next up previous

4.3.1 Solution Representation

ESs are still primarily used to solve optimization problems with continuous control variables, and for applications of this sort the natural representation of the control variables as an n-dimensional real-valued vector x is entirely appropriate. In addition, the representation of a solution may include (depending on the specific ES implementation being employed) up to n different variances and up to covariances of the generalized n-dimensional normal distribution with zero means and a probability density function:

where is the covariance matrix and z the vector of random variables. To ensure that the matrix is positive-definite, ES algorithm implementations usually work in terms of the equivalent rotation angles:

These variances, covariances and rotation angles are known as strategy parameters.