Evolution strategies with Ledoit-Wolf covariance matrix estimation

Evolution strategies are successful blackbox optimization algorithms for continuous solution spaces. The covariance matrix adaptation evolution strategy (CMA-ES) and variants have shown great success on various problems in the past. In this paper, we present an evolution strategy (ES) based on a (1+1)-ES with Rechenberg's 1/5th step size control and Ledoit-Wolf covariance estimation. We compare this algorithm with a variant based on empirical maximum likelihood estimation. In the experimental part, the methods are compared to each other on a short benchmark function set. The ES with Ledoit-Wolf estimation turns out to outperform empirical covariance estimation. The analysis of the covariance estimation population size and the influence of the problem dimensionality allows insights into the choice of parameters.