Over the recent years, ontologies are widely used in various domains such as medical records annotation, medical knowledge representation and sharing, clinical guideline management, and medical decision-making. To implement the cooperation between intelligent applications based on biomedical ontologies, it is crucial to establish correspondences between the heterogeneous biomedical concepts in different ontologies, which is so-called biomedical ontology matching. Although Evolutionary algorithms (EAs) are one of the state-of-the-art methodologies to match the heterogeneous ontologies, huge memory consumption, long runtime, and the bias improvement of the solutions hamper them from efficiently matching biomedical ontologies. To overcome these shortcomings, we propose a compact CoEvolutionary Algorithm to efficiently match the biomedical ontologies. Particularly, a compact EA with local search strategy is able to save the memory consumption and runtime, and three subswarms with different optimal objectives can help one another to avoid the solution's bias improvement. In the experiment, two famous testing cases provided by Ontology Alignment Evaluation Initiative (OAEI 2017), i.e. anatomy track and large biomed track, are utilized to test our approach's performance. The experimental results show the effectiveness of our proposal.