Definitions-of--CEC-13-benchmark-suite

See discussions, stats, and author profiles for this publication at: Definitions and Evaluation Criteria forthe CEC 2013 Special Session on Real-Parameter OptimizationARTICLE · JANUARY 2013CITATIONS53READS4394 AUTHORS, INCLUDING:Jing LiangZhengzhou University51 PUBLICATIONS 2,935 CITATIONS SEE PROFILEPonnuthurai N. SuganthanNanyang Technological University318 PUBLICATIONS 9,996 CITATIONS SEE PROFILEAlfredo García Hernández-DíazUniversidad Pablo de Olavide53 PUBLICATIONS 497 CITATIONS SEE PROFILEAvailable from: Alfredo García Hernández-DíazRetrieved on: 05 October 2015ProblemDefinitionsandEvaluationCriteriafortheCEC2013SpecialSessiononReal-ParameterOptimizationJ.J.Liang1,B.Y.Qu2,P.N.Suganthan3,AlfredoG.Hernández-Díaz41SchoolofElectricalEngineering,ZhengzhouUniversity,Zhengzhou,China2SchoolofElectricandInformationEngineering,ZhongyuanUniversityofTechnology,Zhengzhou,China3SchoolofEEE,NanyangTechnologicalUniversity,Singapore4DepartmentofEconomics,QuantitativeMethodsandEconomicHistory,PablodeOlavideUniversity,Seville,[e-mail],[e-mail],[e-mail],[e-mail]201212,ComputationalIntelligenceLaboratory,ZhengzhouUniversity,ZhengzhouChinaAndTechnicalReport,NanyangTechnologicalUniversity,SingaporeJanuary2013Singleobjectiveoptimizationalgorithmsarethebasisofthemorecomplexoptimizationalgorithmssuchasmulti-objectiveoptimizationsalgorithms,nichingalgorithms,constrainedoptimizationalgorithmsandsoon.Researchonthesingleobjectiveoptimizationalgorithmsinfluencethedevelopmentoftheseoptimizationbranchesmentionedabove.Intherecentyearsvariouskindsofnoveloptimizationalgorithmshavebeenproposedtosolvereal-parameteroptimizationproblems.EightyearshavepassedsincetheCEC’05SpecialSessiononReal-ParameterOptimization[1].ConsideringthecommentsontheCEC’05testsuitereceivedbyus,weproposetoorganizeanewcompetitiononrealparametersingleobjectiveoptimization.IntheCEC’13testsuite,thepreviouslyproposedcompositionfunctions[2]areimprovedandadditionaltestfunctionsareincluded.Thisspecialsessionisdevotedtotheapproaches,algorithmsandtechniquesforsolvingrealparametersingleobjectiveoptimizationwithoutmakinguseoftheexactequationsofthetestfunctions.WeencourageallresearcherstotesttheiralgorithmsontheCEC’13testsuitewhichincludes28benchmarkfunctions.Theparticipantsarerequiredtosendthefinalresultsintheformatspecifiedinthetechnicalreporttotheorganizers.Theorganizerswillpresentanoverallanalysisandcomparisonbasedontheseresults.Wewillalsousestatisticaltestsonconvergenceperformancetocomparealgorithmsthateventuallygeneratesimilarfinalsolutions.Papersonnovelconceptsthathelpusinunderstandingproblemcharacteristicsarealsowelcome.TheCandMatlabcodesforCEC’13testsuitecanbedownloadedfromthewebsitegivenbelow:’13TestFunctions1.1SomeDefinitions:Alltestfunctionsareminimizationproblemsdefinedasfollowing:Minf(x),T12[,,...,]DxxxxD:dimensions.T12[,,...,]Doooo:theshiftedglobaloptimum(definedin“shift_data.txt”),whichisrandomlydistributedin[-80,80]D.Alltestfunctionsareshiftedtooandscalable.Forconvenience,thesamesearchrangesaredefinedforalltestfunctions.Searchrange:[-100,100]D.M1,M2,…,M10:orthogonal(rotation)matrixgeneratedfromstandardnormallydistributedentriesbyGram-Schmidtorthonormalization.(Matrixdataissavedin“M_D2.txt”,“M_D10.txt”,“M_D30.txt”,“M_D50.txt”,“M_D100.txt”.EachfileconcludestenD*Dorthogonalmatrices.):adiagonalmatrixinDdimensionswiththeithdiagonalelementas12(1)iDii,i=1,2,…,D.111:if0,,for1,...,iixDasyiiiTxxxiD[3]Tosz:for12ˆˆˆsign()exp(0.049(sin()sin())),for1andiiiiixxxcxcxiD[3]wherelog()if0ˆ0otherwiseiiixxx,1if0sign()0if01otherwiseiiixxx110if05.5otherwiseixc,and27.9if03.1otherwiseixc1.2Summaryofthe28CEC’13TestFunctionsTableI.Summaryofthe28CEC’13TestFunctionsNo.Functionsfi*=fi(x*)UnimodalFunctions1SphereFunction-14002RotatedHighConditionedEllipticFunction-13003RotatedBentCigarFunction-12004RotatedDiscusFunction-11005DifferentPowersFunction-1000BasicMultimodalFunctions6RotatedRosenbrock’sFunction-9007RotatedSchaffersF7Function-8008RotatedAckley’sFunction-7009RotatedWeierstrassFunction-60010RotatedGriewank’sFunction-50011Rastrigin’sFunction-40012RotatedRastrigin’sFunction-30013Non-ContinuousRotatedRastrigin’sFunction-20014Schwefel'sFunction-10015RotatedSchwefel'sFunction10016RotatedKatsuuraFunction20017LunacekBi_RastriginFunction30018RotatedLunacekBi_RastriginFunction40019ExpandedGriewank’splusRosenbrock’sFunction50020ExpandedScaffer’sF6Function600CompositionFunctions21CompositionFunction1(n=5,Rotated)70022CompositionFunction2(n=3,Unrotated)80023CompositionFunction3(n=3,Rotated)90024CompositionFunction4(n=3,Rotated)100025CompositionFunction5(n=3,Rotated)110026CompositionFunction6(n=5,Rotated)120027CompositionFunction7(n=5,Rotated)130028CompositionFunction8(n=5,Rotated)1400SearchRange:[-100,100]D*PleaseNotice:Theseproblemssh