cma

package documentation

Package cma implements the CMA-ES (Covariance Matrix Adaptation Evolution Strategy).

CMA-ES is a stochastic optimizer for robust non-linear non-convex derivative- and function-value-free numerical optimization.

This release was tested with Python versions 3.8 to 3.13. The implementation is intended to be compatible with Python >= 2.7.

CMA-ES searches for a minimizer (a solution x in Rⁿ) of an objective function f (cost function), such that f(x) is minimal. Regarding f, only a passably reliable ranking of the candidate solutions in each iteration is necessary. Neither the function values themselves, nor the gradient of f need to be available or do matter, like in the downhill simplex Nelder-Mead algorithm. Some termination criteria however depend on actual Delta f-values.

The cma module provides two independent implementations of the CMA-ES algorithm in the classes cma.CMAEvolutionStrategy and cma.purecma.CMAES.

In each implementation two interfaces are provided:

functions fmin2 and purecma.fmin:

run a complete minimization of the passed objective function with CMA-ES. fmin2 also provides optional restarts and noise handling.
class CMAEvolutionStrategy (and the alias CMA) and purecma.CMAES:

allow for minimization such that the control of the iteration loop remains with the user. fmin2 returns an instance of CMAEvolutionStrategy.

Additionally, fmin_con2 provides constrained optimization.

For a quick start see below or confer to the notebook(s) https://github.com/CMA-ES/pycma/blob/development/notebooks/notebook-usecases-basics.ipynb

CMAEvolutionStrategy relies, in contrast to cma.purecma, heavily on numpy and optionally on matplotlib.pyplot (for plot etc., optional but highly recommended).

The source code is available at https://github.com/CMA-ES/pycma.

Testing

From the system shell:

python -m cma.test -h
python -m cma.test
python -c "import cma.test; cma.test.main()"  # the same

or from any (i)python shell:

import cma.test
cma.test.main()

should run without complaints in about between 20 and 100 seconds.

Example

From a python shell:

import cma
help(cma)  # "this" help message, use cma? in ipython
help(cma.fmin)
help(cma.CMAEvolutionStrategy)
help(cma.CMAOptions)
cma.CMAOptions('tol')  # display 'tolerance' termination options
cma.CMAOptions('verb') # display verbosity options
x, es = cma.fmin2(cma.ff.tablet, 15 * [1], 1)
es = cma.CMAEvolutionStrategy(15 * [1], 1).optimize(cma.ff.tablet)
help(es.result)
x, es.result[0]  # best evaluated solution
es.result[5]  # mean solution, presumably better with noise

Authors
Nikolaus Hansen, 2008-
Petr Baudis, 2014
Youhei Akimoto, 2017-
See Also
`fmin` (), `CMAOptions`, `CMAEvolutionStrategy`
Unknown Field: license
BSD 3-Clause, see LICENSE file.

Module	`bbobbenchmarks`	BBOB noiseless testbed.
Module	`boundary_handler`	A collection of boundary (AKA box constraints) handling classes.
Module	`constraints_handler`	A collection of (nonlinear) constraints handling classes and helper functions.
Module	`evolution_strategy`	CMA-ES (evolution strategy), the main sub-module of `cma` implementing in particular `CMAEvolutionStrategy`, `fmin2` and further `fmin_*` functions.
Module	`fitness_functions`	versatile container for test objective functions.
Module	`fitness_models`	Fitness surrogate model classes and handler for incremental evaluations.
Module	`fitness_transformations`	Wrapper for objective functions like noise, rotation, gluing args
Module	`integer_centering`	Integer handling class `IntegerCentering` to be used in combination with CMA-ES.
Module	`interfaces`	Very few interface defining base class definitions
Module	`logger`	logger class mainly to be used with `CMAEvolutionStrategy`
Module	`optimization_tools`	Utility classes and functionalities loosely related to optimization
Module	`options_parameters`	Parameters and Options for CMA-ES.
Module	`purecma`	A minimalistic implemention of CMA-ES without using `numpy`.
Module	`recombination_weights`	`RecombinationWeights` is a list of recombination weights for the CMA-ES.
Module	`restricted_gaussian_sampler`	VD-CMA and VkD-CMA
Module	`s`	versatile shortcuts for quick typing in an (i)python shell or even `from cma.s import *` in interactive sessions.
Module	`sampler`	Collection of classes that sample from parametrized distributions and provide an update mechanism of the distribution parameters.
Module	`sigma_adaptation`	step-size adaptation classes, currently tightly linked to CMA, because `hsig` is computed in the base class
Module	`test`	test module of `cma` package.
Module	`transformations`	Search space transformation and encoding/decoding classes
Package	`utilities`	various unspecific utilities
Module	`wrapper`	Interface wrappers for the `cma` module.

From __init__.py:

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Variable	`__version__`	Undocumented

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