Adaptive encoding for aerodynamic shape optimization using evolution strategies

The evaluation of fluid dynamic properties of various different structures is a computationally very demanding process. This is of particular importance when population based evolutionary algorithms are used for the optimization of aerodynamic structures like wings or turbine blades. Besides choosing algorithms which only need few generations or function evaluations, it is important to reduce the number of object parameters as much as possible. This is usually done by restricting the optimization to certain attributes of the design which are seen as important. By doing so, the freedom for the optimization is restricted to areas of the design space where good solutions are expected. This can be problematic especially if the properties of the design and their interactions are not known sufficiently well like for example for transonic flow conditions. In order to be able to combine the conflicting constraints of a minimal set of parameters and the maximal degree of freedom, we propose an adaptive or growing representation for spline coded structures. In this way, the optimization is started with a simple representation with a minimal description length. The number of describing parameter is adapted during the optimization using a mutation operator working on the structure of the encoding. We compare this method with four different Evolution Strategies using a spline fitting problem as a test function. Of special interest are on the one hand the total number of fitness evaluations, which determine the computational resources necessary for an optimization and on the other hand the final quality of the match measured by the distance between a target curve and the generated spline