When attempting to solve an optimization problem using the SA algorithm, the most obvious representation of the control variables is usually appropriate. However, the way in which new solutions are generated may need some thought. The solution generator should

- introduce small random changes, and
- allow all possible solutions to be reached.

For problems with continuous control values, Vanderbilt and Louie [62] recommend that new trial solutions be generated according to the formula:

where is a vector of random numbers in the range , so that each has zero mean and unit variance, and is a matrix that controls the step size distribution. In order to generate random steps with a covariance matrix is found by solving

by Cholesky decomposition, for example should be updated as the search progresses to include information about the local topography:

(See the Linear Algebra chapter for more details of this methos.)