Invisible image watermarking is a promising method for protecting the copyright of digital images such as photographs, illustrations, and scans. An effective watermarking algorithm embeds a special mark into an image that does not change the image content but can be extracted from it even after some common post-processing operations such as cropping or compression. Many authors use metaheuristic optimization algorithms to achieve a trade-off between imperceptibility and robustness of embedding. In recent years, researchers have been interested in hybrid metaheuristics, which combine operations of individual metaheuristics in some way. However, designs and compositions of hybrid metaheuristic optimization schemes for image watermarking have not been sufficiently studied to date. In this paper, we present an experimental study of various hybrid metaheuristics including sequential, interleaved, and parallel schemes for popular bioinspired optimization algorithms including genetic algorithm, differential evolution algorithm, particle swarm optimization algorithm, firefly algorithm, and artificial bee colony algorithm. We evaluate the effectiveness of hybrid metaheuristics for image watermarking using an algorithm based on changing the ratio between absolute values ​​of sums of discrete cosine transform coefficient groups as an example and perform an experimental comparison of different schemes. The results of the study show that a approach to metaheuristic hybridization and a composition of hybrid scheme significantly affect the imperceptibility and robustness of the image watermarking algorithm. In particular, the interleaved hybridization type provides the best results for the algorithm under consideration.