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

Journal article, 2026

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.