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https://issues.apache.org/jira/browse/MATH-867?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13461853#comment-13461853
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Nikolaus Hansen commented on MATH-867:
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I don't see anything wrong with the new version (the original version better
facilitates the display of the evolution of variables in a single picture). It
seems also clear where the original version fails: taking the difference in the
above computation leads to a loss of significant digits if x[i] and
boundaries[0][i] largely differ, that is, if the solution is far away from the
lower bound.
However the use of boundaries for a range like [0, 5e16] seems not reasonable
to me and it was not meant to be used like that. More specifically, I don't see
a good reason to set an upper bound of 5e16, in particular when the initial
point is 1. I would expect a reasonable initial point to lie roughly in the
middle of the search interval. If the variable is supposed to be as large as
5e16, it is likely advisable to apply a non-linear transformation, e.g. to
optimization its logarithm. More general, when searching in an interval of size
1e16 using double precision, one can, in principle, hardly expect to get a
solution with a precision better than, say, 10 in which case one has identified
the optimum with 15 digits of precision.
> CMAESOptimizer with bounds fits finely near lower bound and coarsely near
> upper bound.
> ---------------------------------------------------------------------------------------
>
> Key: MATH-867
> URL: https://issues.apache.org/jira/browse/MATH-867
> Project: Commons Math
> Issue Type: Bug
> Reporter: Frank Hess
> Attachments: Math867Test.java
>
>
> When fitting with bounds, the CMAESOptimizer fits finely near the lower bound
> and coarsely near the upper bound. This is because it internally maps the
> fitted parameter range into the interval [0,1]. The unit of least precision
> (ulp) between floating point numbers is much smaller near zero than near one.
> Thus, fits have much better resolution near the lower bound (which is mapped
> to zero) than the upper bound (which is mapped to one). I will attach a
> example program to demonstrate.
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