多目标决策法在建筑结构维修加固方案优选中的应用

ApplicationofMulti-targetDecisionMakingonSchemeOptimizationforStructuralMaintenanceandReinforcementAbstract:Theidealpointmethodofamulti-targetdecisionmakingisadoptedinthispaper.Schemeselectionsforbuildingstructuralmaintenanceandreinforcementareevaluatedbythefiveobjectssuchasplancost,anticipateconditionforusing,theanticipateservicedeadline,anticipatefailurelossandreliabilitygain.Thusthebestschemewillbeobtained.Thefeasibilityofmulti-targetdecisionmakinginthebuildingstructuralmaintenanceandreinforcementisshowedthroughcalculationofacertainstructure.Keywords:Multi-targetdecisionmaking,Buildingstructure,Maintenanceandreinforcement,Schemeoptimization1IntroductionAlargenumberofservicestructureshavereachedtheirlifeinoldage,withChina'ssustainedandrapidgrowthincapitalinvestmentandthebiggerandbiggerscaleforinfrastructurefromthe1990s.Intheprocessofusingthem,duetohumanconditions,environmentalconditions,thereexistedallkindsofsecurityrisksinthesestructure,whichthreatenthesafetyofproductionandlife.Thus,thesestructureshaveanurgentneedtoberepairedandreinforced.2Thefeasibilityandnecessityofmulti-targetdecision-makingmethodSelectionofstructuralmaintenanceandreinforcementneedtotakeplancost,anticipateconditionforusing,theanticipateservicedeadline,anticipatefailurelossandreliabilitygainintoconsideration.Butthecontradictionexistsamongtheseindicators[1].Fromthewaysoftacklingproblemsbymulti-objectivedecision-makingmethodsandcharacteristicsofmaintenanceandreinforcementfield,themulti-objectivedecision-makingisverysuitablefordecision-makingproblemsofstructuralmaintenanceandreinforcementscheme.InOptionalschemesofmaintenanceandreinforcement,thereareindicatorsforoneorafewwithadvantage,whileseveralotherindicatorswithdisadvantage.Decision-makingprocessistochooseasatisfactorysolutionfromthem.Inthispaper,afteracomprehensivecomparisonofvariousmulti-objectivedecision-makingsolutions,theidealpointmethodismoresuitable[2].Principlesforitisasfollows.Theoptimalvaluesofeachindexarefoundintheavailableschemestobecomposedastheidealpointwhiletheworstvaluesofeachindexasthemostinferiorpoints.Andthenthedistancebetweentheavailableschemesandthebestorthemostinferiorpointiscalculatedtoidentifytheschemethathasthelatestdistancetothebestpoint,meanwhilehasthefarthestdistancetotheinferiorpointasthebestscheme,soastoachievethepurposeofschemeoptimization[3].3SchemeoptimizationmodelforstructuralmaintenanceandreinforcementSupposetherearemdecision-makingschemeswhichare12,,,mAAAandntargets12,,,nGGGineachschemeofstructuralmaintenanceandreinforcement.ValuesintheScheme),,2,1(njAishouldbeexpressedasija.Decision-makingisbasedoneachija),,2,1,,,2,1(njmi.Thematrixconsistedbyijaisshownasfollows,whichiscalledindexmatrixofschemes12,,,mAAAontargets12,,,nGGG.1111()nijmnmmnaaAaaa（1）Thetargetsareusuallydividedintoforwardonesandreverseones.Thebiggerthevalueis,theforwardtargetsarebetter,oncontrast,thereverseonesareworse.Andthedimensionisdifferentwhenitcomestothetargets.Tomakethetargetcomputationeasy,thereversetargetsareconvertedtoforwardoneswhilethedimensionalvaluestonodimensionalones.Thus,supposetargetreverseisGwhentargetforwardisGwheniiijijijaabmaxmaxmin(1,2,,;1,2,,)ijijbbrimjnbb（2）maxbisthebiggesttargetvalueinthecolumnjwhileminbisthelestone.Then,standardizedmatrixisshownas:1111()nijmnmmnrrRrrr（3）This12(,,,)(1,2,,)iiiinArrrimisadecisionpointinEuclideanspace.Tofindsatisfactorysolutions,requires11min(),max()(1,2,,)ijjijjimimrrrrjn.wecalled1(,,)nArristheoptimalsolution12,,,mAAA.1(,,)nArristheworstsolutionabout12,,,mAAA.SelectthesatisfactoryprogramthatistofindclosetoAandfarfromthedecisionpointA.DecisionpointsiAandA、Adistanceisasfollows:12211221(,)()(,)()niijijjjjniijijjjjddAArrddAArr(4)(5)That1,2,,;(1,2,,)jimjnistheweightofjG,01ijand11njj,order11min,miniiimimdddd，iiiddCddcanreflectthedecisionpointiAclosetoadvantageofAandformthemostinferiorAlevel,wecallittheevaluationofthevalueofiA,accordingtothesizeoftheiCorderprogram,andtheleastiCisthesatisfiedprogram.4TheevaluationofthetargetweightcalculationBeforeprogrammedevaluation,callingouttheweightofeachevaluationindex.Thetraditionalapproachistousejudgmentmatrix,bypairwisecomparisonoftherelativeweightofthefactorsaffectingtheweight,thenuse1-9scaletoquantifytherelativeimportance,andultimatelygettheweights.Inthemethod,tocomparetheimpactofindicators1G,2G…nGtothevariousprograms,everytimetaketwofactorsiGanjG,usingijetoexpresstheinfluenceratioofiGandjG,allresultscanbeexpressedascontrastmatrix1()0ijnnijjiijEeeeeInthequalitativepairedcomparison,becauseofdisadvantagesofthe1-9scale,thispaperproposesanimprovedmethod,thatisthethreescalematrix,thenthroughtheconversion,andgettheweightmatrix.Decision-makersjudgetherelationshipofeachindexwiththreescalevalue(0,1,2),whendecision-makerscomparetwoindicatorsofimportance,mostintuitiveandeasyjudgmentistodeterminetheimportantrelationship,theresultsofthiscomparisoncanbeexpressedby0,1,2.Becauseoft