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Feature selection (FS) is an important task in any classification process and aims to choose the smallest features number that yields higher classification accuracy. FS can be formulated as a combinatorial NP-hard problem for which robust metaheuristics are used as efficient wrapper-based FS approaches. However, when applied for high dimensional datasets that present large features number and few samples, the effectiveness of such wrapper-metaheuristics degraded, and their computation costs increased. To tackle this problem, we propose in this paper a hybrid FS approach based on the ReliefF filter method and a novel metaheuristic Equilibrium Optimizer (EO). The proposed method, called RBEO-LS, is composed of two phases. In the first phase, the ReliefF algorithm is used as a preprocessing step to assign weights for features, which estimate their relevance to the classification task. In the second phase, the binary EO (BEO) is used as a wrapper search approach. The features are ranked according to their weights and are used for the initialization of the BEO population. We embedded the BEO with a local search strategy to improve its performance by adding relevant features and removing redundant ones from the features subset guided by the features ranking and the Pearson coefficient correlation. The performance of the developed algorithm has been evaluated on sixteen UCI datasets and ten high dimensional biological datasets. The UCI datasets contain a high number of samples and a small or medium number of features. The biological datasets present a high number of features with few samples. The results demonstrate that the use of the ReliefF algorithm and the local search strategy improves the performance of the EO algorithm. The results also show the superiority of the RBEO-LS, among other state-of-the-art approaches.