To address the issue that traditional optimization algorithms struggle to find feasible or optimal solutions in the economic optimization scheduling of integrated energy systems, a multi-strategy improved marine predators algorithm is proposed. The Sobol sequence is adopted for population initialization, the pattern search is employed to update position information, and the dynamic opposition-based learning strategy is utilized to expand the search space to further improve the convergence speed and optimization accuracy of the algorithm. By considering system power balance, energy equipment output limitations, and energy storage device constraints, an optimization scheduling model for hydrogen-involved integrated energy systems is established. This model takes into account the coupling of multiple energy forms, including hydrogen fuel generators and cogeneration equipment, with the objective of minimizing overall costs. Case studies based on real-world data from Hebei province demonstrate that the proposed algorithm outperforms four other intelligent optimization algorithms across various scenarios. It effectively coordinates the multi-energy coupling relationships among generation, load, and storage, thereby reducing the overall system operation cost.