Abstract—In secure multicast communication, only authorized group members are able to receive the transmitted data. Key generation, distribution, and management are all carried out by a single entity (called the Key Server) in the centralized system. The main challenges of a dynamic centralized group key management scheme include scalability overhead, rekeying overhead, storage overhead, maintaining forward and backward secrecy, etc. Logical Key Hierarchy (LKH), one of the key management methods, uses a tree structure to manage keys to share with participants. Due to the fact that members may join or exit the group at any time during communication, a crucial problem in centralized group key management (CGKM) is minimizing rekeying costs while maintaining a balanced tree. The majority of CGKM methods effectively update the group key by modifying cryptographic techniques or based on logical/heuristic arguments. One of the efficient approaches is based on an optimization model with the two mentioned important objectives. In this paper, we conduct a survey on optimization-based approaches to dynamic CGKM, which can be divided into two categories based on logical/heuristic arguments and a rigorous mathematical optimization model.