Waypoint-Sequencing Model Predictive Control for Ship Weather Routing Under Forecast Uncertainty

Ship weather routing optimization has evolved from deterministic great-circle navigation to sophisticated frameworks that account for dynamic environmental conditions and operational constraints. This paper presents a waypoint-sequencing Model Predictive Control (MPC) approach for energy-efficient ship weather routing under forecast uncertainty. The proposed rolling horizon framework integrates neural network-based vessel performance models with ensemble weather forecasts to enable real-time route adaptation while balancing fuel efficiency, navigational safety, and path smoothness objectives. The MPC controller operates with a 6 h control horizon and 24 h prediction horizon, re-optimizing every 6 h using updated meteorological forecasts. A multi-objective cost function prioritizes fuel consumption (60%), safety considerations (30%), and trajectory smoothness (10%), with an exponential discount factor (γ = 0.95) to account for increasing forecast uncertainty. The framework discretises planned routes into waypoints and optimizes heading angles and discrete speed options (12.0, 13.5, and 14.5 knots) at each control step. Validation using 21 transatlantic voyage scenarios with real hindcast weather data demonstrates the method’s capability to propagate uncertainties through ship performance models, yielding probabilistic estimates for attainable speed, fuel consumption, and estimated time of arrival (ETA). The methodology establishes a foundation for more advanced stochastic optimization approaches while offering immediate operational value through its computational tractability and integration with existing ship decision support systems.