Voyage optimization using dynamic programming with initial quadtree based route

Abstract

Abstract This research proposes an integrated voyage optimization algorithm that combines quadtree graph generation, visibility graph simplification, Dijkstra’s algorithm, and a 3D dynamic programming (3DDP) method. This approach enables the determination of a minimum distance initial reference route and the creation of a 2D navigational graph for efficient route optimization. We effectively store and process complex terrain information by transforming the GEBCO uniform grid into a quadtree structure. By utilizing a nearest neighbour search algorithm, edges are connected between adjacent ocean nodes, facilitating the generation of a quadtree graph. Applying Dijkstra’s algorithm to the quadtree graph, we derive the shortest initial route and construct a visibility graph based on the waypoints. This results in a simplified reference route with reduced search distance, allowing for more efficient navigation. For each waypoint along the reference route, a boundary is defined angled at 90 degrees to the left and right, based on the waypoint’s reference bearing. A line segment formed by the waypoint and both boundaries is defined as a navigational stage. A navigational graph is defined by connecting adjacent stages. Employing a 3DDP method on the navigational graph, and incorporating weather forecasting data, including wind, wave, and currents, we search for a route that minimizes fuel oil consumption with estimated time of arrival restrictions. Our approach is tested on several shipping routes, demonstrating a fuel consumption reduction compared to other voyage optimization routes. This integrated algorithm offers a potential solution for tackling complex voyage optimization problems in marine environments while considering various weather factors.