optiGTest

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.

Features

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)

First start

• unConstrained problems: Example_unConstrained.m

List of unconstrained functions

(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

List of constrained problems

(see the 2D-3D plots of the 1- and 2-dimensional constrained problems)

List of multiobjective problems (w/- and w/o constraints)

(see the 2D-3D plots of the 1- and 2-dimensional multiobjective problems)

Download

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

Dependency

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.

Documentation

The automatic building of the documentation is based on the m2html software.

The obtained documentation is available here.

References

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]

License

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/>.