Scatter Plot from Scientific Research

In the first generation (generation 1), the CMA-ES creates a generation of points with values of the parameters assigned by an initial Gaussian distribution with a mean at the center of given elliptical bounds and the radii of the ellipse determined by the standard deviations of the distribution (red-dashed lines). CMA-ES ranks the points in terms of how close they are to minimizing the objective function (white locus of the plots) and moves the distribution in the direction of the points with the best ranking regarding objective minimization. In the following generations (generations 2-5), this process is repeated and continues. As the points move closer to the global minimum, the CMA-ES begins to shrink the standard deviation and converge upon the global minimum. The process stops (generation 6) when the standard deviation of the points reaches a specified, small value, indicating that the generated points all converge upon the global minima.

DOI