BWC: A Ballast Water Curve Algorithm for Optimizing Ship Fuel Consumption

During navigation in inland waterways, ships must maintain a certain amount of ballast water to pass safely under bridges with different height limits. In this paper, we propose the Ballast Water Curve (BWC) algorithm, which can dynamically adjust the ballast water of ships during navigation according to the height limit of bridges. By using BWC, ships can pass under bridges safely and efficiently, significantly reducing their fuel consumption. Firstly, a theoretical model is established to quantify the relationship between fuel consumption and ship ballast water. Secondly, the concept of "invalid/inactive constraint bridges" is introduced which have no effect on the ship’s ballast water. Finally, the different distributions of bridges are classified, and the dynamic curve of ballast water is designed based on the greedy principle that the volume of ballast water should be as low as possible. To evaluate the effectiveness of our proposed algorithm, experiments are conducted using real bridge and ship data. The experimental results confirm that BWC can reduce the fuel consumption of ships by approximately 13%-14% compared to the static ballast water strategy. Additionally, the effect of the number of bridges, ship speed, ship ballast water volume, and flow velocity of loading/unloading water on the fuel consumption of ships is evaluated. Formulas are also devised to estimate route fuel consumption by fitting, and the effectiveness of the fitting formulas is verified.