1. A method, in a data processing system, for determining configuration parameter value settings for a computing device to optimize an operational characteristic of the computing device, comprising: obtaining a simplex of points, wherein each point in the simplex represents a set of configuration parameters for the computing device; performing a geometric transformation on the simplex of points to identify a new point to investigate; sampling the operational characteristic at the new point; determining if the operational characteristic associated with the new point is worse than a value of the operational characteristic for each point in the simplex of points; determining a set of points in the simplex that need to be resampled if the new point is worse than a value of the operational characteristic for each point in the simplex of points; resampling the operational characteristic at each of the points in the set of points; and determining a new simplex based on the resampled operational characteristic of points in the set of points.