Evolvability as Concept for the Optimal Design of Free-Form Deformation Control Volumes

The performance of design optimizations which target the improvement of certain physical aspects of real world objects like e. g. in the automotive or aeronautical domain depends on the efficient interplay of optimization algorithm, evaluation method and shape representation. For the development of complex aerodynamic components, evolutionary algorithms as global stochastic optimization algorithms have been successfully coupled to shape morphing methods. Instead of a direct representation of the shapes' boundary, shape morphing methods like free-form deformation (FFD) apply scalable changes to a baseline prototype using a moderate number of parameters mapped to control point movements. The initial spatial arrangement of the control points influences strongly the design flexibility and the optimization performance in combination with the normal distributed mutation operator in evolutionary optimization algorithms. In the present paper, a method is proposed to support the generation process of initial FFD control volumes which is usually carried out manually in practice. The method is based on the concept of evolvability which is considered as the property of initial control volumes to generate favorable design variations within a moderate number of iterations while avoiding unfeasible mutations. We introduce mathematically translational design variability, mutational design variability and the central robust control volume as key features to compute an evolvable distribution of control points. In target shape matching experiments using an evolutionary strategy, the performance for different configurations of evolvability-tuned initial control volumes is shown empirically.