Multi-label classification (MLC) is an ML task of predictive modeling in which a data instance can simultaneously belong to multiple classes. MLC is increasingly gaining interest in different application domains such as text mining, computer vision, and bioinformatics. Several MLC algorithms have been proposed in the literature, resulting in a meta-optimization problem that the user needs to address: which MLC approach to select for a given dataset? To address this algorithm selection problem, we investigate in this work the quality of an automated approach that uses characteristics of the datasets - so-called features - and a trained algorithm selector to choose which algorithm to apply for a given task. For our empirical evaluation, we use a portfolio of 38 datasets. We consider eight MLC algorithms, whose quality we evaluate using six different performance metrics. We show that our automated algorithm selector outperforms any of the single MLC algorithms, and this is for all evaluated performance measures. Our selection approach is explainable, a characteristic that we exploit to investigate which meta-features have the largest influence on the decisions made by the algorithm selector. Finally, we also quantify the importance of the most significant meta-features for various domains.