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


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:
>             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
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 is a very powerful
algorithm for difficult non-linear non-convex optimization problems in continuous domain.
See 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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