libcmaes

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:

• high-level API for simple use in external applications;
• implements several flavors of CMA-ES, IPOP-CMA-ES, BIPOP-CMA-ES, active CMA-ES, active IPOP and BIPOP restart strategies, sep-CMA-ES and VD-CMA (both with linear time & space complexity), IPOP/BIPOP sep and VD-CMA;
• high performances, the fastest implementation (9), some operations benefit from multicores;
• some algorithms can scale up to millions of dimensions;
• support for objective function gradient, when available;
• support for surrogate models(10);
• support for elitism and uncertainty handling;
• support for profile likelihood and contour of objective functions;
• a control exe in the command line for running the algorithm over a range of classical single-objective optimization problems;
• Python bindings along with high-level easy-to-use interface.

Documentation:

• Full documentation is available from https://github.com/beniz/libcmaes/wiki
• API documentation is available from http://beniz.github.io/libcmaes/doc/html/index.html

Dependencies:

• eigen for all matrix operations;
• glog for logging events and debug (optional);
• gflags for command line parsing (optional);
• gtest for unit testing (optional);
• libboost-python for Python bindings (optional);
• numpy for Python bindings (optional).

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

• install 'boost-python', on Debian/Ubuntu systems:

sudo apt-get install libboost-python-dev

• build the libcmaes with support for Python bindings:

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

and with cmake:

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

• test the bindings:

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:

• the initial start point x0;
• the initial value for sigma, the so-called step-size or error guess.

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

• (1) Hansen, N. and A. Ostermeier (2001). Completely Derandomized Self-Adaptation in Evolution Strategies. Evolutionary Computation, 9(2), pp. 159-195.
• (2) Hansen, N. (2009). Benchmarking a BI-Population CMA-ES on the BBOB-2009 Function Testbed. Workshop Proceedings of the GECCO Genetic and Evolutionary Computation Conference, ACM, pp. 2389-2395. http://hal.archives-ouvertes.fr/inria-00382093/en
• (3) N. Hansen, A. Auger, R. Ros, S. Finck, P. Posik: Comparing Results of 31 Algorithms from the Black-Box Optimization Benchmarking BBOB-2009. Workshop Proceedings of the GECCO Genetic and Evolutionary Computation Conference 2010, ACM. http://www.lri.fr/~hansen/ws1p34.pdf
• (4) https://www.lri.fr/~hansen/
• (5) https://www.lri.fr/~hansen/cmaes_inmatlab.html
• (6) Hansen, N., R. Ros (2010). Benchmarking a Weighted Negative Covariance Matrix Update on the BBOB-2010 Noiseless Testbed. Workshop Proceedings of the GECCO Genetic and Evolutionary Computation Conference 2010, ACM, pp. 1673-1680, https://www.lri.fr/~hansen/ws1p32-hansen.pdf
• (7) http://coco.gforge.inria.fr/doku.php?id=bbob-2013
• (8) Y. Akimoto, A. Auger and N. Hansen (2014). Comparison-Based Natural Gradient Optimization in High Dimension. In Proceedings of Genetic and Evolutionary Computation Conference 2014
• (9) #82
• (10) Loshchilov I. (2013) Surrogate-Assisted Evolutionary Algorithms, PhD-Thesis, University Paris-Sud, https://www.lri.fr/~ilya/phd.html

Funding

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