Application of a real-coded genetic algorithm for the fitting of a ship hull surface through a single non-uniform B-spline surface

In digital ship-design processes, surface modeling needs to be as accurate as possible for effectiveness in ship production as well as numerical analysis of the performance. Traditionally, the form of a ship hull is constructed from a set of cross-sectional data. This approach entails difficulties in the cross-sectional spacing and accuracy of the characteristic curves, such as the stern and bow profiles, deck side line, bottom tangential line, and unconnected curves. Genetic algorithms (GAs) have attracted increasing attention as a multimodal optimization solution for surface reconstruction that enable construction of a single non-uniform B-spline (NUB) surface at the initial stage of ship design with constraints such as knuckles, discontinuity conditions, and bulbous bows with high curvatures, . The first, simultaneous multi-fitting GA determines the boundary curves, such as the stem and stern profiles, and finds the common knot values for both curves. Similarly, the same GA technique is applied for other boundary curves at the bottom and the deck. The second GA is employed to fit the interior data points after the boundary curves are fitted. The encoded design variables for surface construction are the locations of the vertices and the knot values. Those variables are modified for improving the surface quality until a predefined degree of precision is attained. In four instances of application, the GA technique developed in this research has been shown to provide good, single, NUB surfaces with high efficiency. In the early design stage, a single NUB surface is more convenient for performance visualization and finite-element methods. It can be readily translated into many CAD/CAM packages, which facilitate the smooth transition of data across the different design stages.