Adaptive encoding for aerodynamic shape optimization using evolution strategies

Abstract

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

Three dimensional evolutionary aerodynamic design optimization with CMA-ES

“…This tradeoff between the flexibility of the model and the search space dimension cannot be resolved easily if the representation is static. Instead, a dynamic and adaptive representation is required as proposed in [11].…”

Real-World Applications of Multiobjective Optimization

“…After that, the number of search parameters can be increased, e.g., by inserting new control points in a B-Spline based representation. Encouraging results have been reported where an adaptive representation for evolutionary optimization of turbine blades has been adopted (Olhofer et al, 2001).…”

On Evolutionary Optimization of Large Problems Using Small Populations

“…Finally, we investigate the performance of the algorithm when we initialize the newly added design parameter to 0, which in this example makes the inclusion of the new search dimension neutral to the fitness value. Such neutral mutations have shown to be essential to the success of adaptive coding when splines are used for geometry description in design optimization [4]. Comparing the results in Fig.…”

“…To this end, an adaptive coding scheme has been suggested where the CMA-ES is employed in aerodynamic shape optimization [4]. The basic idea is to encode the number of parameters to be optimized (the search dimension) in the chromosome and to mutate during the optimization.…”