CMA-ES, Covariance Matrix Adaptation Evolution Strategy for non-linear numerical optimization in Python

optimization, CMA-ES, cmaes
pip install cma==3.3.0



CircleCI Build status DOI [BibTeX] cite as:

Nikolaus Hansen, Youhei Akimoto, and Petr Baudis. CMA-ES/pycma on Github. Zenodo, DOI:10.5281/zenodo.2559634, February 2019.

pycma is a Python implementation of CMA-ES and a few related numerical optimization tools.

The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a stochastic derivative-free numerical optimization algorithm for difficult (non-convex, ill-conditioned, multi-modal, rugged, noisy) optimization problems in continuous search spaces.

Useful links:

Installation of the (almost) latest release


python -m pip install cma

in a system shell to install the latest release from the Python Package Index (PyPI) (which may be behind the lastest release tag on Github). The release link also provides more installation hints and a quick start guide.

conda install --channel cma-es cma

installs from the conda cloud channel cma-es.

Installation of the current master branch

The quick way (requires git to be installed):

pip install git+

The long version: download and unzip the code (see green button above) or git clone and

  • either, copy (or move) the cma source code folder into a folder visible to Python, namely a folder which is in the Python path (e.g. the current folder). Then, import cma works without any further installation.

  • or, install the cma package by typing within the folder, where the cma source code folder is visible,

    pip install -e cma

    Moving the cma folder away from its location would invalidate this installation.

It may be necessary to replace pip with python -m pip and/or prefixing either of these with sudo.

Version History

  • Release 3.3.0 implements

    • diagonal acceleration via diagonal decoding (option CMA_diagonal_decoding, by default still off).
    • fmin_lq_surr2 for running the surrogate assisted lq-CMA-ES.
    • optimization_tools.ShowInFolder to facilitate rapid experimentation.
    • verb_disp_overwrite option starts to overwrite the last line of the display output instead of continuing adding lines to avoid screen flooding with longish runs (off by default).
    • various smallish improvements, bug fixes and additional features and functions.
  • Release 3.2.2 fixes some smallish interface and logging bugs in ConstrainedFitnessAL and a bug when printing a warning. Polishing mainly in the plotting functions. Added a notebook for how to use constraints.

  • Release 3.2.1 fixes plot of principal axes which were shown squared by mistake in version 3.2.0.

  • Release 3.2.0 provides a new interface for constrained optimization ConstrainedFitnessAL and fmin_con2 and many other minor fixes and improvements.

  • Release 3.1.0 fixes the return value of fmin_con, improves its usability and provides a best_feasible attribute in CMAEvolutionStrategy, in addition to various other more minor code fixes and improvements.

  • Release 3.0.3 provides parallelization with OOOptimizer.optimize(..., n_jobs=...) (fix for 3.0.1/2) and improved pickle support.

  • Release 3.0.0 provides non-linear constraints handling, improved plotting and termination options and better resilience to injecting bad solutions, and further various fixes.

  • Version 2.7.1 allows for a list of termination callbacks and a light copy of CMAEvolutionStrategy instances.

  • Release 2.7.0 logger now writes into a folder, new fitness model module, various fixes.

  • Release 2.6.1 allow possibly much larger condition numbers, fix corner case with growing more-to-write list.

  • Release 2.6.0 allows initial solution x0 to be a callable.

  • Version 2.4.2 added the function cma.fmin2 which, similar to cma.purecma.fmin, returns (x_best:numpy.ndarray, es:cma.CMAEvolutionStrategy) instead of a 10-tuple like cma.fmin. The result 10-tuple is accessible in es.result:namedtuple.

  • Version 2.4.1 included bbob testbed.

  • Version 2.2.0 added VkD CMA-ES to the master branch.

  • Version 2.* is a multi-file split-up of the original module.

  • Version 1.x.* is a one file implementation and not available in the history of this repository. The latest 1.* version 1.1.7 can be found here.