Application of Free Form Deformation Techniques in Evolutionary Design Optimisation

1. Abstract In the past decades evolutionary algorithms have been successfully applied to various design optimisation problems. It has been shown that the representation of the problem is crucial for a high performance of the method. One important aspect is the trade-off between the demands for a high geometric variability in shape generation and a minimum number of optimisation parameters. In this paper, free form deformation is coupled with evolutionary design optimisation in order to overcome this trade-off. Free form deformation methods have been initially developed in the field of solid and surface modelling allowing intuitive shape modifications by moving the control points of a lattice which encloses an arbitrary target geometry. Therefore it allows to decouple the complexity of the design to be optimised from the optimisation parameter. Evolutionary computation is a well established optimisation method for shape or design optimisation and belongs to the global stochastic optimisation methods. A population of possible designs is maintained and adapted from generation to generation via reproduction, variation operators like mutation and recombination and a selection method. The combination of free form deformation with evolutionary design optimisation of complex systems is illustrated by an optimisation of a three-dimensional high performance compressor airfoil. Hence the potential of coupling this kind of representation with a fluid mechanical design optimisation problem is emphasized. The optimisation parameters are defined by a lattice of control points which at the same time modify the geometry as well as the computational grid which is needed by the flow solver. Finally, the resulting shapes of the optimisation are presented and compared to the initial design to show the applicability of the proposed method. 2.