Recently, the control plane of the core network (CN) has introduced a flat service-based architecture to improve flexibility, openness, and intelligence. And a novel radio access network (RAN)-CN converged network architecture was proposed to leverage the advantages of virtualization and cloudification, reduce network delay and overhead, and increase the network processing efficiency. In this paper, in order to fully utilize the advantages of the RAN-CN converged network and move services closer to user equipment, a multi-layer network architecture is proposed, where some CN network functions (NFs) are moved from the CN to the edge node (EN) and integrate with corresponding RAN functions to avoid unnecessary signaling and data forwarding. And all NFs in the EN except converged data storage management function (cDSM) are designed to be stateless to decouple the storage resources from these NFs. Based on the proposed multilayer network architecture, a cDSM placement approach based on improved non-dominated sorting genetic algorithm II (iNSGA-II) is proposed to balance the data forwarding cost and the maximum load on cDSMs. Simulation results demonstrate that compared with the conventional NSGA-II, the convergence speed and distribution of the proposed iNSGA-II are improved. And according to different network requirements, the proposed scheme can achieve a trade-off between the data forwarding cost and the maximum load on cDSMs.INDEX TERMS radio access network, core network, network architecture, data storage management function, NSGA-II