Containership route optimization considering ship synchronous rolling and parametric rolling

Maritime transportation is the backbone of global trade, but containerships face severe safety risks of container loss due to synchronous rolling and parametric rolling under complex sea conditions. To address this issue, this study proposes a containership route optimization method integrating these two critical safety constraints. First, ensemble forecasting is adopted to characterize the uncertainty of wave conditions, and safety constraints for synchronous rolling and parametric rolling are constructed based on the Conditional Value-at-Risk (CVaR) framework, with the optimization objective of minimizing the total voyage cost including fuel consumption cost and time cost. Second, the Ant Colony Optimization (ACO) algorithm is employed with a rolling-aware enhancement strategy, which involves initializing pheromones via a normal distribution around the reference route, constructing a heuristic matrix that integrates distance, speed and rolling risk, and introducing an elite ant mechanism to balance global exploration and local exploitation. A case study on the North Atlantic route verifies the proposed approach against the Genetic Algorithm (GA) and A* algorithm. Results show that the ACO based approach achieves optimal comprehensive performance, with average speed reaching 14 kt, 5.26% higher than GA and 3.70% higher than A*; total voyage cost is reduced by 8.2% compared to GA and 16% compared to A*. Meanwhile, it effectively avoids high-risk rolling zones through coordinated adjustments of heading and speed, ensuring navigational safety. This research provides reliable decision support for the safe and economical operation of containerships.