Abstract
Trade imbalances and equipment shortages are making it increasingly important to coordinate container slot allocation with empty container repositioning on liner services. This paper develops an integrated bi-objective mixed-integer model for voyage-level slot planning on a fixed cyclic route. The model jointly decides booking acceptance, inter-voyage shipment, and empty repositioning with port-level empty-inventory dynamics and leg-based vessel capacity constraints. We optimize two conflicting objectives: maximizing operational profit and minimizing empty container TEU-miles. To solve the model at practical scales, we propose a hybrid evolutionary framework, NSGA-II-RL, which uses a lightweight Q-learning controller to adapt operator and repair choices during NSGA-II evolution. Computational experiments on representative service route instances show that NSGA-II-RL produces diverse Pareto-efficient solutions and improves hypervolume relative to fixed-operator and random-control variants, revealing clear trade-offs between profitability and repositioning intensity.