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test_optimization.html
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<html>
<head>
<title>
TEST_OPTIMIZATION - Test Functions for Optimization
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
<p>
<b>TEST_OPTIMIZATION</b> <br> Test Functions for Optimization
</h1>
<hr>
<p>
<b>TEST_OPTIMIZATION</b>
is a FORTRAN90 library which
defines test problems for the scalar function optimization problem.
</p>
<p>
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).
</p>
<p>
A special feature of this library is that all the functions can be
defined for any dimension 1 <= M.
</p>
<p>
The functions defined include:
<ol>
<li>
The sphere model;
</li>
<li>
The axis-parallel hyper-ellipsoid function;
</li>
<li>
The rotated hyper-ellipsoid function;
</li>
<li>
Rosenbrock's valley;
</li>
<li>
Rastrigin's function;
</li>
<li>
Schwefel's function;
</li>
<li>
Griewank's function;
</li>
<li>
The power sum function;
</li>
<li>
Ackley's function;
</li>
<li>
Michalewicz's function;
</li>
<li>
The drop wave function;
</li>
<li>
The deceptive function;
</li>
</ol>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this
web page are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TEST_OPTIMIZATION</b> is available in
<a href = "../../f77_src/test_optimization/test_optimization.html">a FORTRAN77 version</a> and
<a href = "../../f_src/test_optimization/test_optimization.html">a FORTRAN90 version</a> and
<a href = "../../m_src/test_optimization/test_optimization.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/asa047/asa047.html">
ASA047</a>,
a FORTRAN90 library which
minimizes a scalar function of several variables using the Nelder-Mead algorithm.
</p>
<p>
<a href = "../../f_src/brent/brent.html">
BRENT</a>,
a FORTRAN90 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.
</p>
<p>
<a href = "../../f_src/compass_search/compass_search.html">
COMPASS_SEARCH</a>,
a FORTRAN90 library which
seeks the minimizer of a scalar function of several variables
using compass search, a direct search algorithm that does not use derivatives.
</p>
<p>
<a href = "../../f_src/dqed/dqed.html">
DQED</a>,
a FORTRAN90 library which
solves constrained least squares problems.
</p>
<p>
<a href = "../../m_src/entrust/entrust.html">
ENTRUST</a>,
a MATLAB program which
minimizes a scalar function of several variables using trust region methods,
by Jeff Borggaard and Gene Cliff.
</p>
<p>
<a href = "../../f_src/minpack/minpack.html">
MINPACK</a>,
a FORTRAN90 library which
carries out the least squares minimization of the residual
of a set of linear or nonlinear equations.
</p>
<p>
<a href = "../../m_src/nelder_mead/nelder_mead.html">
NELDER_MEAD</a>,
a MATLAB program which
minimizes a scalar function of several variables using the Nelder-Mead algorithm.
</p>
<p>
<a href = "../../f_src/nl2sol/nl2sol.html">
NL2SOL</a>,
a FORTRAN90 library which
implements an adaptive nonlinear least-squares algorithm.
</p>
<p>
<a href = "../../f_src/praxis/praxis.html">
PRAXIS</a>,
a FORTRAN90 library which
minimizes a scalar function of several variables.
</p>
<p>
<a href = "../../f_src/test_opt/test_opt.html">
TEST_OPT</a>,
a FORTRAN90 library which
defines a number of problems for the scalar optimization problem.
</p>
<p>
<a href = "../../f_src/test_opt_con/test_opt_con.html">
TEST_OPT_CON</a>,
a FORTRAN90 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.
</p>
<p>
<a href = "../../f_src/toms611/toms611.html">
TOMS611</a>,
a FORTRAN90 library which
minimizes a scalar functional of multiple variables.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Marcin Molga, Czeslaw Smutnicki,<br>
Test functions for optimization needs.
</li>
<li>
David Ackley,<br>
A connectionist machine for genetic hillclimbing,<br>
Springer, 1987,<br>
ISBN13: 978-0898382365,<br>
LC: Q336.A25.
</li>
<li>
Hugues Bersini, Marco Dorigo, Stefan Langerman, Gregory Seront, Luca Gambardella,<br>
Results of the first international contest on evolutionary optimisation,<br>
In Proceedings of 1996 IEEE International Conference on Evolutionary Computation,<br>
IEEE Press, pages 611-615, 1996.
</li>
<li>
Laurence Dixon, Gabor Szego,<br>
The optimization problem: An introduction,<br>
in Towards Global Optimisation,<br>
edited by Laurence Dixon, Gabor Szego,<br>
North-Holland, 1975,<br>
ISBN: 0444109552,<br>
LC: QA402.5.T7.
</li>
<li>
Zbigniew Michalewicz,<br>
Genetic Algorithms + Data Structures = Evolution Programs,<br>
Third Edition,<br>
Springer, 1996,<br>
ISBN: 3-540-60676-9,<br>
LC: QA76.618.M53.
</li>
<li>
Leonard Rastrigin,<br>
Extremal control systems,<br>
in Theoretical Foundations of Engineering Cybernetics Series,<br>
Moscow: Nauka, Russian, 1974.
</li>
<li>
Howard Rosenbrock,<br>
An Automatic Method for Finding the Greatest or Least Value of a Function,<br>
Computer Journal,<br>
Volume 3, 1960, pages 175-184.
</li>
<li>
Hans-Paul Schwefel,<br>
Numerical optimization of computer models,<br>
Wiley, 1981,<br>
ISBN13: 978-0471099888,<br>
LC: QA402.5.S3813.
</li>
<li>
Bruno Shubert,<br>
A sequential method seeking the global maximum of a function,<br>
SIAM Journal on Numerical Analysis,<br>
Volume 9, pages 379-388, 1972.
</li>
<li>
Aimo Toern, Antanas Zilinskas,<br>
Global Optimization,<br>
Lecture Notes in Computer Science, Number 350,<br>
Springer, 1989,<br>
ISBN13: 978-0387508719,<br>
LC: QA402.T685
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "test_optimization.f90">test_optimization.f90</a>, the source code.
</li>
<li>
<a href = "test_optimization.sh">test_optimization.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "test_optimization_prb.f90">test_optimization_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_optimization_prb.sh">test_optimization_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "test_optimization_prb_output.txt">test_optimization_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>P00_AB</b> evaluates the limits of the optimization region for any problem.
</li>
<li>
<b>P00_COMPASS_SEARCH</b> carries out a direct search minimization algorithm.
</li>
<li>
<b>P00_F</b> evaluates the objective function for any problem.
</li>
<li>
<b>P00_PROBLEM_NUM</b> returns the number of problems available.
</li>
<li>
<b>P00_SOL</b> returns the solution for any problem.
</li>
<li>
<b>P00_TITLE</b> returns a title for any problem.
</li>
<li>
<b>P01_AB</b> evaluates the limits of the optimization region for problem 01.
</li>
<li>
<b>P01_F</b> evaluates the objective function for problem 01.
</li>
<li>
<b>P01_SOL</b> returns the solution for problem 01.
</li>
<li>
<b>P01_TITLE</b> returns a title for problem 01.
</li>
<li>
<b>P02_AB</b> evaluates the limits of the optimization region for problem 02.
</li>
<li>
<b>P02_F</b> evaluates the objective function for problem 02.
</li>
<li>
<b>P02_SOL</b> returns the solution for problem 02.
</li>
<li>
<b>P02_TITLE</b> returns a title for problem 02.
</li>
<li>
<b>P03_AB</b> evaluates the limits of the optimization region for problem 03.
</li>
<li>
<b>P03_F</b> evaluates the objective function for problem 03.
</li>
<li>
<b>P03_SOL</b> returns the solution for problem 03.
</li>
<li>
<b>P03_TITLE</b> returns a title for problem 03.
</li>
<li>
<b>P04_AB</b> evaluates the limits of the optimization region for problem 04.
</li>
<li>
<b>P04_F</b> evaluates the objective function for problem 04.
</li>
<li>
<b>P04_SOL</b> returns the solution for problem 04.
</li>
<li>
<b>P04_TITLE</b> returns a title for problem 04.
</li>
<li>
<b>P05_AB</b> evaluates the limits of the optimization region for problem 05.
</li>
<li>
<b>P05_F</b> evaluates the objective function for problem 05.
</li>
<li>
<b>P05_SOL</b> returns the solution for problem 05.
</li>
<li>
<b>P05_TITLE</b> returns a title for problem 05.
</li>
<li>
<b>P06_AB</b> evaluates the limits of the optimization region for problem 06.
</li>
<li>
<b>P06_F</b> evaluates the objective function for problem 06.
</li>
<li>
<b>P06_SOL</b> returns the solution for problem 06.
</li>
<li>
<b>P06_TITLE</b> returns a title for problem 06.
</li>
<li>
<b>P07_AB</b> evaluates the limits of the optimization region for problem 07.
</li>
<li>
<b>P07_F</b> evaluates the objective function for problem 07.
</li>
<li>
<b>P07_SOL</b> returns the solution for problem 07.
</li>
<li>
<b>P07_TITLE</b> returns a title for problem 07.
</li>
<li>
<b>P08_AB</b> evaluates the limits of the optimization region for problem 08.
</li>
<li>
<b>P08_F</b> evaluates the objective function for problem 08.
</li>
<li>
<b>P08_SOL</b> returns the solution for problem 08.
</li>
<li>
<b>P08_TITLE</b> returns a title for problem 08.
</li>
<li>
<b>P09_AB</b> evaluates the limits of the optimization region for problem 09.
</li>
<li>
<b>P09_F</b> evaluates the objective function for problem 09.
</li>
<li>
<b>P09_SOL</b> returns the solution for problem 09.
</li>
<li>
<b>P09_TITLE</b> returns a title for problem 09.
</li>
<li>
<b>P10_AB</b> evaluates the limits of the optimization region for problem 10.
</li>
<li>
<b>P10_F</b> evaluates the objective function for problem 10.
</li>
<li>
<b>P10_SOL</b> returns the solution for problem 10.
</li>
<li>
<b>P10_TITLE</b> returns a title for problem 10.
</li>
<li>
<b>P11_AB</b> evaluates the limits of the optimization region for problem 11.
</li>
<li>
<b>P11_F</b> evaluates the objective function for problem 11.
</li>
<li>
<b>P11_SOL</b> returns the solution for problem 11.
</li>
<li>
<b>P11_TITLE</b> returns a title for problem 11.
</li>
<li>
<b>P12_AB</b> evaluates the limits of the optimization region for problem 12.
</li>
<li>
<b>P12_F</b> evaluates the objective function for problem 12.
</li>
<li>
<b>P12_SOL</b> returns the solution for problem 12.
</li>
<li>
<b>P12_TITLE</b> returns a title for problem 12.
</li>
<li>
<b>R8COL_UNIFORM</b> fills an R8COL with scaled pseudorandom numbers.
</li>
<li>
<b>R8VEC_INDICATOR</b> sets an R8VEC to the indicator vector.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 02 February 2012.
</i>
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