Forward dynamic programming-informed Bayesian method for optimal power allocation in short-sea shipping

• Discrete-to-continuous optimization method is proposed to enhance power allocation. • Constraint-aware Bayesian optimization improves convergence rate and stability. • Full-scale measurements are used in this study for comparison. • Up to about 5–10% energy reduction is achieved by the proposed method. Optimising propulsion power along a ship’s voyage is critical for energy efficient voyage planning, as it enables the distribution of propulsion settings along a route to minimise fuel consumption while satisfying operational constraints such as target arrival time. This study proposes a structured discrete-to-continuous optimisation framework to enhance propulsion power allocation strategies. Feasible solutions generated by a modified parallel coupling dynamic programming approach serve as prior knowledge (PCDP), and are subsequently refined using constraint-aware Bayesian optimisation (BO). When combined with a smooth exponential penalty function (BO+EP), the Bayesian optimiser embeds convex constraints directly within the optimisation process, improving convergence behaviour. The framework is validated using full-scale data from four voyages of a chemical tanker. Results demonstrate that the proposed method achieves a tenfold reduction in computational cost compared with explicit constraint (EC), while providing up to around 3% additional fuel savings compared with dynamic programming. Overall, the proposed power allocation strategy reduces fuel consumption by up to 9% on average while satisfying arrival time requirements.