optiGTest is a MATLAB's toolbox which regroups many test functions used for studying the performance of approximation techniques and optimization strategy. In particular, gradient sof the test functions are provided.
optiGTest is able to
- Provide derivatives of the test functions
- Dealing with any dimension chosen by the user
- Provide global minimum (value and associated set of parameters)
- unConstrained problems:
Example_unConstrained.m
(see the 3D plots of the 2-dimensional unconstrained functions)
- | - | - |
---|---|---|
Ackley1 | DixonPrice | Quintic |
Ackley2 | Dolan | Rastrigin |
Ackley3 | DropWave | RHE |
Ackley4 | Easom | Ripple01 |
Adjiman | ElAttarVidyasogarDutta | Ripple25 |
Alpine1 | EggCrate | Rosenbrock |
Alpine2 | EggHolder | RosenbrockM |
AHE | Exponential | RosenbrockMS |
AMGM | EX1 | RotatedEllipse1 |
BartelsConn | Exp2 | RotatedEllipse2 |
Beale | Exp3 | Rump |
BiggsExp2 | Exp4 | Salomon |
BiggsExp3 | Exp5 | Sargan |
BiggsExp4 | Exp6 | Schaffer1 |
BiggsExp5 | FreudensteinRoth | Schaffer2 |
BiggsExp6 | Gear | Schaffer3 |
Bird | Giunta | Schaffer4 |
Bohachevsky1 | GoldsteinPrice | Schaffer6 |
Bohachevsky2 | Griewank | SchmidtVetters |
Bohachevsky3 | GulfResearch | Schwefel01 |
Booth | Hansen | Schwefel02 |
BoxBetts | Hartmann3 | Schwefel04 |
Brad | Hartmann6 | Schwefel06 |
Branin1 | HelicalValley | Schwefel20 |
Branin2 | Himmelblau | Schwefel21 |
Brent | Holzman | Schwefel22 |
Brown | Hosaki | Schwefel23 |
Bukin01 | Infiniti | Schwefel25 |
Bukin02 | JennrichSampson | Schwefel26 |
Bukin03 | Judge | Schwefel36 |
Bukin04 | Katsuura | Shekel05 |
Bukin05 | Keane | Shekel07 |
Bukin06 | Kowalik | Shekel10 |
Bukin07 | Langermann52 | Shubert1 |
Bukin08 | Langermann5 | Shubert3 |
Bukin09 | Leon | Shubert4 |
Bukin10 | Levy03 | SineEnveloppe |
Bukin11 | Levy05 | Sodp |
Bukin12 | Levy13 | Slope |
Bukin13 | Matyas | Sphere |
Bukin14 | McCormick | Step |
Bukin15 | Michalewicz | Step1 |
Bukin16 | MieleCantrell | Step2 |
Bukin17 | Mishra01 | Step3 |
Bukin18 | Mishra02 | StepInt |
Bukin19 | Mishra03 | Stochastic |
Bukin20 | Mishra04 | StretchedV |
CamelbackThreeHump | Mishra05 | StyblinskiTang |
CamelbackSixHump | Mishra06 | SumSquare |
CarromTable | Mishra07 | Treccani |
ChenV | Mishra08 | Trefethen |
ChenBird | Mishra09 | Trid |
Chichinadze | Mishra10 | Trigonometric1 |
ChungReynolds | Mishra11 | Trigonometric2 |
Cigar | Mystery | Tripod |
Cola | NeedleEye | TubeHolder |
Colville | NewFunction1 | Ursem1 |
Corana | NewFunction2 | Ursem3 |
CosineMixture | NewFunction3 | Ursem4 |
CrossInTray | Null | UrsemWaves |
CrossLegTable | OddSquare | VenterSobiezcczanskiSobieski |
CrownedCross | Parsopoulos | Vincent |
Csendes | Pathological | Watson |
Cst | Paviani | Wavy |
Cube | Peaks | WayburnSeader1 |
Custom01 | PeaksN | WayburnSeader2 |
Custom02 | Penalty1 | Weibull |
Custom03 | Penalty2 | Weierstrass |
Custom04 | PenHolder | Whitley |
Custom05 | Periodic | Wolfe |
Damavandi | Pinter | XinSheYang1 |
Deb1 | Plateau | XinSheYang2 |
Deb2 | Powell | XinSheYang3 |
Deb3 | PowerSum | XinSheYang4 |
Deb4 | Price1 | Xor |
Decanomial | Price2 | YaoLiu4 |
Deceptive | Price3 | YaoLiu9 |
DeckkersAarts | Price4 | Zacharov |
DeflectedCorrugatedSpring | Qing | Zettl |
DeVilliersGlasser1 | Quadratic | Zimmerman |
DeVilliersGlasser2 | Quartic | Zirilli |
(see the 2D-3D plots of the 1- and 2-dimensional constrained problems)
(see the 2D-3D plots of the 1- and 2-dimensional multiobjective problems)
The toolbox can be downloaded here or here.
If you use git
, you can clone the repository using the following command
git clone --recursive git@bitbucket.org:luclaurent/optigtest.git optiGTest
or
git clone --recursive git@github.com:luclaurent/optiGTest.git optiGTest
optiGTest uses the gradFD class for checking gradients computation. Loading this class is optional but some functionalities will not be available which is not very important if you only want to use the main purpose of this toolbox (computing responses of objective and constraints functions and their gradients).
If you forget to use the --recursive
option when you clone the repository, please use the command submodule --init
in order to initialize the missing class gradFD.
The automatic building of the documentation is based on the m2html software.
The obtained documentation is available here.
This toolbox is inspired by many existing codes and papers
- AMPGO (and github repository)
- E. P. Adorio and U. P. Diliman. MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization.
- P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger and S. Tiwari. Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. KanGAL report, 2005.Link
- V. Bicik, Continuous optimization algorithms, Master thesis, Czech Technical University in Prague, 2010 Link
- M. Jamil and Xin-She Yang, A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modelling and Numerical Optimisation, Vol. 4, No. 2, pp. 150--194 (2013) doi: 10.1504/IJMMNO.2013.055204 arXiv: 1308.4008 PDF
- M. Molga, C. Smutnick. Test functions for optimization needs, Comput. Inform. Sci., 1-43, 2005. Link
- M. M. Ali, C. Khompatraporn and Z. B. Zabinsky, Journal of Global Optimisation (2005) 31:635. doi: 10.1007/s10898-004-9972-2 PDF
- Virtual Library of Simulation Experiments
- Wikipedia. Test functions for optimization, 2018. [Online; accessed 13-May-2018]
optiGTest - set of testing functions A toolbox to easy manipulate functions.
Copyright (C) 2017 Luc LAURENT <luc.laurent@lecnam.net>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.