'Hybrid meta-heuristics' is one of the most interesting recent trends in the field of optimization and feature selection (FS). In this paper, we have proposed a binary variant of Atom Search Optimization (ASO) and its hybrid with Simulated Annealing called ASO-SA techniques for FS. In order to map the real values used by ASO to the binary domain of FS, we have used two different transfer functions: S-shaped and V-shaped. We have hybridized this technique with a local search technique called, SA We have applied the proposed feature selection methods on 25 datasets from 4 different categories: UCI, Handwritten digit recognition, Text, non-text separation, and Facial emotion recognition. We have used 3 different classifiers (K-Nearest Neighbor, Multi-Layer Perceptron and Random Forest) for evaluating the strength of the selected featured by the binary ASO, ASO-SA and compared the results with some recent wrapper-based algorithms. The experimental results confirm the superiority of the proposed method both in terms of classification accuracy and number of selected features.