布谷鸟搜索寻优算法Cuckoo-search-Optimization-Algorithm

AppliedSoftComputing11(2011)5508–5518ContentslistsavailableatScienceDirectAppliedSoftComputingjournalhomepage:∗ControlandIntelligentProcessingCentreofExcellence(CIPCE),SchoolofElectricalandComputerEngineering,UniversityofTehran,Tehran,IranarticleinfoArticlehistory:Received17September2009Receivedinrevisedform28August2010Accepted1May2011Availableonline13May2011Keywords:CuckooOptimizationAlgorithm(COA)EvolutionaryalgorithmsNonlinearoptimizationabstractInthispaperanovelevolutionaryalgorithm,suitableforcontinuousnonlinearoptimizationproblems,isintroduced.Thisoptimizationalgorithmisinspiredbythelifeofabirdfamily,calledCuckoo.Speciallifestyleofthesebirdsandtheircharacteristicsinegglayingandbreedinghasbeenthebasicmotivationfordevelopmentofthisnewevolutionaryoptimizationalgorithm.Similartootherevolutionarymethods,CuckooOptimizationAlgorithm(COA)startswithaninitialpopulation.Thecuckoopopulation,indiffer-entsocieties,isintwotypes:maturecuckoosandeggs.TheefforttosurviveamongcuckoosconstitutesthebasisofCuckooOptimizationAlgorithm.Duringthesurvivalcompetitionsomeofthecuckoosortheireggs,demise.Thesurvivedcuckoosocietiesimmigratetoabetterenvironmentandstartreproducingandlayingeggs.Cuckoos’survivalefforthopefullyconvergestoastatethatthereisonlyonecuckoosociety,allwiththesameprofitvalues.Applicationoftheproposedalgorithmtosomebenchmarkfunctionsandarealproblemhasprovenitscapabilitytodealwithdifficultoptimizationproblems.©2011ElsevierB.V.Allrightsreserved.1.IntroductionOptimizationistheprocessofmakingsomethingbetter.Inotherwords,optimizationistheprocessofadjustingtheinputstoorchar-acteristicsofadevice,mathematicalprocess,orexperimenttofindtheminimumormaximumoutputorresult.Theinputconsistsofvariables:theprocessorfunctionisknownasthecostfunction,objectivefunction,orfitnessfunction;andtheoutputisthecostorfitness[1].Therearedifferentmethodsforsolvinganoptimiza-tionproblem.Someofthesemethodsareinspiredfromnaturalprocesses.Thesemethodsusuallystartwithaninitialsetofvari-ablesandthenevolvetoobtaintheglobalminimumormaximumoftheobjectivefunction.GeneticAlgorithm(GA)hasbeenthemostpopulartechniqueinevolutionarycomputationresearch.GeneticAlgorithmusesoperatorsinspiredbynaturalgeneticvariationandnaturalselection[2,3].AnotherexampleisParticleSwarmOpti-mization(PSO)whichwasdevelopedbyEberhartandKennedyin1995.Thisstochasticoptimizationalgorithmisinspiredbysocialbehaviorofbirdflockingorfishschooling[3–5].AntColonyOpti-mization(ACO)isanotherevolutionaryoptimizationalgorithmwhichisinspiredbythepheromonetraillayingbehaviorofrealantcolonies[3,6,7].OntheotherhandSimulatedAnnealingsim-ulatestheannealingprocessinwhichasubstanceisheatedaboveitsmeltingtemperatureandthengraduallycoolstoproducethecrystallinelattice,whichminimizesitsenergyprobabilitydistribu-∗Correspondenceaddress:FacultyofEngineering,Campus#2,UniversityofTehran,KargarShomaliSt.,P.O.Box14395-515,Tehran,Iran.Tel.:[phone].E-mailaddresses:[e-mail],[e-mail][1,8,9].Besidesthesewellknownmethods,theinvestigationsonnatureinspiredoptimizationalgorithmsarestillbeingdoneandnewmethodsarebeingdevelopedtocontinuallysolvesomesortofnonlinearproblems.In[10],makinguseoftheergodicityandinternalrandomnessofchaositerations,anovelimmuneevolu-tionaryalgorithmbasedonthechaosoptimizationalgorithmandimmuneevolutionaryalgorithmispresentedtoimprovethecon-vergenceperformanceoftheimmuneevolutionaryalgorithm.Thenovelalgorithmintegratesadvantagesoftheimmuneevolution-aryalgorithmandchaosoptimizationalgorithm.[11]introducesanewoptimizationtechniquecalledGrenadeExplosionMethod(GEM)anditsunderlyingideas,includingtheconceptofOptimalSearchDirection(OSD),areelaborated.In[12]anewparticleswarmoptimizationmethodbasedontheclonalselectionalgorithmispro-posedtoavoidprematureconvergenceandguaranteethediversityofthepopulation.Themainadvantagesofevolutionaryalgorithmsare[3]:(1)Beingrobusttodynamicchanges:Traditionalmethodsofopti-mizationarenotrobusttodynamicchangesintheenvironmentandtheyrequireacompleterestartforprovidingasolution.Incontrary,evolutionarycomputationcanbeusedtoadaptsolutionstochangingcircumstances.(2)Broadapplicability:Evolutionaryalgorithmscanbeappliedtoanyproblemsthatcanbeformulatedasfunctionoptimizationproblems.(3)Hybridizationwithothermethods:Evolutionaryalgorithmscanbecombinedwithmoretraditionaloptimizationtechniques.(4)Solvesproblemsthathavenosolutions:Theadvantageofevolu-tionaryalgorithmsincludestheabilitytoaddressproblemsfor1568-4946/$–seefrontmatter©2011ElsevierB.V.Allrightsreserved.doi:10.1016/j.asoc.2011.05.008R.Rajabioun/AppliedSoftComputing11(2011)5508–55185509Fig.1.FlowchartofCuckooOptimizationAlgorithm.whichthereisnohumanexpertise.Eventhoughhumanexper-tiseshouldbeusedwhenitisneededandavailable;itoftenproveslessadequateforautomatedproblem-solvingroutines.Consideringthesefeatures,evolutionaryalgorithmscanbeappliedtovariousapplicationsincluding:PowerSystemsoper-ationsandcontrol[13,19,20],NP-Hardcombinatorialprobl