Many of the problems addressed at the industrial level are of a combinatorial type and a sub-assembly not less than these are of the NP-hard type. The design of algorithms that solve combinatorial problems based on the continuous metaheuristic of swarm intelligence is an area of interest at an industrial level. In this article, we explore a general binarization mechanism of continuous metaheuristics based on the k-means technique. In particular, we apply the k-means technique to the Grasshopper optimization algorithm in order to solve the set covering problem (SCP). The experiments are designed with the aim of demonstrating the usefulness of the k-means technique in binarization. Additionally, we verify the effectiveness of our algorithm through reference instances. The results indicate the K-means binary grasshopper optimization algorithm (KBGOA) obtains adequate results when evaluated with a combinatorial problem such as the SCP.