Aiming at the uncertain arrival time of external container trucks， the dynamic operation sequence of Automated Stacking Crane （ASC） was optimized to improve the operation efficiency of automated container terminal yard with objective of reducing the completion time of ASCs as well as the waiting time of ASCs and external container trucks. Firstly， combining the characteristics of container operation types and dynamic arrival of external container trucks in mixed stacking mode， a strategy of ASCs dynamically matching the operation tasks of external container trucks were proposed. Then， a multi-objective model with the shortest operating time of ASCs as well as the shortest waiting time of ASCs and external container trucks was constructed. Finally， a Non-dominated Sorting Genetic Algorithm Ⅱ based on Dynamic Rules （DRNSGA Ⅱ） was designed as the solving algorithm. In small-scale example experiments， DRNSGA Ⅱ and Genetic Algorithm （GA） were used to solve ASC operation problems under dynamic strategy and random strategy， respectively. The experimental results show that the target function value solved by DRNSGA Ⅱ under dynamic strategy is 28.2% better than that under random strategy， and the result solved by DRNSGA Ⅱ is 23.3% better than that solved by Genetic Algorithm （GA） when using dynamic strategy. The performance of DRNSGA Ⅱ and Multi-Objective Particle Swarm Optimization （MOPSO） algorithm were compared in large-scale experiments. The experimental results show that the result solved by DRNSGA Ⅱ is 6.7% better than that solved by MOPSO algorithm. It can be seen that DRNSGA Ⅱ can quickly generate a variety of non-dominated solutions to provide decision support for ASC dynamic operation in mixed stacking mode.