TEST_OPTIMIZATION
Test Functions for Optimization

TEST_OPTIMIZATION is a C++ library which defines test problems for the scalar function optimization problem.

The scalar function optimization problem is to find a value for the M-dimensional vector X which minimizes the value of the given scalar function F(X).

A special feature of this library is that all the functions can be defined for any dimension 1 <= M.

The functions defined include:

1. The sphere model;
2. The axis-parallel hyper-ellipsoid function;
3. The rotated hyper-ellipsoid function;
4. Rosenbrock's valley;
5. Rastrigin's function;
6. Schwefel's function;
7. Griewank's function;
8. The power sum function;
9. Ackley's function;
10. Michalewicz's function;
11. The drop wave function;
12. 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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ASA047, a C++ library which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

BRENT, a C++ library 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 C++ library which seeks the minimizer of a scalar function of several variables using compass search, a direct search algorithm that does not use derivatives.

DQED, a FORTRAN90 library which solves constrained least squares problems.

ENTRUST, a MATLAB program which minimizes a scalar function of several variables using trust region methods, by Jeff Borggaard and Gene Cliff.

MINPACK, a FORTRAN90 library which carries out the least squares minimization of the residual of a set of linear or nonlinear equations.

NELDER_MEAD, a MATLAB program which minimizes a scalar function of several variables using the Nelder-Mead algorithm.

NL2SOL, a FORTRAN90 library which implements an adaptive nonlinear least-squares algorithm.

PRAXIS, a FORTRAN90 library which minimizes a scalar function of several variables.

TEST_OPT, a FORTRAN90 library which defines a number of problems for the scalar optimization problem.

TEST_OPT_CON, a C++ library which defines test problems for the minimization of a scalar function of several variables, with the search constrained to lie within a specified hyper-rectangle.

TOMS611, a FORTRAN90 library which minimizes a scalar functional of multiple variables.

Reference:

1. Marcin Molga, Czeslaw Smutnicki,
   Test functions for optimization needs.
2. David Ackley,
   A connectionist machine for genetic hillclimbing,
   Springer, 1987,
   ISBN13: 978-0898382365,
   LC: Q336.A25.
3. 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 611-615, 1996.
4. Laurence Dixon, Gabor Szego,
   The optimization problem: An introduction,
   in Towards Global Optimisation,
   edited by Laurence Dixon, Gabor Szego,
   North-Holland, 1975,
   ISBN: 0444109552,
   LC: QA402.5.T7.
5. Zbigniew Michalewicz,
   Genetic Algorithms + Data Structures = Evolution Programs,
   Third Edition,
   Springer, 1996,
   ISBN: 3-540-60676-9,
   LC: QA76.618.M53.
6. Leonard Rastrigin,
   Extremal control systems,
   in Theoretical Foundations of Engineering Cybernetics Series,
   Moscow: Nauka, Russian, 1974.
7. Howard Rosenbrock,
   An Automatic Method for Finding the Greatest or Least Value of a Function,
   Computer Journal,
   Volume 3, 1960, pages 175-184.
8. Hans-Paul Schwefel,
   Numerical optimization of computer models,
   Wiley, 1981,
   ISBN13: 978-0471099888,
   LC: QA402.5.S3813.
9. Bruno Shubert,
   A sequential method seeking the global maximum of a function,
   SIAM Journal on Numerical Analysis,
   Volume 9, pages 379-388, 1972.
10. Aimo Toern, Antanas Zilinskas,
    Global Optimization,
    Lecture Notes in Computer Science, Number 350,
    Springer, 1989,
    ISBN13: 978-0387508719,
    LC: QA402.T685

Source Code:

• test_optimization.cpp, the source code.
• test_optimization.hpp, the include file.
• test_optimization.sh, BASH commands to compile the source code.

Examples and Tests:

• test_optimization_prb.cpp, a sample calling program.
• test_optimization_prb.sh, BASH commands to compile and run the sample program.
• test_optimization_prb_output.txt, the output file.

List of Routines:

• P00_AB evaluates the limits of the optimization region for any problem.
• P00_COMPASS_SEARCH carries out a direct search minimization algorithm.
• P00_F evaluates the objective function for any problem.
• P00_PROBLEM_NUM returns the number of problems available.
• P00_SOL returns the solution for any problem.
• P00_TITLE returns a title for any problem.
• P01_AB evaluates the limits of the optimization region for problem 01.
• P01_F evaluates the objective function for problem 01.
• P01_SOL returns the solution for problem 01.
• P01_TITLE returns a title for problem 01.
• P02_AB evaluates the limits of the optimization region for problem 02.
• P02_F evaluates the objective function for problem 02.
• P02_SOL returns the solution for problem 02.
• P02_TITLE returns a title for problem 02.
• P03_AB evaluates the limits of the optimization region for problem 03.
• P03_F evaluates the objective function for problem 03.
• P03_SOL returns the solution for problem 03.
• P03_TITLE returns a title for problem 03.
• P04_AB evaluates the limits of the optimization region for problem 04.
• P04_F evaluates the objective function for problem 04.
• P04_SOL returns the solution for problem 04.
• P04_TITLE returns a title for problem 04.
• P05_AB evaluates the limits of the optimization region for problem 05.
• P05_F evaluates the objective function for problem 05.
• P05_SOL returns the solution for problem 05.
• P05_TITLE returns a title for problem 05.
• P06_AB evaluates the limits of the optimization region for problem 06.
• P06_F evaluates the objective function for problem 06.
• P06_SOL returns the solution for problem 06.
• P06_TITLE returns a title for problem 06.
• P07_AB evaluates the limits of the optimization region for problem 07.
• P07_F evaluates the objective function for problem 07.
• P07_SOL returns the solution for problem 07.
• P07_TITLE returns a title for problem 07.
• P08_AB evaluates the limits of the optimization region for problem 08.
• P08_F evaluates the objective function for problem 08.
• P08_SOL returns the solution for problem 08.
• P08_TITLE returns a title for problem 08.
• P09_AB evaluates the limits of the optimization region for problem 09.
• P09_F evaluates the objective function for problem 09.
• P09_SOL returns the solution for problem 09.
• P09_TITLE returns a title for problem 09.
• P10_AB evaluates the limits of the optimization region for problem 10.
• P10_F evaluates the objective function for problem 10.
• P10_SOL returns the solution for problem 10.
• P10_TITLE returns a title for problem 10.
• P11_AB evaluates the limits of the optimization region for problem 11.
• P11_F evaluates the objective function for problem 11.
• P11_SOL returns the solution for problem 11.
• P11_TITLE returns a title for problem 11.
• P12_AB evaluates the limits of the optimization region for problem 12.
• P12_F evaluates the objective function for problem 12.
• P12_SOL returns the solution for problem 12.
• P12_TITLE returns a title for problem 12.
• R8COL_UNIFORM fills an R8COL with scaled pseudorandom numbers.
• R8VEC_INDICATOR sets an R8VEC to the indicator vector.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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