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libcmaes is a multithreaded C++11 implementation (with Python bindings) of algorithms of the CMA-ES family for optimization of nonlinear non-convex 'blackbox' functions. The implemented algorithms have a wide range of applications in various disciplines, ranging from pure function minimization, optimization in industrial and scientific applications, to the solving of reinforcement and machine learning problems.

Over the past decade, both the original CMA-ES and its improved flavors have proven very effective in optimizing functions when no gradient is available. Typically, the algorithm does find the minimum value of an objective function in a minimal number of function calls, compared to other methods. For a full report of recent results, see (3).

CMA-ES is mostly the work of Nikolaus Hansen (4) and a few others (8). Other implementations can be found in (5).

Main functionalities: At the moment, the library implements many of the most effective CMA-ES algorihms, and defaults to the 'vanilla' version (1). Current features include:

Documentation:

Dependencies:

Implementation: The library makes use of C++ policy design for modularity, performance and putting the maximum burden on the checks at compile time. The implementation closely follows the algorithms described in (2), (6) and few other publications.

Authors

libcmaes was designed and implemented by Emmanuel Benazera with help of Nikolaus Hansen and contributors, on behalf of Inria Saclay / Research group TAO and Laboratoire de l'Accélérateur linéaire, research group Appstats.

Build

Below are instruction for Linux systems, for building on Mac OSX, see https://github.com/beniz/libcmaes/wiki/Building-libcmaes-on-Mac-OSX

Beware of dependencies, typically on Debian/Ubuntu Linux, do:

sudo apt-get install autoconf automake libtool libgoogle-glog-dev libgflags-dev libeigen3-dev

For compiling with basic options enabled:

./autogen.sh
echo "#define CMAES_EXPORT" > include/libcmaes/cmaes_export.h
./configure
make

For compiling with CMake:

mkdir build
cd build
cmake .. -DCMAKE_INSTALL_PREFIX=~/.local/ -DLIBCMAES_BUILD_TESTS=ON
make -j2
make install

Run examples

cd tests
./test_functions --dim 30 --lambda 100 --max_iter 120 --fname fsphere

to minimize the sphere function in 30D with 100 offsprings per generation,

./test_functions --dim 20 --lambda 100 --max_iter 1000 --fname rosenbrock

to minimize the Rosenbrock function in 20D with 100 offsprings. To see available function, do

./test_functions --list

to plot results, use a file output and then the included Gnuplot script

./test_functions --fname rastrigin --dim 10 --lambda 200 --max_iter 130 --fplot out.dat -sigma0 5 -x0 5 -seed 5489
gnuplot -e "filename='out.dat'" cma_multiplt.dem

to plot results with matplotlib instead

python ../python/cma_multiplt.py out.dat

to run a check across a range of classical single-objective optimization functions:

./test_functions --all

for help, do

./test_functions --help

Sample code

#include "cmaes.h"
#include <iostream>

using namespace libcmaes;

FitFunc fsphere = [](const double *x, const int N)
{
  double val = 0.0;
  for (int i=0;i<N;i++)
    val += x[i]*x[i];
  return val;
};

int main(int argc, char *argv[])
{
  int dim = 10; // problem dimensions.
  std::vector<double> x0(dim,10.0);
  double sigma = 0.1;
  //int lambda = 100; // offsprings at each generation.
  CMAParameters<> cmaparams(x0,sigma);
  //cmaparams.set_algo(BIPOP_CMAES);
  CMASolutions cmasols = cmaes<>(fsphere,cmaparams);
  std::cout << "best solution: " << cmasols << std::endl;
  std::cout << "optimization took " << cmasols.elapsed_time() / 1000.0 << " seconds\n";
  return cmasols.run_status();
}

Python bindings

To build the Python bindings and use libcmaes from Python code, see instructions below, and for more details, see https://github.com/beniz/libcmaes/wiki/Python-bindings

sudo apt-get install libboost-python-dev

./autogen.sh
./configure --enable-python --prefix=/home/yourusername
make
make install

and with cmake:

cmake .. -DCMAKE_INSTALL_PREFIX=~/.local/ -DLIBCMAES_BUILD_PYTHON=ON

cd python
export LD_LIBRARY_PATH=/home/yourusername/lib
python ptest.py

Sample python code:

import lcmaes

# input parameters for a 10-D problem
x = [10]*10
olambda = 10 # lambda is a reserved keyword in python, using olambda instead.
seed = 0 # 0 for seed auto-generated within the lib.
sigma = 0.1
p = lcmaes.make_simple_parameters(x,sigma,olambda,seed)

# objective function.
def nfitfunc(x,n):
    val = 0.0
    for i in range(0,n):
        val += x[i]*x[i]
    return val

# generate a function object
objfunc = lcmaes.fitfunc_pbf.from_callable(nfitfunc);

# pass the function and parameter to cmaes, run optimization and collect solution object.
cmasols = lcmaes.pcmaes(objfunc,p)

# collect and inspect results
bcand = cmasols.best_candidate()
bx = lcmaes.get_candidate_x(bcand)
print "best x=",bx
print "distribution mean=",lcmaes.get_solution_xmean(cmasols)
cov = lcmaes.get_solution_cov(cmasols) # numpy array
print "cov=",cov
print "elapsed time=",cmasols.elapsed_time(),"ms"

Practical hints

CMA-ES requires two components from the user:

In short: the optimum that is looked after should better not be far away from the interval [x0 - sigma0, x0 + sigma0] in each dimension, where distance is defined by sigma0.

See https://github.com/beniz/libcmaes/wiki/Practical-hints and https://www.lri.fr/~hansen/cmaes_inmatlab.html#practical for more detailed useful advices using CMA-ES.

Run BBOB 2013 Black-Box Optimization Benchmark

There's an install script in the repository. Do:

cd tests
./bbobsetup.sh

you can now benchmark any of the implemented flavors of CMA-ES (beware, this make take a while, ~hours):

./bbobexperiment -alg bipop

for the command above, results will be in repository bipop_bbob See (7) for more information and details.

References

Funding

This work was supported by the ANR-2010-COSI-002 grant of the French NationalA Research Agency.