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https://issues.apache.org/jira/browse/MATH-867?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13465719#comment-13465719
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Nikolaus Hansen commented on MATH-867:
--------------------------------------
{quote}
I believe the reason is that defaulting sigma to 0.3 times the range causes the
fitter to jump from the initial value (which is order of 1 away from the
target) to some huge value on the order of 1e16 on the first step.
{quote}
Right. I suggest to make sigmaArray independent of the boundary values.
Otherwise setting boundaries like [1e-15,1e15] still will most likely lead to
an unexpected behavior: the user just does not want to exceed this value, while
the algorithm interprets the interval as being reasonable values to be checked
out. Still it makes perfectly sense to check consistency between the initial
guess, sigmaArray and boundaries, in that, say,
{code}
fitfun.encode(guess)[i] - sigmaArray[i]/2. > fitfun.encode(boundaries[0])[i]
{code}
in case of a lower bound.
{quote}
It doesn't reach the target exactly due to one of the many stop conditions
hard-coded into the generationLoop which decide that the fit is "good enough"
and quit.
{quote}
more specifically, stopTolX is defined relative to the initial value of
sigmaArray. This specific problem should therefore go away if stopTolX is
defined as an absolute value like 1e-11. I think absolute and relative
definition of stopTolX are both justified.
Generally, the patch becomes buggy, when encode and decode are changed/reused.
In this case, where solutions are compared with boundaries, like
{code}
if(x[i] < boundaries[0][i])
{code}
the comparison must be done with encoded boundaries:
{code}
encLboundaries = fitfun.encode(boundaries[0]);
if (x[i] < encLboundaries[i])
{code}
> 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: MATH867_patch, 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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