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The whale optimization algorithm (WOA) is an intelligence-based technique that simulates the hunting behaviour of humpback whales in nature. In this article, an adaptation of the original version of the WOA is made for handling binary optimization problems. For this purpose, two transfer functions (S-shaped and V-shaped) are presented to map a continuous search space to a binary one. To illustrate the functionality and performance of the proposed binary whale optimization algorithm (bWOA), its results when applied on twenty-two benchmark functions, three engineering optimization problems and a real-world travelling salesman problem are found. Furthermore, the proposed bWOA is compared with five well-known metaheuristic algorithms. The experimental results show its superiority in comparison with other state-of-the-art metaheuristics in terms of accuracy and speed. Finally, Wilcoxon's rank-sum non-parametric statistical test is carried out at the 5% significance level to judge whether the results of the proposed algorithm differ from those of the other comparison algorithms in a statistically significant way.