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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.

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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. –  Michael E2 Feb 20 at 11:43
    
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? –  fcpenha Feb 20 at 18:51
    
@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. –  fcpenha Mar 11 at 17:06
    
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. –  Michael E2 Mar 11 at 17:21
    
@MichaelE2 Yes, I've read the documentation. Thank you a lot for the time spent on this subject. –  fcpenha Mar 11 at 21:05
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