遗传算法Word格式文档下载.docx
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（
一般取0.0001-0.1）随机地对个体中某个字符进行补运算（即若原来字符为0，则改为1；
若原来为1则改为0）。
具体的，针对每个个体的每个自负产生一个[0,1]区间上的均匀分布的随机数
，若
，则将该字符进行变异，否则不进行变异。
变异运算具有增加群体多样性的效果。
（7）终止反复进行（3）—（6）项工作，直至得到满意解。
终止的条件也可用事先规定进化的代数，一般取100—500。
二、算法框图
图1
三、算法程序
function[x,fval,exitFlag,output,population,scores]=ga（fun,nvars,Aineq,bineq,Aeq,beq,lb,ub,nonlcon,options）
%GAConstrainedoptimizationusinggeneticalgorithm.
%GAattemptstosolveproblemsoftheform:
%minF（X）subjectto:
A*X<
=B,Aeq*X=Beq（linearconstraints）
%XC（X）<
=0,Ceq（X）=0（nonlinearconstraints）
%LB<
=X<
=ub
%
%X=GA（FITNESSFCN,NVARS）findsalocalunconstrainedminimumXtothe
%FITNESSFCNusingGA.NVARSisthedimension（numberofdesign
%variables）oftheFITNESSFCN.FITNESSFCNacceptsavectorXofsize
%1-by-NVARS,andreturnsascalarevaluatedatX.
%X=GA（FITNESSFCN,NVARS,A,b）findsalocalminimumXtothefunction
%FITNESSFCN,subjecttothelinearinequalitiesA*X<
=B.Linear
%constraintsarenotsatisfiedwhenthePopulationTypeoptionissetto
%'
bitString'
or'
custom'
.Seethedocumentationfordetails.
%X=GA（FITNESSFCN,NVARS,A,b,Aeq,beq）findsalocalminimumXtothe
%functionFITNESSFCN,subjecttothelinearequalitiesAeq*X=beqas
%wellasA*X<
=B.（SetA=[]andB=[]ifnoinequalitiesexist.）Linear
%X=GA（FITNESSFCN,NVARS,A,b,Aeq,beq,lb,ub）definesasetoflowerand
%upperboundsonthedesignvariables,X,sothatasolutionisfoundin
%therangelb<
=ub.Useemptymatricesforlbandubifnobounds
%exist.Setlb（i）=-InfifX（i）isunboundedbelow;
setub（i）=Infif
%X（i）isunboundedabove.Linearconstraintsarenotsatisfiedwhenthe
%PopulationTypeoptionissetto'
.Seethe
%documentationfordetails.
%X=GA（FITNESSFCN,NVARS,A,b,Aeq,beq,lb,ub,NONLCON）subjectsthe
%minimizationtotheconstraintsdefinedinNONLCON.Thefunction
%NONLCONacceptsXandreturnsthevectorsCandCeq,representingthe
%nonlinearinequalitiesandequalitiesrespectively.GAminimizes
%FITNESSFCNsuchthatC（X）<
=0andCeq（X）=0.（Setlb=[]and/orub=[]if
%noboundsexist.）Nonlinearconstraintsarenotsatisfiedwhenthe
%X=GA（FITNESSFCN,NVARS,A,b,Aeq,beq,lb,ub,NONLCON,options）minimizes
%withthedefaultoptimizationparametersreplacedbyvaluesinthe
%structureOPTIONS.OPTIONScanbecreatedwiththeGAOPTIMSETfunction.
%SeeGAOPTIMSETfordetails.
%X=GA（PROBLEM）findstheminimumforPROBLEM.PROBLEMisastructure
%thathasthefollowingfields:
%fitnessfcn:
<
Fitnessfunction>
%nvars:
Numberofdesignvariables>
%Aineq:
Amatrixforinequalityconstraints>
%bineq:
bvectorforinequalityconstraints>
%Aeq:
Aeqmatrixforequalityconstraints>
%beq:
beqvectorforequalityconstraints>
%lb:
LowerboundonX>
%ub:
UpperboundonX>
%nonlcon:
nonlinearconstraintfunction>
%options:
OptionsstructurecreatedwithGAOPTIMSET>
%rngstate:
Stateoftherandomnumbergenerator>
%[X,FVAL]=GA（FITNESSFCN,...）returnsFVAL,thevalueofthefitness
%functionFITNESSFCNatthesolutionX.
%[X,FVAL,EXITFLAG]=GA（FITNESSFCN,...）returnsEXITFLAGwhich
%describestheexitconditionofGA.PossiblevaluesofEXITFLAGandthe
%correspondingexitconditionsare
%1Averagechangeinvalueofthefitnessfunctionover
%options.StallGenLimitgenerationslessthanoptions.TolFunand
%constraintviolationlessthanoptions.TolCon.
%3Thevalueofthefitnessfunctiondidnotchangein
%options.StallGenLimitgenerationsandconstraintviolationless
%thanoptions.TolCon.
%4Magnitudeofstepsmallerthanmachineprecisionandconstraint
%violationlessthanoptions.TolCon.Thisexitconditionapplies
%onlytononlinearconstraints.
%5Fitnesslimitreachedandconstraintviolationlessthan
%options.TolCon.
%0Maximumnumberofgenerationsexceeded.
%-1Optimizationterminatedbytheoutputorplotfunction.
%-2Nofeasiblepointfound.
%-4Stalltimelimitexceeded.
%-5Timelimitexceeded.
%[X,FVAL,EXITFLAG,OUTPUT]=GA（FITNESSFCN,...）returnsa
%structureOUTPUTwiththefollowinginformation:
StateoftherandomnumbergeneratorbeforeGAstarted>
%generations:
Totalgenerations,excludingHybridFcniterations>
%funccount:
Totalfunctionevaluations>
%maxconstraint:
Maximumconstraintviolation>
ifany
%message:
GAterminationmessage>
%[X,FVAL,EXITFLAG,OUTPUT,POPULATION]=GA（FITNESSFCN,...）returnsthe
%finalPOPULATIONattermination.
%[X,FVAL,EXITFLAG,OUTPUT,POPULATION,SCORES]=GA（FITNESSFCN,...）returns
%theSCORESofthefinalPOPULATION.
%Example:
%Unconstrainedminimizationof'
rastriginsfcn'
fitnessfunctionof
%numberOfVariables=2
%x=ga（@rastriginsfcn,2）
%DisplayplottingfunctionswhileGAminimizes
%options=gaoptimset（'
PlotFcns'
...
%{@gaplotbestf,@gaplotbestindiv,@gaplotexpectation,@gaplotstopping}）;
%[x,fval,exitflag,output]=ga（@rastriginsfcn,2,[],[],[],[],[],[],[],options）
%Anexamplewithinequalityconstraintsandlowerbounds
%A=[11;
-12;
21];
b=[2;
2;
3];
lb=zeros（2,1）;
%%Usemutationfunctionwhichcanhandleconstraints
MutationFcn'
@mutationadaptfeasible）;
%[x,fval,exitflag]=ga（@lincontest6,2,A,b,[],[],lb,[],[],options）;
%FITNESSFCNcanalsobeananonymousfunction:
%x=ga（@（x）3*sin（x
（1））+exp（x
（2））,2）
%IfFITNESSFCNorNONLCONareparameterized,youcanuseanonymous
%functionstocapturetheproblem-dependentparameters.Supposeyouwant
%tominimizethefitnessgiveninthefunctionmyfit,subjecttothe
%nonlinearconstraintmyconstr,wherethesetwofunctionsare
%parameterizedbytheirsecondargumenta1anda2,respectively.Here
%myfitandmyconstrareMATLABfilefunctionssuchas
%functionf=myfit（x,a1）
%f=exp（x
（1））*（4*x
（1）^2+2*x
（2）^2+4*x
（1）*x
（2）+2*x
（2）+a1）;
%and
%function[c,ceq]=myconstr（x,a2）
%c=[1.5+x
（1）*x
（2）-x
（1）-x
（2）;
%-x
（1）*x
（2）-a2];
%%Nononlinearequalityconstraints:
%ceq=[];
%Tooptimizeforspecificvaluesofa1anda2,firstassignthevalues
%tothesetwoparameters.Thencreatetwoone-argumentanonymous
%functionsthatcapturethevaluesofa1anda2,andcallmyfitand
%myconstrwithtwoarguments.Finally,passtheseanonymousfunctionsto
%GA:
%a1=1;
a2=10;
%defineparametersfirst
%%Mutationfunctionforconstrainedminimization
%x=ga（@（x）myfit（x,a1）,2,[],[],[],[],[],[],@（x）myconstr（x,a2）,options）
%SeealsoGAOPTIMSET,FITNESSFUNCTION,GAOUTPUTFCNTEMPLATE,PATTERNSEARCH,@.
%Copyright2003-2010TheMathWorks,Inc.
%$Revision:
1.1.6.3$$Date:
2010/02/0822:
34:
19$
%Ifthefirstargisnotagaoptimset,thenit'
safitnessfunctionfollowedbyagenome
%length.Herewemakeagaoptimsetfromtheargs.
defaultopt=struct（'
PopulationType'
'
doubleVector'
...
'
PopInitRange'
[0;
1],...
PopulationSize'
20,...
EliteCount'
2,...
CrossoverFraction'
0.8,...
MigrationDirection'
'
forward'
MigrationInterval'
20,...
MigrationFraction'
0.2,...
Generations'
100,...
TimeLimit'
inf,...
FitnessLimit'
-inf,...
StallGenLimit'
50,...
StallTimeLimit'
TolFun'
1e-6,...
TolCon'
InitialPopulation'
[],...
InitialScores'
[],...
InitialPenalty'
10,...
PenaltyFactor'
PlotInterval'
1,...
CreationFcn'
@gacreationuniform,...
FitnessScalingFcn'
@fitscalingrank,...
SelectionFcn'
@selectionstochunif,...
CrossoverFcn'
@crossoverscattered,...
{{@mutationgaussian11}},...
HybridFcn'
Display'
final'
OutputFcns'
Vectorized'
off'
UseParallel'
never'
）;
%Checknumberofinputarguments
errmsg=nargchk（1,10,nargin）;
if~isempty（errmsg）
error（'
globaloptim:
ga:
numberOfInputs'
[errmsg,'
GArequiresatleast1inputargument.'
]）;
end
%Ifjust'
defaults'
passedin,returnthedefaultoptionsinX
ifnargin==1&
&
nargout<
=1&
isequal（fun,'
）
x=defaultopt;
return
ifnargin<
10,options=[];
ifnargin<
9,nonlcon=[];
8,ub=[];
7,lb=[];
6,beq=[];
5,Aeq=[];
4,bineq=[];
3,Aineq=[];
end
%Isthirdargumentastructure
ifnargin==3&
isstruct（Aineq）%Oldsyntax
options=Aineq;
Aineq=[];
%Oneinputargumentisforproblemstructure
ifnargin==1
ifisa（fun,'
struct'
[fun,nvars,Aineq,bineq,Aeq,beq,lb,ub,nonlcon,rngstate,options]=separateOptimStruct（fun）;
%Resettherandomnumbergenerators
resetDfltRng（rngstate）;
else%Singlei
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