Modeling stochastic fuel consumption for ship voyage optimization with integrated weather conditions: A machine learning approach

Journal article, 2026

Improving the energy efficiency of ships is a key pathway towards meeting the greenhouse gas reduction targets set by the International Maritime Organization. Voyage optimization is widely used to reduce fuel consumption and emissions, but its reliability depends critically on the ship performance model. However, uncertainties are often associated with today’s ship performance models, especially when many planning variables are considered. This study aims to investigate and clarify the impact of uncertainties in ship performance models on voyage optimization. A genetic algorithm (GA) is implemented in deep neural networks (DNN) to model engine shaft power in terms of its operational and metocean weather conditions. This GA-DNN model improved predictive performance R² by 50% over the semi empirical. The specific fuel oil consumption (SFOC) used to estimate fuel consumption from engine shaft power is proposed and described as a stochastic model, due to its strong dependence on engine settings related control variables that are often unknown in advance for voyage planning. The Gaussian process regression (GPR) method is utilized to establish the stochastic SFOC model, achieving an average RMSE of 2.91 g/kWh while also providing confidence intervals for uncertainty quantification. The Three-Dimensional Dijkstra Algorithm (3DDA) is used to investigate uncertainties of voyage optimization due to the uncertain SFOC. Finally, Monte Carlo simulation is employed to examine fuel consumption uncertainty from stochastic SFOC in voyage optimization and assess sensitivity of voyage optimization using different objective functions, such as deterministic power consumption, or stochastic fuel consumption with varying expected time of arrival (ETA). The proposed stochastic fuel consumption prediction model can provide more valuable information for the decision support of practical voyage planning, in terms of varying ETA and energy efficiency.