A Scalable Evolution Strategy with Directional Gaussian Smoothing for Blackbox Optimization

We developed a new scalable evolution strategy with directional Gaussian smoothing (DGS-ES) for high-dimensional blackbox optimization. Standard ES methods have been proved to suffer from the curse of dimensionality, due to the random directional search and low accuracy of Monte Carlo estimation. The key idea of this work is to develop Gaussian smoothing approach which only averages the original objective function along $d$ orthogonal directions. In this way, the partial derivatives of the smoothed function along those directions can be represented by one-dimensional integrals, instead of $d$-dimensional integrals in the standard ES methods. As such, the averaged partial derivatives can be approximated using the Gauss-Hermite quadrature rule, as opposed to MC, which significantly improves the accuracy of the averaged gradients. Moreover, the smoothing technique reduces the barrier of local minima, such that global minima become easier to achieve. We provide three sets of examples to demonstrate the performance of our method, including benchmark functions for global optimization, and a rocket shell design problem.