Deep learning algorithms or ensemble machine learning models often increase accuracy in industry artificial intelligence applications. However, their complexity makes them difficult to understand and show their underlying logic and decisions. In safety-critical applications or for audit purposes, this opaqueness is undesirable. To this end, explainable artificial intelligence techniques attempt to show how these complex models work. One of these techniques is the global surrogate generation method, where simpler, intrinsically interpretable models are trained to provide predictions as close as possible to their complex counterparts. However, these methods often only consider a single error measure to generate these simpler models. In order to solve this problem, we propose a multi-objective optimization problem to generate surrogates optimizing multiple error metrics simultaneously. Results show that this proposal can generate surrogates for classification and regression problems, often outperforming the current state-of-the-art method.