HADAD: Hexagonal A-Star with Differential Algorithm Designed for weather routing

We present HADAD (Hexagonal A-Star with Differential Algorithm Designed for weather routing), a novel optimization algorithm for weather routing. HADAD conducts a global exploration using an A ⋆ search on a hexagonal grid with higher-order neighbors, enhancing directional flexibility and overcoming limitations of traditional graph searches that constrain vessel movements. It then refines the solution using a discrete Newton–Jacobi variational method, ensuring convergence to a locally optimal, smooth route in continuous space. To evaluate the effectiveness of HADAD, we developed a benchmark comprising 1,560 instances over a full year, varying in origin–destination pairs, vessel speeds and oceanographic conditions. Our results show that HADAD outperforms pure A ⋆ graph search methods by an extra 4% savings with respect to the shortest-distance route, thanks to more flexible smoother trajectories obtained by gradient descent. In our seasonal study we observe that the savings distribution shows large seasonal variations (double savings on average in winter with respect to summer) and contains a significant number of outliers. Savings reach 27% in these cases of extreme weather events. Validation of the algorithm performed with synthetic vector fields has been conducted. In this setting, the algorithm has been adapted to handle fuel consumption optimization for Just-in-Time arrival. By integrating global search and local optimization, HADAD effectively balances computational efficiency with route optimality, offering a practical and adaptable solution for real-world weather routing applications. • Introduce HADAD: an algorithm combining A ⋆ graph search and variational methods for weather routing. • HADAD uses hexagonal grids and higher-order neighbors for increased directional flexibility. • Evaluated HADAD on a benchmark of 1,560 instances across various vessel speeds, routes, and seasons. • Achieved significant travel time reductions, especially at lower vessel speeds. • Analyzed the impact of vessel speed, geographical variation, and seasonality on performance.