Ship domain is an important theory in ship collision avoidance and an effective collision detection method. First, several classical ship domain models are used in experiments. The results show that the alarm rate is too high in busy waters, leading to greatly reduced practicality of the model. Potential collision risk cannot be detected effectively, especially for a ship with restricted manoeuvrability, which is usually regarded as an overtaken ship due to its navigation characteristics. Therefore, it is necessary to fully consider the interference of other ships to ships with limited manoeuvrability in an encounter situation. A novel ship domain model for ships with restricted manoeuvrability in busy waters is proposed. Considering the navigation characteristics of a ship with restricted manoeuvrability and the influence of the ship–ship effect, an algorithm to determine the boundary of the ship domain model is given by force and moment equations. AIS trajectory data of the North Channel of the Yangtze River Estuary are used to perform a comparative experiment, and four classical ship domain models are employed to perform comparative experiments. The results show that the alarm rates of the novel ship domain model are 7⋅608%, 15⋅131%, 55⋅785% and 7⋅608% lower than those of the other four classical models, and this outcome can effectively reduce the high false alarm rate produced by other models in this environment.

To address the challenges posed by dense shipping traffic and the difficulty of identifying navigation risks in open waters, this paper introduces an Especial Cautious Navigation Angle (ECNA) model for ships, grounded in ship collision avoidance geometry. The ECNA model dynamically identifies the range of navigation angles where collision risks may arise between ships. Building upon this model, a comprehensive scoring algorithm is proposed to assess ship collision risks in open waters. This algorithm not only effectively tracks the evolving risk of collisions but also prioritizes ships with the most imminent danger of collision. Experimental results demonstrate that the ECNA model can accurately define the range of collision risk navigation angles. Furthermore, the scoring algorithm provides a quantitative analysis of the development trends in collision risks and offers continuous monitoring of these risks during navigation in open waters. The proposed model and algorithm exhibit strong practical applicability and operability in identifying ship collision risks in both open and dense navigable areas. These findings not only offer valuable guidance for real-world collision risk identification but also contribute to the theoretical advancement of ship collision risk analysis, presenting a novel solution to this pressing issue.

To enhance fleet replenishment efficiency and ensure navigational safety, this paper investigates the Underway Replenishment Routing Problem (URRP), focusing on the dynamic characteristics of receiving ships. Mathematical models for replenishment ship travel time and formation vessel speed adjustment are formulated, explicitly considering navigational state transitions and formation stability (risk control). Consequently, a dynamic route optimization model is constructed to provide intelligent decision support for fleet commanders. An intelligent optimization algorithm, the Hybrid Genetic Algorithm with Adaptive Variable Neighborhood Search (HGA-AVNS), is proposed to solve this model. Computational results demonstrate that the proposed approach outperforms the traditional empirical replenishment strategy, validating its effectiveness in enhancing maritime safety and operational efficiency. Extensive sensitivity analyses further reveal that under the strict premise of maintaining formation stability, appropriately reducing the cruise speed can offset the increase in overall speed over ground (SOG) induced by following ocean currents, thereby preventing systematic time loss. Additionally, fine-tuning the execution timing of sudden tactical turning based on the replenishment ship’s real-time operational status can further maximize overall replenishment efficiency without compromising navigational safety.