Multi-Objective Optimization of Motor Vessel Route

This paper presents an original method that allows computation of the optimal route of a motor vessel by minimizing its fuel consumption. The proposed method is based on a new and efficient meshing procedure that is used to define a set of possible routes. A consumption prediction tool has been developed in order to estimate the fuel consumption along a given trajectory. The consumption model involves the effects of the meteorological conditions, the shape of the hull and the power train characteristics. Pareto-optimization with a Multi-Objective Genetic Algorithm (MOGA) is taken as a framework for the definition and the solution of the multi-objective optimization problem addressed. The final goal of this study is to provide a decision helping tool giving the route that minimizes the fuel consumption in a limited or optimum time. method for large motor vessels using MultiObjective Genetic Algorithms. Hinnethal and Saertra (2005) improved this method considering the stochastic nature of weather along the route. Böttner (2007) recently used this work combined with dynamic programming for costal approach in order to propose the best possible track from harbor to harbor. These methods are characterized by a low number of free variables to describe both the course and the speed of the boat. Moreover, a high number of route variants can be considered from which Pareto optimal solutions may be identified. In the four different approaches, the scheme for optimisation is almost the same : • Mathematical modeling of the ship to compute the objectives, • 3-D interpolation (time and space) of weather and sea state data, • Parametric route definition, • Optimization of the route using an algorithm. Our work is based on a new discretization of the research space based on few physical parameters. This parametric definition of the griding makes it understandable and easy to tune. Moreover this kind of meshing may be applicable for all type of vessels, journeys and all weather conditions are easily taken into account. The gridding of the sail area is systematic and uniform since it is based on spherical geometry and accepts constrains like bathymetric data. Our work is related to the method proposed by Harries & al. because we kept their definition of both the geography and speed since it allows the complete location of the boat in space and time. The modeling of motor vessels is not the purpose of this work and will just be briefly presented. Future works concern the identification of the vessel model using fuzzy logic technique in order to obtain an accurate consumption model. Since this identification is not achieved yet, a model from the literature will be used to present this new gridding method. The meshing of the explored area is presented first. Then, the way of constructing routes is shown and a sensitivity of the meshing is presented. Next, the way of modeling a motor vessel is introduced. Finally, results of numerical optimizations are presented in order to evaluate the limitations and benefits of the proposed meshing method. 2 MESHING OF THE EXPLORED AREA The new automatic meshing method that we propose is based on spherical rhombus where two of the opposite vertexes are the departure and the arrival points. The main advantages of this discretization of the sailing area are : • The genericity of its construction taking into account the sea-beds geography, the time dependant meteorological data and the characteristics of the vessel. • The systematic gridding of the explored area with few physical parameters. The automation of its calculation leading to optimizable routes. • The possible reactualization of the rhombus to change the routing policy during the sailing. 2.1 Rhombus definition In this part denotes the departure point, the arrival one and is the center of Earth considered spherical. is the plane containing the lines and carrying respectively vectors and . is the angle between these two vectors and is their bisectrix. is one vector normal both to and . We also define the two related unit vectors and . Let be the plane containing , , the two remain vertexes of the rhombus and and point . The lines and are directed by vectors and . We defined . This notation is recalled in the figure 1. Figure 1: Main planes to define the meshing Point denotes the intersection between the great circles and . is the plane containing and , we have . This angle is the image of the orthodromic distance between and . Knowing the maximal speed of the vessel , imposed by the design of the hull and the power train characteristics, and the desired time of sailing , the maximal distance that can cross the vessel during the time window is : By this mean we can set the maximal distance on the great circle route :