Optimization of the Dynamic Positioning problem under unchanging weather conditions - How to remain stationary in stormy seas - Lauritzson, Peter Lindgren (My University, 2015)
This thesis concerns dynamic positioning, which is important in the shipping industry. Dynamic positioning uses thrusters to stabilize marine vessels horizontally, in contrast to the more traditionally used anchors. This is important because better dynamic positioning solutions enable the use of vessels in rougher ocean conditions. We were provided with model data to review, develop, and implement optimization algorithms suited for the problem. There are several different results, each important in its own right. Solutions found by different algorithms are contrasted to what is currently used, and it is shown that many standard optimization algorithms find sub par solutions. The discontinuous nature of the model data can be well approximated with a smooth function, using a Gaussian filter, on which the Augmented Lagrangian method can be used. The Augmented Lagrangian method is one of the algorithms with the highest convergence rates. Lastly, there is no guarantee that any solution found is close to a local optimum. The thesis concludes with a recommendation of algorithms that improve on the current solution. The main recommendation is to use the Augmented Lagrangian method on the smooth approximation of the problem, starting from the solution found by currently used algorithms. Another recommendation is to further look into the branch and bound algorithm. The implementation of the branch and bound algorithm given in this thesis is intractable, but possible improvements are suggested.
Keywords: Matematik; Grundläggande vetenskaper; Mathematics; Basic Sciences