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.

  • $\begingroup$ I tried "ScalingFactor" :> RandomReal[{0.5, 1}] which appeared to fail. So did setting the option to a list of factors. So I gave up as it probably being impossible. $\endgroup$ – Michael E2 Feb 20 '14 at 11:43
  • $\begingroup$ Maybe I am talking nonsense, but is there any way to control each step of the process of the function NMinimize, so we can sort this random value for "ScalingFactor"each time? $\endgroup$ – fcpenha Feb 20 '14 at 18:51
  • $\begingroup$ @MichaelE2 , could you give some references or hints on how to control the steps of NMinimize and similar functions? Maybe I can't implement this specific problem that I proposed, but I feel I could learn a lot with this. $\endgroup$ – fcpenha Mar 11 '14 at 17:06
  • $\begingroup$ You can read about diff. evol. in tutorial/ConstrainedOptimizationGlobalNumerical -- you probably already have. That's about all I know about how to use it in Mma. What I tried were random guesses based on the description of the implementation in the tutorial. Occasionally I've gotten lucky and found an undocumented feature. Sorry I can't help further. $\endgroup$ – Michael E2 Mar 11 '14 at 17:21
  • $\begingroup$ @MichaelE2 Yes, I've read the documentation. Thank you a lot for the time spent on this subject. $\endgroup$ – fcpenha Mar 11 '14 at 21:05

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 *)



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.

  • $\begingroup$ Nice adjustment. I think it would be good if the DE implementation could be updated with some other mutators in the future. The classical rand/1 is not bad, but the best choice is, as always, problem-specific. Empirically, I found that MDE5 is a very good default choice for many problems. Dither also does not seem to improve rand/1/bin as dramatically as it does some other mutators. $\endgroup$ – Oleksandr R. Sep 27 '15 at 1:30

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