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From "Nikolaus Hansen (JIRA)" <j...@apache.org>
Subject [jira] Commented: (MATH-442) CMA evolution strategy is missing in optimization
Date Wed, 17 Nov 2010 19:05:13 GMT

    [ https://issues.apache.org/jira/browse/MATH-442?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12933083#action_12933083
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Nikolaus Hansen commented on MATH-442:
--------------------------------------

I think the CMA-ES fits fine into to direct category (but I am familiar with the meaning of
the word direct search, I don't assume everyone is).

Nelder-Mead and CMA-ES are similar in that they do not need derivatives and they do not even
need function values: they are comparison based and only use a ranking between a number of
candidate solutions. Moreover, Nelder-Mead and CMA-ES share all their invariance properties
(not many other optimization algorithms do). Being rank-based implies invariance under monotonous
transformations of the objective function value, but there are others (e.g. invariance under
coordinate system changes). I believe these are important properties, also from the application
viewpoint. The main conceptional different to Nelder-Mead: CMA-ES is stochastic (randomized,
if you like).  The main practical difference: CMA-ES works also in large dimension and there
is a control parameter for tuning the locality of search. 

You could have an elaborate discussion whether CMA-ES estimates a gradient. My take on it:
methods that move opposite to the gradient will regularly fail anyway. 

I also find it strange that algorithms in the general category are in fact less general. 

Where can I subscribe to the list? 

> CMA evolution strategy is missing in optimization
> -------------------------------------------------
>
>                 Key: MATH-442
>                 URL: https://issues.apache.org/jira/browse/MATH-442
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 3.0
>            Reporter: Dr. Dietmar Wolz
>   Original Estimate: 48h
>  Remaining Estimate: 48h
>
> Recently I implemented the optimization algorithm CMA-ES based on org.apache.commons.math.linear
and used it for the GTOC5 global trajectory optimization contest http://gtoc5.math.msu.su/.
It implements the MultivariateRealOptimizer interface and would nicely fit into the org.apache.commons.math.optimization
package. The original author of CMA-ES (Nikolaus Hansen) volunteered to support me (proof-reading
+ testing) in the creation of a CMA-ES contribution for commons.math. 
> The CMA evolution strategy http://www.lri.fr/~hansen/cmaesintro.html is a very powerful
algorithm for difficult non-linear non-convex optimization problems in continuous domain.
See http://www.lri.fr/~hansen/cec2005.html for a comparison chart. If there is interest I
will create a patch including the proposed Implementation for evaluation. It seems we would
need an additional sub-package - org.apache.commons.math.optimization.evolutionary.

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