the Strength Pareto Evolutionary Algorithm (or SPEA), the Preference-Inspired CoEvolutionary Algorithm with goal vectors (or PICEA), and the Nondominated Sorting Genetic Algorithm II (or NSGA-II). Performances of the proposed algorithms were compared against conventional feature selection methods on a number of emotional speech corpora. The study revealed that for some of the corpora the proposed approach significantly outperforms the baseline feature selection methods up to 5.4% of relative difference.