test_optimization
test_optimization,
a Python code which
defines test problems for the scalar function optimization problem.
The scalar function optimization problem is to find a value for the
Mdimensional vector X which minimizes the value of the given scalar
function F(X).
A special feature of this code is that all the functions can be
defined for any dimension 1 <= M.
The functions defined include:

The sphere model;

The axisparallel hyperellipsoid function;

The rotated hyperellipsoid function;

Rosenbrock's valley;

Rastrigin's function;

Schwefel's function;

Griewank's function;

The power sum function;

Ackley's function;

Michalewicz's function;

The drop wave function;

The deceptive function;
Licensing:
The computer code and data files described and made available on this
web page are distributed under
the GNU LGPL license.
Languages:
test_optimization is available in
a C version and
a C++ version and
a FORTRAN90 version and
a MATLAB version and
a Python version.
Related Data and Programs:
ASA047,
a Python code which
minimizes a scalar function of several variables using the NelderMead
algorithm.
BRENT,
a Python code which
contains Richard Brent's routines for finding the zero, local minimizer,
or global minimizer of a scalar function of a scalar argument, without
the use of derivative information.
COMPASS_SEARCH,
a Python code which
seeks the minimizer of a scalar function of several variables
using compass search, a direct search algorithm that does not use derivatives.
POLYNOMIALS,
a Python code which
defines multivariate polynomials over rectangular domains, for
which certain information is to be determined, such as the maximum
and minimum values.
PRAXIS,
a Python code which
minimizes a scalar function of several variables, without
requiring derivative information,
by Richard Brent.
Reference:

Marcin Molga, Czeslaw Smutnicki,
Test functions for optimization needs.

David Ackley,
A connectionist machine for genetic hillclimbing,
Springer, 1987,
ISBN13: 9780898382365,
LC: Q336.A25.

Hugues Bersini, Marco Dorigo, Stefan Langerman, Gregory Seront, Luca Gambardella,
Results of the first international contest on evolutionary optimisation,
In Proceedings of 1996 IEEE International Conference on Evolutionary Computation,
IEEE Press, pages 611615, 1996.

Laurence Dixon, Gabor Szego,
The optimization problem: An introduction,
in Towards Global Optimisation,
edited by Laurence Dixon, Gabor Szego,
NorthHolland, 1975,
ISBN: 0444109552,
LC: QA402.5.T7.

Zbigniew Michalewicz,
Genetic Algorithms + Data Structures = Evolution Programs,
Third Edition,
Springer, 1996,
ISBN: 3540606769,
LC: QA76.618.M53.

Leonard Rastrigin,
Extremal control systems,
in Theoretical Foundations of Engineering Cybernetics Series,
Moscow: Nauka, Russian, 1974.

Howard Rosenbrock,
An Automatic Method for Finding the Greatest or Least Value of a Function,
Computer Journal,
Volume 3, 1960, pages 175184.

HansPaul Schwefel,
Numerical optimization of computer models,
Wiley, 1981,
ISBN13: 9780471099888,
LC: QA402.5.S3813.

Bruno Shubert,
A sequential method seeking the global maximum of a function,
SIAM Journal on Numerical Analysis,
Volume 9, pages 379388, 1972.

Aimo Toern, Antanas Zilinskas,
Global Optimization,
Lecture Notes in Computer Science, Number 350,
Springer, 1989,
ISBN13: 9780387508719,
LC: QA402.T685
Source Code:
Last revised on 08 December 2016.