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From "Gilles (JIRA)" <>
Subject [jira] [Commented] (MATH-867) CMAESOptimizer with bounds fits finely near lower bound and coarsely near upper bound.
Date Sat, 29 Sep 2012 21:36:07 GMT


Gilles commented on MATH-867:

bq. to me it makes perfectly sense: luckily enough line 589 performs the same transformation
on inputSigma as the encode function on getStartPoint() [...]

I may be missing something (and I can just make wild guesses since I have no clue about the
CMAES algorithm) but I would be expecting that the code behaves the same way without boundaries
as with boundaries that become arbitrarily large (i.e. when the [loBound, hiBound] interval
becomes [-inf, +inf]).
The line that uses "inputSigma" does not behave that way since the "range" becomes arbitrarily
large as the bounds grow although when there is no boundaries it is set 1.0.

This is also shown by some unit tests which I've just set up, by copying existing ones which
minimized a function without constraint and specifying a very large allowed interval (e.g.
[-1e20, 1e20]): those tests fail.
Intuitively, when the solution is far from the bounds (and the initial point also), whether
there are bounds or not should not matter. But with the current implementation that's clearly
not the case.

> CMAESOptimizer with bounds fits finely near lower bound and coarsely near upper bound.

> ---------------------------------------------------------------------------------------
>                 Key: MATH-867
>                 URL:
>             Project: Commons Math
>          Issue Type: Bug
>            Reporter: Frank Hess
>         Attachments: MATH867_patch,
> 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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