Voyage optimization using dynamic programming with initial quadtree based route

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.