The application of continuous metaheuristic algorithms to combinatorial problems is an area of interest at the engineering level. This interest is related to the fact that many of the problems that are addressed at the industrial level are of the combinatorial type and a not lesser subset of these are of the NP-hard type. In this article, we propose a binarization mechanism for continuous metaheuristics that uses the concept of percentile. This percentile concept is applied to the firefly optimization algorithm to solve the set covering problem (SCP). To determine the importance of the percentile concept, experiments were designed to identify its contribution. Additionally, to see that the proposal is adequate, the efficiency of the algorithm is compared using reference instances. The results indicate that the binary percentile firefly algorithm (BPFA) obtains adequate results when evaluated with a combinatorial problem such as the SCP.