The significant growth of modern technology and smart systems has left a massive production of big data. Not only are the dimensional problems that face the big data, but there are also other emerging problems such as redundancy, irrelevance, or noise of the features. Therefore, feature selection (FS) has become an urgent need to search for the optimal subset of features. This paper presents a hybrid version of the Harris Hawks Optimization algorithm based on Bitwise operations and Simulated Annealing (HHOBSA) to solve the FS problem for classification purposes using wrapper methods. Two bitwise operations (AND bitwise operation and OR bitwise operation) can randomly transfer the most informative features from the best solution to the others in the populations to raise their qualities. The Simulate Annealing (SA) boosts the performance of the HHOBSA algorithm and helps to flee from the local optima. A standard wrapper method K-nearest neighbors with Euclidean distance metric works as an evaluator for the new solutions. A comparison between HHOBSA and other state-of-the-art algorithms is presented based on 24 standard datasets and 19 artificial datasets and their dimension sizes can reach up to thousands. The artificial datasets help to study the effects of different dimensions of data, noise ratios, and the size of samples on the FS process. We employ several performance measures, including classification accuracy, fitness values, size of selected features, and computational time. We conduct two statistical significance tests of HHOBSA like paired-samples T and Wilcoxon signed ranks. The proposed algorithm presented superior results compared to other algorithms.