A novel federated learning-based two-stage approach for ship energy consumption optimization considering both shipping data security and statistical heterogeneity

Ship energy consumption (SEC) efficiency optimization is crucial to sustainable maritime transportation. Due to commercial confidentiality, shipping data cannot be freely shared. Federated learning (FL) addresses this by predicting fuel consumption while maintaining data privacy. Traditional FL struggles with accuracy due to statistical heterogeneity in shipping data. To address it, an FL framework incorporating adaptive regularization terms is proposed. Alongside, given the scarcity of maritime communication resources, a tailored convolutional neural network-gated recurrent unit (CNN-GRU) model is designed for ship clients. Furthermore, based on the prediction results, a Mixed Integer Non-Linear Programming (MINLP) model is formulated to derive optimal speeds and establish a joint database for trim strategy output. Through the prediction and optimization approach, three optimized SEC efficiency metrics are obtained. Experimental results on data from eight bulk carriers show that the proposed FL framework with adaptive regularization terms improves prediction accuracy over individual, FedAvg, and FL with classical regularization term models. The CNN-GRU model outperforms IGWO-LSTM, GRU, and CNN-LSTM models in RMSE and adjusted R-squared value. The optimization approach enhances SEC efficiency by 1.42%–3.94 %. These findings provide practical recommendations for maritime organizations to set efficient speeds and trim strategies for fleet management under secured data conditions.