On the minimal time vessel routing problem.

摘要

During the last two decades there has been a growing interest in methods for calculating the optimal trajectory of a ship. The purpose of this dissertation is the derivation of solution techniques for the minimal time vessel routing problem. Methodologies derived are relatively general and after minor modifications could be utilized for optimal planning of an autonomous vehicle traveling in a variable routing terrain.;The minimal time routing for a vessel traveling in deterministic stationary seas is first examined. Variational calculus has been used to treat the general version of the problem. A discretization of the feasible sailing terrain into a finite number of subregions within which the ship possesses similar dynamics has been used. Local variational considerations combined with global boundary conditions result in efficient solution procedures. Finally, the presense of constraints and their effect on the calculation of the optimal trajectory is discussed.;The minimal time trajectory for a vessel traveling from one origin to several ordered destination points sailing in deterministic time dependent sea states is analyzed next. General properties of the extremal trajectories and the associated optimal controls have been derived. A discretization, similar to that used for the stationary problem but with time dependent geometry, has been used. Within the framework of this discretization, appropriate first variation considerations lead to local optimality conditions which, combined with global boundary conditions form the basis of the algorithmic schemes developed. Predefined or free departure times in addition to constrained versions of the problem are also considered.;Finally, the stochastic minimal time problem is considered. A procedure to calculate an isochrone line is described. This line is considered as the first stage in a Dynamic Programming (DP) network. The rest of the routing space is characterized by stochastic sea states. The probabilistic properties of the sea state characteristics are analyzed using Bayesian statistical methods. This estimation takes place at the beginning of the trip and utilizes past observation and current sea state forecast as well as seasonal statistical properties. Bounds on the optimal state evolution, resulting in a serious reduction of the problem dimensionality, are also derived. (Abstract shortened with permission of author.)