DifferentialEvolution scaling factor randomization

Question

Using NMinimize for finding global minima, one can choose the DifferentialEvolution method. You can find a (not so) detailed description in the link Constrained Optimization.

That being said, I would like to know if there is a simple way to implement the randomization of the value attributed to the option ScalingFactor. Such a feature should enhance the method:

It has been found recently that selecting F from the interval [0.5, 1.0] randomly for each generation or for each difference vector, a technique called dither, improves convergence behaviour significantly (Differential Evolution Homepage)

where the F mentioned in the quote corresponds to the value of ScalingFactor in Mathematica.

Probably, this is my lack of knowledge on the details of Mathematica showing up, but I don't know how to tell that in each step of NMinimize it should put RandomReal[{0.5,1.}] in the option ScalingFactor.

Answer 1

What follows is, of course, a terrible hack... since NMinimize is implemented entirely in top-level Mathematica, its code allows inspection by spelunking tools. The relevant function is

NMinimize[1, x]; (* force autoloading *)

Needs["GeneralUtilities`"]

PrintDefinitions[Optimization`NMinimizeDump`CoreDE]

and the desired behavior can be achieved by replacing scale in

mutateout[j, vecs, Length[vars], crossprob, scale]

with RandomReal[{0.5, 1}] and reevaluating the definition.

This change will only be in effect for the current kernel session and until the NMinimize definitions are read-in again. For a more persistent patch, one could load NMinimize and set DownValues[Optimization`NMinimizeDump`CoreDE] in an init.m file.