A Q-Learning-Based hybrid optimization algorithm for storage space allocation and yard Crane cooperative scheduling in double U-shaped Automated container terminals

With the rapid growth of global trade, container throughput at ports has continued to increase, posing an urgent challenge to terminal operational efficiency. To this end, this study investigates the storage space allocation and cooperative scheduling of yard cranes (YCs) in Double U-shaped Automated Container Terminals (DU-ACTs). By considering the layout characteristics of the DU‑ACT and the operational process of YCs, we propose a classification stacking strategy. Based on this, we formulate a mixed-integer programming model to minimize the makespan of YCs. To solve this model, a Q-learning-guided hybrid variable neighborhood search genetic algorithm is developed, in which container priorities are determined according to the principle of early loading and early pickup. Furthermore, the proposed algorithm innovatively incorporates Q-learning for dynamically optimizing the selection of insertion and swap operators, enabling adaptive adjustment of local search operations through iterative reinforcement feedback. The effectiveness of the proposed algorithm is validated through comparative experiments on instances of different scales. In addition, the impact of storage space allocation for containers of different sizes on YC operational efficiency is examined. Collectively, the results demonstrate that the proposed approach effectively addresses the joint problem of storage space allocation and YC cooperative scheduling by reducing YC makespan, thereby facilitating earlier vessel departure and providing practical guidance for scheduling in DU-ACT operations.