Feature selection is a complex problem aimed at identifying the subset of features that optimizes a performance metric for a given machine learning model. We focus on a version of this problem where the maximum number of features to retain must be selected by the user. This problem can be effectively addressed with metaheuristic algorithms, but they are often computationally expensive. In this article, we propose two versions of the binary Grey Wolf Optimizer tailored to our version of the problem: a classical version and an advanced one. Additionally, we also propose an accelerated version of the classical algorithm using a surrogate model based on a binary classifier. On average, this surrogate model reduces the computation time of the algorithm by 40%. We also compared the results of our algorithms to those of a state-of-the-art genetic algorithm specialized for this task. Tests conducted on ten datasets demonstrate that the proposed algorithms either match or outperform GAAM in 8 out of 9 cases.