Motivated by the operational scenarios of lock scheduling, we propose a serial-lock chain navigation problem (SLCNP) modeled on the Three Gorges-Gezhouba Dam (TGGD) for the first time. Ship grouping, synchronized moving, and grouped waiting operations are integrated into the ship navigation process. A mixed integer programming (MIP) model that incorporates real-world constraints such as ship priority, service fairness, traffic flow equilibrium, and phased ship placement is presented to optimize ship throughput and ship stay time. To solve the SLCNP, a sort-pick strategy-based swarm intelligence algorithm (SPSSIA) framework is developed that integrates the characteristics of SLCNP through a hybrid multi-section encoding method and a two-stage heuristic decoding approach. A swarm intelligence evolution mechanism is used to improve the search ability and robustness of the framework. Several instances are generated based on real data to verify the correctness and effectiveness of the model and algorithm. Computational results demonstrate the applicability and effectiveness of the proposed SPSSIA. Further analysis of the experimental results indicates that the key impact factors significantly influence the navigational performance of the TGGD system. The results of this study will provide practical guidance for the operational processes of inland river hubs with comparable characteristics.