For the scheduling problem of no cross-over twin Rail-Mounted Gantry (RMG) and container slot selection, considering the safety distance between the two RMGs and the buffer capacity, a coupled model of twin RMG scheduling and container slot selection was proposed with the goal of minimizing the completion time by setting the twin RMG scheduling as the main line and setting the container slot selection as the auxiliary line. The basic idea of it is to set the decision variable to describe the relationship between the tasks. A Genetic Algorithm-Ant Algorithm (GAAA) was designed for solving the coupled model, and the CPLEX was developed for comparisons by analyzing the efficiency in relay mode and mixed mode. The experimental results show that the efficiency in relay mode is better than that of mixed mode when dealing with 8 to 150 container tasks; in small and medium-large sized experiments, the minimum completion time of GAAA is reduced by about 2.65% and 18.50%, respectively; the running time of GAAA is reduced by 88.6% and 99.19% respectively on average compared with CPLEX, which validates the validity of the model.