In engineering and science, there are many combinatorial optimization problems. A lot of these problems are NP-hard and can hardly be addressed by full techniques. Therefore, designing binary algorithms based on swarm intelligence continuous metaheuristics is an area of interest in operational research. In this paper we use a general binarization mechanism based on the k-means technique. We apply the k-means technique to grasshopper algorithm to solve multidimensional knapsack problem (MKP). Experiments are designed to demonstrate the utility of the k-means technique in binarization. Additionally we verify the efficiency of our algorithm through benchmark instances, showing that binary k-means grasshopper algorithm (BKGOA) obtains adequate results when it is evaluated against another state of the art algorithm.