Global shape optimization methods based on surrogate models for the case of B-spline shape parameterization

Ivo Marinić-Kragić, Damir Vučina

Engineering shape optimization often involves computationally expensive numerical simulations such as computational fluid dynamics. Furthermore, these technical objects are almost always complex three-dimensional shapes that cannot adequately be described with a small number of shape variables. These problems are usually solved by gradient methods starting from an initial solution. This approach is computationally efficient especially when the gradients are calculated by the adjoint method. However, this approach can be used only to obtain a local optimum. To obtain the global optimal solution, a different approach is required. A possible path is to use B-spline surfaces to describe the shape and genetic algorithms for optimization of the B-spline control point coordinates. The problem with this approach is that many computationally expensive numerical simulations are required.

The objective of this paper is the evaluation of different surrogate models in cases of global shape optimization which involve B-spline shape parameterization and computational fluid dynamics. The first step is solving several selected problems using a genetic algorithm starting from a randomly generated population. The optimization variables are only the coordinates of the B-spline control points. After the optimal solution is obtained by a genetic algorithm, several surrogate models were tested in various stages of the optimization procedure. The results are used to propose which surrogate models are appropriate for different stages of the global optimization problem at hand. This leads to a surrogate based optimization method developed specifically for global shape optimization based on B-spline shape parameterization.