Evolutionary shape optimization with self-adapting mutation distribution based on the Cholesky decomposition

The investigations in the paper have been carried out against the background of an integrated approach to the structural design problem. Due to the complex nature of the search space and the continous-discrete-binary system vector in the general case of structural optimization, conventional methods can not be used. Evolution strategies have shown their general capability to solve the sizing and the topology problem. On the other hand when employing evolution strategies to the subproblem of shape optimization they tend to get stuck due to an unsufficient step size adaptation. Therefore, a covariance matrix approach has been used for the self-adaptation of the mutation distribution during the evolutionary shape optimization process. The necessary decomposition of the covariance matrix has been carried out with the Cholesky method. The results of this approach are compared to the usual general and individual step size adaptation procedures of evolution strategies.