Representing the Change - Free Form Deformation for Evolutionary Design Optimization

The representation of a design influences the success of any kind of optimization significantly. The perfect trade-off between the number of parameters which de- fine the search space and the achievable design flexibility is very crucial since it influences the convergence speed of the chosen optimization algorithm as well as the possibility to find the design which provides the best performance. Classical methods mostly define the design directly, e.g. via spline surfaces or by repre- sentations which are specialized to one design task. In the present chapter, the so-called deformation methods are focused which follow a different approach. Instead of describing the shape directly, deformation terms are used to morph an initial design into new ones. This decouples a complex design from an expensive shape description while relying purely on mapping terms which are responsible for the geometry transformations. Thus, the designer is encouraged to determine the optimal relation between parameter set and design flexibility according to the given task. With respect to the optimization, these mapping terms are con- sidered as parameters. In this chapter, the combination of two state of the art deformation algorithms with evolutionary optimization is focused. After an in- troduction of these techniques, a framework for an autonomous design optimiza- tion is sketched in more detail. By means of two optimizations, which feature a stator blade of a jet turbine the workability is shown and the advantages of such representations are highlighted.