A multi-objective ship voyage optimisation method within sulfur emission control zones

Ship weather routing planning has always been one of the most effective ways to improve navigation efficiency and economy. It is crucial to consider meteorological conditions, sulfur emissions, and ship kinematics constraints when planning methods that align more closely with actual navigation paths. In this paper, a two-stage multi-objective voyage optimisation algorithm is proposed. Ship velocity, engine power, heading, and angular velocity are optimised to reduce fuel consumption and sulfur emissions. In the first stage, to optimize node coordinates on a large-scale route, a time dimension and different cost weights are introduced to generate optimal routes. In the second stage, to optimize the ship's navigation characteristics, a novel three-dimensional dynamic programming algorithm is proposed. This method discretizes the ship's initial and final states into multiple levels. Additionally, the multi-shooting algorithm is used to solve a set of sub-states (position, heading, angular velocity) that meet the ship's kinematic requirements, aiming to achieve the objective of minimizing costs within specific regions. Further optimisation of the global optimal trajectory and ship kinematics is achieved through multi-level decision-making. The results show that compared to actual navigation routes and traditional path planning methods, the proposed approach can identify optimal target paths with lower economic and emission costs in maritime environments. In regions requiring more steering changes, Multi-objective costs are reduced compared to curve optimisation methods, optimizing ship heading and angular velocity to facilitate smoother, safer, and more efficient steering operations during navigation. • A two-stage multi-objective voyage optimisation under multiple constraints, is proposed, dealing with low-sulfur fuel. • Ship velocity, engine power, heading and angular velocity are optimised to reduce fuel consumption and sulfur emission. • The A∗-DME algorithm proposed here introduces the time and weights to generate paths based on different objectives. • A novel 3D-dynamic programming algorithm divides different regions that need to be optimised. • The global optimal trajectory and ship kinematics are further solved using multi-level decision-making.