Misunderstanding about the number of trial points in Globalsearch
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I check both pages http://www.mathworks.com/help/gads/globalsearch-class.html and http://www.mathworks.com/help/gads/how-globalsearch-and-multistart-work.html but apparently I didn't understand the roles of NumTrialPoints and NumStageOnePoints clearly.
I thought that the NumStageOnePoints trial points are evaluated in Stage 1 and the best point will be chosen (such that fmincon starts from there), and then NumTrialPoints will be evaluated only in Stage 2. If that's the case, why NumTrialPoints should be >= NumStageOnePoints?
Also, what does it mean when NumTrialPoints is > NumStageOnePoints?
Thanks,
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Alan Weiss
2014-4-30
In the description of the algorithm, Obtain Stage 1 Start Point, Run there is the sentence GlobalSearch removes the set of NumStageOnePoints trial points from its list of points to examine. GlobalSearch then goes on to examine the remaining (NumTrialPoints - NumStageOnePoints) trial points to see if they run, and to run fmincon starting from them if appropriate.
So you have to have more trial points than Stage 1 points for the algorithm to make sense.
Alan Weiss
MATLAB mathematical toolbox documentation
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Alan Weiss
2014-5-1
The description of the algorithm really does contain all the information about how GlobalSearch works. It is hard for me to add to that description.
I wonder, though, if you would be better served by MultiStart. It sounds to me as if your objective function is time-consuming to evaluate. If so, then you can probably get better control over the amount of time the solver takes by using MultiStart. You see, GlobalSearch evalueates the objective function quite a large number of times without calling fmincon. In contrast, MultiStart calls fmincon repeatedly. So perhaps, in your case, you would get a good solution in less time, and in a more controlled amount of time, by using MultiStart, and having all computations be directed at finding a minimum, rather than at determining whether or not it is worthwhile to run fmincon.
Alan Weiss
MATLAB mathematical toolbox documentation
P.S. If you believe I answered your original question adequately, please accept the answer.
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