To solve the problem of storage space allocation for both inbound and outbound containers and twin automated stacking cranes scheduling in the automated container terminals, a new repositioning strategy is designed and a cooperative optimization model is established. The model considers the constraints of safety distance and handshake area capacity. The objective of the model is to minimize the makespan of all storage requests and the total rehandling time during the retrieval process, which is calculated according to the priority of inbound and outbound containers defined by the early retrieval and early loading rule respectively. A variable neighborhood search based hybrid genetic algorithm is designed to solve the model. Numerical experiments show that the sum of the makespan of all storage requests and the total rehandling time during the retrieval process is reduced by approximately 10% compared to the traditional repositioning strategy by optimizing the sequence of container repositioning from the handshake area to the seaside or landside designated storage space. The research is beneficial to improve the operation efficiency of automated container terminal yards.