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Nikolaus Hansen commented on MATH867:

Why are variables transformations generally desirable? Because, for example, if a parameter
x_i should only have positive values, the transformation x_i > x_i^2 makes the objective
function compatible to any unbounded optimizer. Or, for example, rescaling of variables (e.g.
unit m in km etc) can change an illconditioned problem to a wellconditioned one.
> CMAESOptimizer with bounds fits finely near lower bound and coarsely near upper bound.
> 
>
> Key: MATH867
> URL: https://issues.apache.org/jira/browse/MATH867
> 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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