GitHub Newsletter Discord

Version: 0.6.1.3

Test Problems

In the future, we are planning to provide a comprehensive overview of the problems. So far, we have managed to describe a view of them and plot the functions. Please note that we have used for some problems the descriptions from here.

We want to keep the function definitions as error-free as possible and matching with the implementation. If you find any deviation, please let us know.

Various test problems are already implemented and available by providing the corresponding problem name we have assigned to it. A couple of problems can be further parameterized by providing the number of variables, constraints, or other problem-dependent constants.

from pymoo.problems import get_problem

# create a simple test problem from string
p = get_problem("Ackley")

# the input name is not case sensitive
p = get_problem("ackley")

# also input parameter can be provided directly
p = get_problem("dtlz1^-1", n_var=20, n_obj=5)

Many-Objective

Problem	Description
DTLZ1	many-objective
DTLZ2
DTLZ3
DTLZ4
DTLZ5
DTLZ6
DTLZ7
DTLZ1^-1
Scaled DTLZ
Convex DTLZ
WFG1
WFG2
WFG3
WFG4
WFG5
WFG6
WFG7
WFG8
WFG9

Multi-Objective

Problem	Variables	Objectives	Constraints	Description
BNH	2	2	2
Carside	7	3	10
Kursawe	3	2
OSY	6	2	6
TNK	2	2	2
Truss2D	3	2	1
Welded Beam	4	2	4
CTP1	2	2	s
CTP2	2	2	s
CTP3	2	2	s
CTP4	2	2	s
CTP5	2	2	s
CTP6	2	2	s
CTP7	2	2	s
CTP8	2	2	s
ZDT1	30	2
ZDT2	30	2
ZDT3	30	2
ZDT4	10	2
ZDT5	80	2
ZDT6	10	2
DASCMOP1	30	2	11
DASCMOP2	30	2	11
DASCMOP3	30	2	11
DASCMOP4	30	2	11
DASCMOP5	30	2	11
DASCMOP6	30	2	11
DASCMOP7	30	3	7
DASCMOP8	30	3	7
DASCMOP9	30	3	7
MW1	15	2	1
MW2	15	2	1
MW3	15	2	2
MW4	15	3	1
MW5	15	2	3
MW6	15	2	1
MW7	15	2	2
MW8	15	3	1
MW9	15	2	1
MW10	15	2	3
MW11	15	2	4
MW12	15	2	2
MW13	15	2	2
MW14	15	3	1
SymPart	2	2
OmniTest	s	2
MODAct	20	2-5	7-10	Real-world mechanical design problems

Single-Objective

Problem	Variables	Constraints	Type
Ackley	s
Cantilevered Beams	4	2
Griewank	s
Himmelblau	2
Knapsack	s	1
Pressure Vessel	4	4
Rastrigin	s
Rosenbrock	s
Schwefel	s
Sphere	s
Zakharov	s
G01	13	9
G02	20	2
G03	10	1
G04	5	6
G05	4	5
G06	2	2
G07	10	8
G08	2	2
G09	8	6

Global Optimization

Implementations are taken from (SciPy)[https://github.com/scipy/scipy/tree/master/benchmarks/benchmarks/go_benchmark_functions] where a variety of global optimization benchmark problems are provided. Pymoo uses a wrapper class to make all those functions available.

Problem	Variables	Constraints	Name
AMGM	2		“go-amgm”
Ackley01	2		“go-ackley01”
Ackley02	2		“go-ackley02”
Ackley03	2		“go-ackley03”
Adjiman	2		“go-adjiman”
Alpine01	2		“go-alpine01”
Alpine02	2		“go-alpine02”
BartelsConn	2		“go-bartelsconn”
Beale	2		“go-beale”
BiggsExp02	2		“go-biggsexp02”
BiggsExp03	3		“go-biggsexp03”
BiggsExp04	4		“go-biggsexp04”
BiggsExp05	5		“go-biggsexp05”
Bird	2		“go-bird”
Bohachevsky1	2		“go-bohachevsky1”
Bohachevsky2	2		“go-bohachevsky2”
Bohachevsky3	2		“go-bohachevsky3”
BoxBetts	3		“go-boxbetts”
Branin01	2		“go-branin01”
Branin02	2		“go-branin02”
Brent	2		“go-brent”
Brown	2		“go-brown”
Bukin02	2		“go-bukin02”
Bukin04	2		“go-bukin04”
Bukin06	2		“go-bukin06”
CarromTable	2		“go-carromtable”
Chichinadze	2		“go-chichinadze”
Cigar	2		“go-cigar”
Cola	17		“go-cola”
Colville	4		“go-colville”
Corana	4		“go-corana”
CosineMixture	2		“go-cosinemixture”
CrossInTray	2		“go-crossintray”
CrossLegTable	2		“go-crosslegtable”
CrownedCross	2		“go-crownedcross”
Csendes	2		“go-csendes”
Cube	2		“go-cube”
Damavandi	2		“go-damavandi”
DeVilliersGlasser01	4		“go-devilliersglasser01”
DeVilliersGlasser02	5		“go-devilliersglasser02”
Deb01	2		“go-deb01”
Deb03	2		“go-deb03”
Decanomial	2		“go-decanomial”
Deceptive	2		“go-deceptive”
DeckkersAarts	2		“go-deckkersaarts”
DeflectedCorrugatedSpring	2		“go-deflectedcorrugatedspring”
DixonPrice	2		“go-dixonprice”
Dolan	5		“go-dolan”
DropWave	2		“go-dropwave”
Easom	2		“go-easom”
Eckerle4	3		“go-eckerle4”
EggCrate	2		“go-eggcrate”
EggHolder	2		“go-eggholder”
ElAttarVidyasagarDutta	2		“go-elattarvidyasagardutta”
Exp2	2		“go-exp2”
Exponential	2		“go-exponential”
FreudensteinRoth	2		“go-freudensteinroth”
Gear	4		“go-gear”
Giunta	2		“go-giunta”
GoldsteinPrice	2		“go-goldsteinprice”
Griewank	2		“go-griewank”
Gulf	3		“go-gulf”
Hansen	2		“go-hansen”
Hartmann3	3		“go-hartmann3”
Hartmann6	6		“go-hartmann6”
HelicalValley	3		“go-helicalvalley”
HimmelBlau	2		“go-himmelblau”
HolderTable	2		“go-holdertable”
Hosaki	2		“go-hosaki”
Infinity	2		“go-infinity”
JennrichSampson	2		“go-jennrichsampson”
Judge	2		“go-judge”
Katsuura	2		“go-katsuura”
Keane	2		“go-keane”
Kowalik	4		“go-kowalik”
Langermann	2		“go-langermann”
LennardJones	6		“go-lennardjones”
Leon	2		“go-leon”
Levy03	2		“go-levy03”
Levy05	2		“go-levy05”
Levy13	2		“go-levy13”
Matyas	2		“go-matyas”
McCormick	2		“go-mccormick”
Meyer	3		“go-meyer”
Michalewicz	2		“go-michalewicz”
MieleCantrell	4		“go-mielecantrell”
Mishra01	2		“go-mishra01”
Mishra02	2		“go-mishra02”
Mishra03	2		“go-mishra03”
Mishra04	2		“go-mishra04”
Mishra05	2		“go-mishra05”
Mishra06	2		“go-mishra06”
Mishra07	2		“go-mishra07”
Mishra08	2		“go-mishra08”
Mishra09	3		“go-mishra09”
Mishra10	2		“go-mishra10”
Mishra11	2		“go-mishra11”
MultiModal	2		“go-multimodal”
NeedleEye	2		“go-needleeye”
NewFunction01	2		“go-newfunction01”
NewFunction02	2		“go-newfunction02”
OddSquare	2		“go-oddsquare”
Parsopoulos	2		“go-parsopoulos”
Pathological	2		“go-pathological”
Paviani	10		“go-paviani”
PenHolder	2		“go-penholder”
Penalty01	2		“go-penalty01”
Penalty02	2		“go-penalty02”
PermFunction01	2		“go-permfunction01”
PermFunction02	2		“go-permfunction02”
Pinter	2		“go-pinter”
Plateau	2		“go-plateau”
Powell	4		“go-powell”
PowerSum	4		“go-powersum”
Price01	2		“go-price01”
Price02	2		“go-price02”
Price03	2		“go-price03”
Price04	2		“go-price04”
Qing	2		“go-qing”
Quadratic	2		“go-quadratic”
Quintic	2		“go-quintic”
Rana	2		“go-rana”
Rastrigin	2		“go-rastrigin”
Ratkowsky01	4		“go-ratkowsky01”
Ratkowsky02	3		“go-ratkowsky02”
Ripple01	2		“go-ripple01”
Ripple25	2		“go-ripple25”
Rosenbrock	2		“go-rosenbrock”
RosenbrockModified	2		“go-rosenbrockmodified”
RotatedEllipse01	2		“go-rotatedellipse01”
RotatedEllipse02	2		“go-rotatedellipse02”
Salomon	2		“go-salomon”
Sargan	2		“go-sargan”
Schaffer01	2		“go-schaffer01”
Schaffer02	2		“go-schaffer02”
Schaffer03	2		“go-schaffer03”
Schaffer04	2		“go-schaffer04”
Schwefel01	2		“go-schwefel01”
Schwefel02	2		“go-schwefel02”
Schwefel04	2		“go-schwefel04”
Schwefel06	2		“go-schwefel06”
Schwefel20	2		“go-schwefel20”
Schwefel21	2		“go-schwefel21”
Schwefel22	2		“go-schwefel22”
Schwefel26	2		“go-schwefel26”
Schwefel36	2		“go-schwefel36”
Shekel05	4		“go-shekel05”
Shekel07	4		“go-shekel07”
Shekel10	4		“go-shekel10”
Shubert01	2		“go-shubert01”
Shubert03	2		“go-shubert03”
Shubert04	2		“go-shubert04”
SineEnvelope	2		“go-sineenvelope”
SixHumpCamel	2		“go-sixhumpcamel”
Sodp	2		“go-sodp”
Sphere	2		“go-sphere”
Step	2		“go-step”
Step2	2		“go-step2”
Stochastic	2		“go-stochastic”
StretchedV	2		“go-stretchedv”
StyblinskiTang	2		“go-styblinskitang”
TestTubeHolder	2		“go-testtubeholder”
ThreeHumpCamel	2		“go-threehumpcamel”
Thurber	7		“go-thurber”
Treccani	2		“go-treccani”
Trefethen	2		“go-trefethen”
Trid	6		“go-trid”
Trigonometric01	2		“go-trigonometric01”
Trigonometric02	2		“go-trigonometric02”
Tripod	2		“go-tripod”
Ursem01	2		“go-ursem01”
Ursem03	2		“go-ursem03”
Ursem04	2		“go-ursem04”
UrsemWaves	2		“go-ursemwaves”
VenterSobiezcczanskiSobieski	2		“go-ventersobiezcczanskisobieski”
Vincent	2		“go-vincent”
Watson	6		“go-watson”
Wavy	2		“go-wavy”
WayburnSeader01	2		“go-wayburnseader01”
WayburnSeader02	2		“go-wayburnseader02”
Weierstrass	2		“go-weierstrass”
Whitley	2		“go-whitley”
Wolfe	3		“go-wolfe”
XinSheYang01	2		“go-xinsheyang01”
XinSheYang02	2		“go-xinsheyang02”
XinSheYang03	2		“go-xinsheyang03”
XinSheYang04	2		“go-xinsheyang04”
Xor	9		“go-xor”
YaoLiu04	2		“go-yaoliu04”
YaoLiu09	2		“go-yaoliu09”
Zacharov	2		“go-zacharov”
ZeroSum	2		“go-zerosum”
Zettl	2		“go-zettl”
Zimmerman	2		“go-zimmerman”
Zirilli	2		“go-zirilli”

<< Definition

Ackley >>