Covariance matrix adaption in evolution strategies

This animation illustrates the concept of covariance matrix adaption (CMA) in evolution strategies (ES). While searching the minimum of the objective function, the topography of which is indicated by the contour lines, the initially isotropic mutation distribution of the CMA-ES (blue dots) adapts to the elongated topography of the objective function, up until the distribution's covariance matrix has approached the inverse Hessian of the objective function. The red dot marks the center of the mutation distribution, which eventually contracts to a point when the minimum of the objective function is found.This research has been funded by the Verbundforschung of the BMBF/DLR under Grant No. 50 OR9911 1 and by the DFG under Re 353/48