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https://issues.apache.org/jira/browse/MATH-867?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13461891#comment-13461891
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Nikolaus Hansen commented on MATH-867:
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It seems important to point out that a parameter transformation or scaling and
variable boundaries are two different things. That they are mixed in the
code/interface I would indeed consider as a bug. Generally, the boundary
handling can be done without any variable transformation and therefore does not
need to effect precision.
If we want positive variable values only, the code should support only applying
a lower bound in some way.
My suggestion would be indeed to have as interface boundaries and a unit-scale
for each parameter (by default one). Only the latter would control the
"encoding", in the way suggested above as "diff".
Maybe it is still important to mention: a relevant initial parameter to CMA-ES
is an initial step-size (a standard deviation) related to the unit-scale, which
seem to be hidden from the user as it is now. You might think of this step-size
as similar to the width of the initial simplex in Nelder&Mead.
> 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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