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From "Nikolaus Hansen (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-867) CMAESOptimizer with bounds fits finely near lower bound and coarsely near upper bound.
Date Tue, 02 Oct 2012 14:47:07 GMT

    [ https://issues.apache.org/jira/browse/MATH-867?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13467764#comment-13467764
] 

Nikolaus Hansen commented on MATH-867:
--------------------------------------

{quote}
And I have no idea how to improve the documentation...
{quote}

Here are my suggestions: Replace (several times) 
{code}
     * @param inputSigma Initial search volume; sigma of offspring objective variables.
{code}
with 

{code}
     * @param inputSigma Initial standard deviations to sample new points from startPoint
{code}

and

{code}
    /**
     * Individual sigma values - initial search volume. inputSigma determines
     * the initial coordinate wise standard deviations for the search. Setting
     * SIGMA one third of the initial search region is appropriate.
     */
{code}

with 

{code}
    /**
     * Values in inputSigma define the initial coordinate-wise 
     * standard deviations for sampling new search points about 
     * startPoint. 
     * Setting inputSigma roughly to the predicted distance of 
     * startPoint to the actually desired optimum is appropriate. 
     * Small values for inputSigma induce the search to be more local
     * and very small values are more likely to find a local optimum 
     * close to startPoint. 
     * Extremely small values will however lead to early termination. 
     */
{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
>             Fix For: 3.1
>
>         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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