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County medical alliances (CMAs) in China are considered to be effective in optimizing the layout of medical resources and improving primary healthcare services. To facilitate the implementation of CMAs in multiple geographical clusters, we examine a cluster-based healthcare network design (CHND) problem with patient referral in uncapacitated and capacitated cases. Considering the uncertainty of health demand and unit referral cost, we develop adaptive distributionally robust models for the CHND problem, where the location and allocation decisions anticipate the worst-case expected patient treatment and referral cost over an ambiguity set. In terms of tractability, we reformulate the adaptive distributionally robust models as tractable forms. Further, a hybrid genetic algorithm that combines a genetic algorithm with a commercial solver is designed to improve the computational efficiency for large-scale instances. Finally, we apply our models to a real-world case in Shenzhen, China, to verify the effectiveness of the proposed algorithm and assess the value of the adaptive distributionally robust models over the corresponding robust model. The results show that our algorithm has outstanding efficiency and accuracy when compared to the hybrid particle swarm algorithm and the commercial solver. Moreover, the adaptive distributionally robust model outperforms the robust model in terms of solution quality. [ABSTRACT FROM AUTHOR]