With the rapid development of global trade, the cargo throughput of automated container terminals (ACTs) has increased significantly. To meet the demands of large-scale, high-intensity, and high-efficiency ACT operations, the seamless integration of various terminal facilities has become crucial, particularly the collaboration between yard cranes (YCs) and automated guided vehicles (AGVs). Therefore, an integrated scheduling problem for YCs and AGVs (YAAISP) is proposed and formulated in this paper, considering stacking containers and bidirectional transport of AGVs. As the YAAISP is an NP-hard problem, an Improved Whale Optimization Algorithm (IWOA) is proposed in which a reverse learning strategy is used for the population to enhance population diversity; a random difference variation strategy is employed to improve individual exploration capabilities; and a nonlinear convergence factor alongside an adaptive weighting mechanism to dynamically balance global exploration and local exploitation. For container tasks of size 100, the objective function value (OFV) of the IWOA was reduced by 9.25% compared to the standard Whale Optimization Algorithm. Comparisons with other algorithms, such as the Genetic Algorithm, Particle Swarm Optimization, and Grey Wolf Optimizer, showed an OFV reduction of 9.61% to 11.75%. This validates the superiority of the proposed method.