An ontology can formally present the domain knowledge by specifying the domain concepts and their relationships, which is a kernel technique for addressing the data heterogeneity issue in the semantic web. However, since existing ontologies are developed and maintained independently by different communities, a concept and its relationship with the others could be described in different ways, yielding the ontology heterogeneity problem. To solve this problem, in this work, we formally construct an optimal model for it, and propose a similarity measure for distinguishing identical ontology entities. Since determining the high-quality ontology alignment is a complex process, we propose to utilize a Brain Storm Optimization algorithm (BSO) to optimize the alignment. BSO is a recently developed Swarm Intelligence algorithm (SI), which can effectively solve the complex optimization problem by imitating the human's idea generating process. However, classic BSO needs to cluster various ideas in each generation and carry out the evolving operators on all ideas, which increases the computational complexity. To improve the efficiency of BSO-based ontology matcher, a Compact BSO (CBSO) is further proposed, which can reduce the memory consumption by utilizing the probabilistic representation on the idea cluster, and improve the algorithm's speed through the compact crossover operator and perturbation operator. The experiment uses the benchmark track provided by the Ontology Alignment Evaluation Initiative (OAEI) to test our approach's performance. The comparisons among the state-of-the-art ontology matchers and our proposal show that CBSO-based ontology matcher can efficiently determine high-quality ontology alignments.INDEX TERMS Ontology matching, compact brain storm optimization algorithm, ontology alignment evaluation initiative.