Evolving the Structure of Evolution Strategies

Various variants of the well known Covariance Matrix Adaptation Evolution Strategy (CMA-ES) have been proposed recently, which improve the empirical performance of the original algorithm by structural modifications. However, in practice it is often unclear which variation is best suited to the specific optimization problem at hand. As one approach to tackle this issue, algorithmic mechanisms attached to CMA-ES variants are considered and extracted as functional \emph{modules}, allowing for combinations of them. This leads to a configuration space over ES structures, which enables the exploration of algorithm structures and paves the way toward novel algorithm generation. Specifically, eleven modules are incorporated in this framework with two or three alternative configurations for each module, resulting in $4\,608$ algorithms. A self-adaptive Genetic Algorithm (GA) is used to efficiently evolve effective ES-structures for given classes of optimization problems, outperforming any classical CMA-ES variants from literature. The proposed approach is evaluated on noiseless functions from BBOB suite. Furthermore, such an observation is again confirmed on different function groups and dimensionality, indicating the feasibility of ES configuration on real-world problem classes.