NEW OPTIMIZATION ALGORITHMS ANDTHEIR APPLICATIONS
Atom-Based, Ecosystem-Basedand Economics-Based
WEIGUOZHAO
Professor,SchoolofWaterConservancyandHydroelectric Power,HebeiUniversityofEngineering,China
LIYINGWANG
Professor,SchoolofWaterConservancyandHydroelectric Power,HebeiuniversityofEngineering,China
ZHENXINGZHANG
Hydrologist,UniversityofIllinoisatUrbanaChampaign,USA
Elsevier
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Preface vii Acknowledgmentsix
1.Introduction1
1.1 Optimizationalgorithms1
1.2 Ashortoutlineofoptimizationalgorithms2
1.3 Organizationofthisbook6 References7
2.Atomsearchoptimizationalgorithm13
2.1 Introduction13
2.2 Basicmoleculardynamics15
2.3 Atomsearchoptimization18
2.4 Experimentalresults26
2.5 Conclusions43 References44
3.Engineeringapplicationsofatomsearchoptimization algorithm47
3.1 Introduction47
3.2 Parameterestimationforchaoticsystem47
3.3 Circularantennaarraydesignproblem51
3.4 Spreadspectrumradarpolyphasecodedesign52
3.5 Conclusions56 References57
4.Artificialecosystem-basedoptimizationalgorithm59
4.1 Introduction59
4.2 Artificialecosystem-basedoptimization61
4.3 Resultsanddiscussion68
4.4 Conclusions88 References88
5.Engineeringapplicationsofartificialecosystem-based optimization93
5.1 EngineeringoptimizationusingtheAEOalgorithm93
5.2 Staticeconomicloaddispatchproblem103
5.3 Hydrothermalschedulingproblem111
5.4 Conclusions119 References120
6.Supply-demand-basedoptimization123
6.1 Introduction123
6.2 Supply-demand-basedoptimization124
6.3 Experimentalresultsanddiscussion134
6.4 Conclusions141 References141
7.Engineeringapplicationsofsupply-demand-based optimization143
7.1 Introduction143
7.2 Three-bartrussdesign143
7.3 Cantileverbeamdesign146
7.4 Rollingelementbearingdesign147
7.5 Geartraindesign150
7.6 Conclusions151 References152 Appendix153 Index 163
Preface
Optimizationmeanstosearchforoptimalsolutionseffectivelyandefficientlyfromagivensolutionspaceunderthegivenconstraints,byeither maximizingorminimizingtheobjectivefunction.Metaheuristicoptimizationalgorithms,whicharepowerfultoolsforaddressingthesechallenging optimizationproblems,arebecomingincreasinglypopular.Forthisbook, threenovelintelligentoptimizationtechniques,basedonatomicdynamics, artificialecosystems,andeconomicsweredeveloped,tested,andappliedto practicalengineeringissues.Thebookisorganizedasfollows:
Chapter1 introducesthedevelopmentofintelligentoptimizationalgorithmsandtheiradvantagesanddisadvantages.
Chapter2 introducestheprocessandbasicprinciplesoftheatomsearch optimizationalgorithmandteststhealgorithm.
Chapter3 appliestheatomsearchoptimizationalgorithminengineering issues.
Chapter4 introducestheproposedprocessandbasicprincipleoftheartificialecosystem-basedoptimizationalgorithmandteststhealgorithm.
Chapter5 employstheartificialecosystem-basedoptimizationalgorithm inengineeringapplications.
Chapter6 presentstheinspirationanddescriptionofthesupplydemand-basedoptimization.
Chapter7 demonstratestheapplicationsofthesupply-demand-based optimizationindifferentengineeringcases.
AppendixA listsmathematicalbenchmarkfunctionsusedtotesttheperformanceofvariousalgorithms.
AppendixB listsoptimizationformulationsofvariousengineering problems.
AppendixC providestheMATLABcodesofthreealgorithms. Wehavebeenworkingonintelligentoptimizationalgorithmsformany yearsandhavemadesomeachievements.Thebookiscompiledonthebasis oftheresultsoftheseachievements.
Weappreciatethesupportoftheadministrationandcolleaguesofthe SchoolofWaterResourcesandHydropower,HebeiUniversityofEngineering,China,aswellasprofessorsfromotheruniversities.Wewouldlike toexpressourrespectandgratitudeforthereferencesinthebook.Wealso
acknowledgethepublisherswhopermittedourpaperstobeadoptedand utilizedinthepreparationofthisbook.
Thisbookcanbeusedbytechnicianswhoareengagedincomputingand intelligentalgorithmsandvariousengineeringpracticesthatuseoptimization.Itisalsoagoodreferenceforpostgraduatesandteachersofrelevant specialtiesincollegesanduniversities.
Ourwarmestgratitudeisduetoourfamiliesfortheircontinuedsupport inthecourseofpreparingthisbook.Dr.Zhaoworkedontheideasand papers,whichmotivatedthepreparationofthisbook,inIllinoisStateWater Survey,UniversityofIllinoisatUrbana-Champaign,USA.Preparingthe bookbroughtbackallthebeautifulmemoriesinChampaign,IL.Owing tothelimitationofourknowledge,wearenotabletoeradicateincompletenessorerrorsinthebook.Yoursuggestionswouldbemuchappreciated. Pleasecontactuswithyoursuggestions via thepublisher.
Acknowledgments
AcknowledgmentisgiventoSpringerforpermissiontoreprintmaterial fromthefollowingpaper:
ZhaoW,WangL,ZhangZ.2020.Artificialecosystem-basedoptimization:Anovelnature-inspiredmeta-heuristicalgorithm,NeuralComputingandApplications32:9383–9425.
AcknowledgmentisgiventotheInstituteofElectricalandElectronicEngineers(IEEE)forpermissiontoreprintaportionofthematerialfromthefollowingpaper:
ZhaoW,WangL,ZhangZ.2019.Supply-demand-basedoptimization: Anoveleconomics-inspiredalgorithmforglobaloptimization,IEEE Access7:73182–73206. © [2019]IEEE.
AcknowledgmentisalsogiventoElsevierforpermissiontoreprintmaterial fromthefollowingpapers:
ZhaoW,WangL.2016.Aneffectivebacterialforagingoptimizerfor globaloptimization,InformationSciences329:719–735.
ZhaoW,WangL,ZhangZ.2019.Atomsearchoptimizationandits applicationtosolveahydrogeologicparameterestimationproblem, Knowledge-BasedSystems163:283–304.
Theauthorsaregratefulthatthecopyrightpermissionwasgrantedfromthe abovepublishers.
1.2Ashortoutlineofoptimizationalgorithms
Sincethe1970s,manyoptimizationalgorithmshavebeendevelopedand appliedtodifferentoptimizationproblems.Thesealgorithms,whichmimic naturalorphysicalphenomena,haveprovidedeffectiveandrobusttechniquesforsolvingcomplexoptimizationproblemsinawidespectrumof disciplines.Manymetaheuristicalgorithmswithdifferentinspirationshave beenproposedandsuccessfullyusedinavarietyoffields,whichareroughly classifiedintofourcategories(Hareetal.,2013):evolution-inspired, (M € uhlenbeinetal.,1988; Gongetal.,2013,2014),physics-inspired (Geemetal.,2001),swarm-inspired(Krauseetal.,2013),andhumaninspired(Montieletal.,2007).
Evolution-inspiredalgorithmsareastochastic,population-based approach.Protectingapopulation’sdiversityisveryimportantforthesustainabledevelopmentofthealgorithmsiteratively.Manyevolution-inspired algorithmsmaintainapopulation’sdiversitybymimickingbasicgenetic rules,includingreproduction,mutation, selection,chemotaxis,elimination, andmigration(Passino,2002; Falcoetal.,2012).Thesealgorithmsrandomlyinitializeapopulationevolvedfromsubsequentiterationsandevaluatetheindividualqualityusingafitnessfunction.Geneticalgorithm(GA), originallypresentedby Holland(1975),isawell-knownclassicevolutionary algorithm(EA).AsGAcangenerallyobtainhigh-qualitysolutionsusing mutation,crossover,andselectionsteps,theoriginalversionanditsvariants arewidelyappliedtomanyreal-worldproblems(Gongetal.,2018).Since itsemergence,aseriesofschemesaimingtoenhanceGAhavebeendeveloped.WithincreasingpopularityofGA,anumberofotherevolution-based algorithmsintheliterature,includingevolutionarystrategies(ES)(Beyer andSchwefel,2002),differentialevolution(DE)(Roccaetal.,2011),evolutionaryprogramming(EP)( Justeetal.,1999),andmemeticalgorithms (MA)(Moscatoetal.,2007),havebeenproposed.Additionally,manytypes ofnewEAshavebeenproposedrecently,suchasbacterialforagingoptimization(BFO)(Passino,2002),batalgorithm(BA)(YangandHossein,2012), fruitflyoptimizationalgorithm(FOA)(Pan,2012),monkeykingevolutionary(MKE)(MengandPan,2016),artificialalgaealgorithm(AAA) (Uymazetal.,2015),biogeography-basedoptimization(BBO)(Simon, 2009),yin-yang-pairoptimization(YYPO)(PunnathanamandKotecha, 2016),invasiveweedoptimization(IWO)(MehrabianandLucas,2006), anddynamicvirtualbatsalgorithm(DVBA)(TopalandAltun,2016).
Physics-inspiredalgorithmssimulatephysicallawsintheuniverse, amongwhich,simulatedannealing(SA)(Kirkpatricketal.,1983)isone ofthemostwell-knownalgorithms.SAisinspiredfromtheannealingprocessusedinphysicalmaterialinwhichaheatedmetalcoolsandfreezesintoa crystaltexturewithaminimumamountofenergy.Recently,manynovel physics-inspiredalgorithmshavebeenproposed,suchasgravitationalsearch algorithm(GSA)(Rashedietal.,2009),electromagnetism-likemechanism (EM)algorithm(BirbilandFang,2003),particlecollisionalgorithm(PCA) (SaccoandDeOliveira,2015),vortexsearchalgorithm(VSA)(Doganand € Olmez,2015),waterevaporationoptimization(WEO)(KavehandBakhshpoori,2016),spacegravitationalalgorithm(SGA)(Hsiaoetal.,2005),big bang-bigcrunchalgorithm(BB-BC)(Genc ¸ etal.,2010),galaxybasedalgorithm(GBA)(Shah-Hosseini,2009),bigcrunchalgorithm(BCA)(Kripka andKripka,2008),integratedradiationalgorithm(IRA)(ChuangandJiang, 2007),waterdropsalgorithm(WDA)(Shah-Hosseini,2009),chargedsystemsearch(CSS)(KavehandTalatahari,2010),magneticoptimizationalgorithm(MOA)(MirjaliliandHashim,2012),gravitationfieldalgorithm (GFA)(Zhengetal.,2010),ionsmotionalgorithm(IMA)( Javidyetal., 2015),waterwaveoptimization(WWO)(Zheng,2015),gravitationalinteractionsoptimization(GIO)(Floresetal.,2011),teaching-learning-based optimization(TLBO)(Raoetal.,2012),hystereticoptimization(HO) (Zarandetal.,2002),thermalexchangeoptimization(TEO)(Kavehand Dadras,2017),lightrayoptimization(LRO)(ShenandLi,2009),heattransfersearch(HTS)(PatelandSavsani,2015),spiraloptimizationalgorithm (SOA)(TamuraandYasuda,2011),watercyclealgorithm(WCA) (Eskandaretal.,2012),andcurvedspaceoptimization(CSO) (Moghaddametal.,2012).
Swarm-inspiredalgorithmsmimicthecollectivebehaviorsofselforganizationandshape-formation,beitnaturalorartificial(BeniandWang, 1993).Therearetwoclassicswarm-inspiredalgorithms.Oneisparticle swarmoptimization(PSO)(KennedyandEberhart,1995),whichmimics bird-flockingbehaviors.InPSO,everyagentmovesaroundthesearchspace toimproveitssolution,andtheirpersonalbestpositionsandthegloballybest positionfoundsofararereserved,bywhichtheirpositionsareupdated locallyandsocially.Theotherisantcolonyoptimization(ACO)(Dorigo etal.,1996),whichfollowstheforagingprocessofanantcolony.Essentially, antscommunicatewitheachotherbypheromonetrailsthroughpathformations,whichassisttheminfindingtheshortestpathbetweenthenestand
foodsource.Therearemanynewlydevelopedswarm-inspiredalgorithms, suchasartificialbeecolony(ABC)(AkayandKaraboga,2012),salpswarm algorithm(SSA)(Mirjalilietal.,2017),krillherdalgorithm(KH)(Gandomi andAlavi,2012),tree-seedalgorithm(TSA)(Kiran,2015),socialspider optimization(SSO)(Cuevasetal.,2013),birdmatingoptimizer(BMO) (Askarzadeh,2014),cuckoosearch(CS)(YangandDeb,2019),grasshopper optimizationalgorithm(GOA)(Saremietal.,2017),sine-cosinealgorithm (SCA)(Mirjalili,2016),mothswarmalgorithm(MSA)(Mohamedetal., 2017),dolphinecholocation(DE)algorithm(KavehandFarhoudi,2013), huntingsearch(HS)algorithm(Oftadehetal.,2010),migratingbirdsoptimization(MBO)(Dumanetal.,2012),fireflyalgorithm(FA)(Yang,2010), monkeysearch(MS)algorithm(MucherinoandSeref,2007),andsquirrel searchalgorithm(SSA)( Jainetal.,2018).
Human-inspiredalgorithmsarearecentlydevelopedcategoryinintelligencecomputing.Theymathematicallystimulatesocialactivitiesandideologyinhumanstofindnear-optimalsolutions.Thesocietyandcivilization algorithm(SCA)(RayandLiew,2003)isatypicalrepresentativeof human-inspiredalgorithms.SCAimitatestheintraandsocialinteractions withinaformalsocietyandthecivilizationmodel.Asocietycorresponds toasetofmutuallyinteractingindividualsandacivilizationisasetofallsuch societies.Allindividualsineachsocietyinteractwitheachotherandmake improvementsundertheguidanceofaleaderbelongingtothesamesociety. Meanwhile,eachleaderinteractswithleadersofothersocietiestomigratetoa developedsociety.ThisleadermigrationmechanismhelpsSCAglobally searchpromisingregionsinthevariablespace.Additionally,SCAisadvantageousindealingwithconstrainedoptimizationproblemsowingtotheleader identificationmechanism.Someofotherhuman-inspiredalgorithmsinclude leaguechampionshipalgorithm(LCA)(Kashan,2009),socialgroupoptimization(SGO)(SatapathyandNaik,2016),socialemotionaloptimizationalgorithm(SOA)(Xuetal.,2010),socioevolutionandlearningoptimization algorithm(SELO)(Kumaretal.,2018),ideologyalgorithm(IA)(Huan etal.,2017),andculturalevolutionalgorithm(CEA)(KuoandLin,2013).
Comparedwithevolution-inspiredorphysics-inspiredalgorithms, swarm-inspiredalgorithmshavesomedistinctivecharacteristics.Onthe onehand,partorallofthehistoricalinformationaboutthepopulationneeds tobepreserved,becauseeveryagentdependsontheinformationtodetermine anewpositioninthesearchspaceoversubsequentiterations.However, evolution-inspiredalgorithmsrequiremoreoperators.Swarm-inspiredalgorithmsgenerallyupdatepositionsofthepopulationbyinteractionrulesas
standardformulas.Ontheotherhand,swarm-inspiredalgorithmsgenerally havetwobehaviors:explorationandexploitation(AlbaandDorronsoro, 2005; LynnandSuganthan,2015).Explorationmeanstheabilityofthealgorithmstosearchfornewsolutionsfarfromthecurrentsolutionintheentire searchspace.Exploitationmeanstheabilityofthealgorithmstosearchforthe bestsolutionnearanewsolutionthathasalreadybeenfound.Insuchalgorithms,therangeofeveryagentinthesearchspaceisscaledtoaconsensusin itsneighborhood,andagentsrandomlyexplorethewholesearchspace.Ifan agentoritsneighborsfindagoodregion,thisregionwillbeintensively exploited.Otherwise,theystillextensivelyexploreotherregions,thusindicatingtheirbetterself-adaptationinsearchingtheglobaloptima.Fromthese perspectives,swarm-inspiredalgorithmshavemanyadvantagesoverother algorithms.Manyevolution-inspiredorphysics-inspiredalgorithmshave swarm-inspiredcharacteristics,suchasPSO,ACO,CS,BFO,GSA,andso on.Thesealgorithmsnotonlyreflectthenatureofbiologicalphenomena orphysicallaws,butalsoshareacommoncharacteristicofexplorationand exploitation.Thus,theyaremorecompetitivethanthosewithoutswarminspiredcharacteristics.However,providingaproperbalancebetweenexplorationandexploitationwillleadtoanoptimalperformanceofthealgorithms, soitisoneofthemostimportanttasksinthedevelopmentofanystochastic optimizationalgorithm.
Withthedevelopmentofeconomy,society,andtechnology,agreat numberofcomplexandchallengingoptimizationproblemshaveaccordinglyarisenindifferentfields.Asanillustration,theemergenceofridesharingcompaniesthatoffertransportationondemandonalargescale, togetherwiththeincreasingavailabilityofcorrespondingdemanddatasets, developsanewcomplexoptimizationproblemofeffectivehandlingofthe routingnetwork(Bertsimasetal.,2018).Atpresent,trackingthegrowing interestinaclosed-loopsupplychainbybothpractitionersandacademiais easilypossible.Manyfactors,includingenvironmentallegislation,customer awareness,andtheeconomicalmotivationsoftheorganizations,cantransformclosed-loopsupplychainissuesintoauniqueandvitalsubjectinsupply chainmanagement.Designingandplanningaclosed-loopsupplychainis performedbyaneffectiveoptimizerinareasonabletime(Soleimaniand Kannan,2015).Solvingthelarge-scale,highlynonlinear,nonconvex,nonsmooth,nondifferential,noncontinuous,andcomplexcombinedheatand powereconomicdispatch(CHPED)problemsurgentlyrequiresoptimizationalgorithms(Beigvandetal.,2017).Anotherchallengingoptimization problemistheidentificationofpollutant sourcesforriverpollution
incidents,whicharecausedbyaccidentorillegalemissions(Zhangand Xin,2017).
Althoughanumberofoptimizationalgorithmshavebeenintroducedso far,newoptimizationalgorithmsarestillbeingdevelopedtotackleemerging complexoptimizationproblemstoobtainabetteroutcome.Furthermore, accordingtotheNoFreeLunchTheoremofOptimization(Wolpertand Macready,1997),thereisnooneoptimizationalgorithmperformingthe bestforalltypesofproblems.Thistheoremkeepsthisresearchfieldactive andencouragesrelevantscholarstodevelopnewalgorithmsforbetteroptimization.Basedontheabove,threemetaheuristicalgorithmswithswarm characteristicsincludingatomsearchoptimization,artificialecosystembasedoptimization,andsupply-demand-basedoptimization,havebeen developedandexaminedusingvarioustypesofbenchmarkfunctions,and thenengineeringapplicationshavedemonstratedtheirfeasibilityandeffectivenessintacklingreal-worldproblems(Zhaoetal.,2019).
1.3Organizationofthisbook
Thisbookisorganizedinthefollowingmanner: Thischapterintroducesthedefinitionofoptimization,thedevelopment processandthedetailedprocessestosolvetheproblem.
Chapter2 isorganizedasfollows. Section2.2 presentstheinspirationof anatomsearchoptimizationalgorithm; Section2.3 describesthenovel atomsearchoptimizationalgorithm; Section2.4 givesacomparative studyanddiscussiononthebenchmarkfunctions;andfinally, Section2.5 presentssomeconclusionsandsuggestssomefutureresearch directions.
Chapter3 isorganizedasfollows. Sections3.2and3.3 describetheapplicationofatomsearchoptimizationalgorithmforparameterestimation forachaoticsystemandthecircularantennaarraydesignproblems, whichdemonstratesitsavailabilityandeffectivenessinsolvingreal-world problems. Section3.4 presentsthespreadspectrumradarpolyphasecode designproblemwhichiscomparedwithitscounterparts.Theexperimentalresultssuggestthatatomsearchoptimizationiseffectiveandthat itisapromisingalternativetoPSO,GA,andBFOextensivelyusedin manyreal-worldproblems.
Chapter4 introducesanovelnature-inspiredmetaheuristicoptimization algorithm,namedartificialecosystem-basedoptimization. Section4.2
describesthealgorithmandtheconceptsbehinditindetail.Somemathematicaloptimizationproblemsareutilizedtotestthevalidityoftheproposedoptimizerformdifferentperspectivesin Section4.3. Section4.4 givesaconclusion.
Chapter5 investigatestheapplicationsofartificialecosystem-basedoptimizationtosomeengineeringdesigncasesandthestaticeconomicload dispatchproblemandhydrothermalschedulingproblem.
Chapter6 presentstheinspirationandsupply-demand-basedoptimizationindetail,andthentheexperimentalresultsonasetofmathematical benchmarkfunctionsareanalyzed.
Chapter7 demonstratestheeffectivenessofsupply-demand-basedoptimizationinsolvingfourengineeringproblems.Finallyweconcludethe workandsuggestseveraldirectionsforfutureresearch.
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