Admin am 15. Februar 2013 um 21:45 Uhr

2013-02-15T21:45:26Z

Dirk: Created page with "= The Elitist Evolution Strategy with Covariance Matrix Adaptation = ==Summary== This optimization module is an implementation of the elitist Evolution Strategy with Covarianc..."

2013-02-15T20:35:26Z

Created page with "= The Elitist Evolution Strategy with Covariance Matrix Adaptation = ==Summary== This optimization module is an implementation of the elitist Evolution Strategy with Covarianc..."

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= The Elitist Evolution Strategy with Covariance Matrix Adaptation =

==Summary==

This optimization module is an implementation of the elitist Evolution Strategy with Covariance Matrix Adaptation (CMA-ES) for single- and multi-objective optimization [[#References | (1)]], however it contains some modifications to the publication.

The algorithm uses one or multiple parents. Each parent generates one or multiple children. The algorithm is elitist: Always the best individuals among all parents and children are selected as parents of the next generation.

This algorithm is designed for continuous variables and can not handle discrete problems.
Furthermore, the algorithm is implemented for minimizing a single and multiple objective function(s).

==Properties==

===General===

{| class="wikitable" style="text-align:left" border="2" cellpadding="5" cellspacing="5"
|-
! Algorithm
| stochastic - deterministic adaptation of the covariance matrix.
|-
! Design Variables
| Written for continuous variables. No discrete or mixed variables are possible.
|-
! Objectives
| single- and multi-objective for minimization.
|-
! Constraint handling
| no
|-
! Boundary handling
| no
|-
! Initialization
| Requires at least one of the following: initial solution, initial search region, or bounds.
|-
|}

===Connections===
{| class="wikitable" style="text-align:left" border="1" cellpadding="5" cellspacing="0"
|-
! Starting at his module
| Module requires exactly one connection of type <code>optimization</code>.
|-
! Ending at this module
| -
|-
|}

===Actions===
{| class="wikitable" style="text-align:left" border="1" cellpadding="5" cellspacing="0"
|-
! Name !! Description
|-
! '''Run'''
| starts the optimization.
|-
|}

===Options===
The options are currently described in the pop-up help.

==Module Description==

=== Initialization ===

The initial parents are randomly generated within the <code>initial search region</code> (if existing) or otherwise between the <code>bounds</code>.

=== Optimization ===
The algorithm contains stochastic processes and operates with a population. Parallelization on the basis of the population size is implemented.

The (<code>mu+lambda</code>)-ES has a population of <code>mu</code> parents and <code>lambda</code> children. The population size depends on the number of objectives and the following values are recommended:
# <code>mu=1</code> and <code>lambda >= 1</code> for ''single objective optimization''.
# <code>mu=50</code> and <code>lambda = 1</code> , for ''multi-objective optimization'' (here it is recommended that each parent has only one child).

While evolutionary algorithms typically use the 3 natural inspired operators mutation, recombination and selection, this algorithms uses mutation and selection only.

The selection is elitist: Among all parents and children, the best <code>mu</code> individuals are selected as parents of the next generation.

The mutation is based on a multivariate normal distribution and the mutation distribution is adapted by a deterministic rule: A child '''x'''c is created by mutating the design variables of the parent:

'''x'''c = '''x'''p + '''z''',

where '''z''' is a random vector, taken from a normal distribution (i.e. a Gaussian distribution):

'''z''' ~ S * ''N''(0,'''C'''),

with zero mean and covariance matrix '''C'''. The step size ''S'' controls the strength and the covariance matrix '''C''' the correlation of the mutation. The step size ''S'' and the covariance matrix '''C''' is adapted by a deterministic rule in order to take into account the convergence of the algorithm towards the minimum. In the beginning of an optimization, the parent may be far from the optimum and large step sizes are preferred. The step size should then decrease while approaching to the minimum.

==Usage==

... todo

==Source Code==

ToDo:Link to SVN

==References==

(1) Igel, C., N. Hansen and S. Roth (2007). Covariance Matrix Adaptation for Multi-objective Optimization. Evolutionary Computation, 15(1), pp.1-28

(2) http://www.lri.fr/~hansen

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Documentation/Modules/OptAlgMoCMA - Versionsgeschichte

Admin am 15. Februar 2013 um 21:45 Uhr

Dirk: Created page with "= The Elitist Evolution Strategy with Covariance Matrix Adaptation = ==Summary== This optimization module is an implementation of the elitist Evolution Strategy with Covarianc..."