Surrogate-assisted multi-objective optimization of a hydrofoil craft using a backpropagation neural network and MORBMO

This study investigates the hydrodynamic optimization of a custom-designed dual-hydrofoil craft operating at 8–10 m/s. Hydrofoil span, longitudinal spacing, and front hydrofoil sweep angle are selected as design variables, and their effects on rise-up, trim, and total resistance coefficient are first examined using computational fluid dynamics (CFD). Free-surface wave patterns and hydrofoil pressure distributions are further analyzed to clarify the hydrodynamic mechanisms associated with different geometric configurations. To reduce the cost of direct CFD-based optimization, a surrogate-assisted multi-objective framework is developed by coupling a backpropagation neural network (BPNN) with a Multi-Objective Red-Billed Blue Magpie Optimizer (MORBMO). The BPNN is trained using 112 CFD samples and achieves R 2 values of 0.9616, 0.9835, and 0.9490 for rise-up, trim, and total resistance coefficient, respectively. MORBMO is then used to identify a compromise solution that simultaneously accounts for resistance and running attitude. The selected optimized configuration has a front hydrofoil sweep angle of 12°, a hydrofoil span of 2001.49 mm, and a longitudinal spacing of 3292.89 mm. Compared with the baseline design, the optimized craft reduces rise-up by 2.63%, trim by 8.16%, and total resistance coefficient by 0.90%. The stern diverging wave crest height is also reduced by 10.09%. These results indicate that the optimized hydrofoil arrangement mainly improves the running attitude and wave pattern while producing a modest reduction in resistance, providing a practical configuration for balanced hydrodynamic performance.