NSGAII源程序.docx
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NSGAII源程序
functionf=crowding_distance（x,problem）
%Thisfunctioncalculatesthecrowdingdistance
[N,M]=size（x）;
switchproblem
case1
M=2;
V=6;
case2
M=3;
V=12;
end
%Crowdingdistanceforeachfront
fori=1:
length（F（front）.f）
y（i,:
）=x（F（front）.f（i）,:
）;
end
fori=1:
M
[sorted（i）.individual,sorted（i）.index]=sort（y（:
V+i））;
distance（sorted（i）.index
（1））.individual=Inf;
distance（sorted（i）.index（length（sorted（i）.index）））.individual=Inf;
end
[num,len]=size（y）;
%Initializeallthedistanceofindividualsaszero.
fori=1:
M
forj=2:
num-1
distance（j）.individual=0;
end
objective（i）.range=...
sorted（i）.individual（length（sorted（i）.individual））-...
sorted（i）.individual
（1）;
%Maximumandminimumobjectivesvaluefortheithobjective
end
%Caluclatethecrowdingdistanceforfrontone.
fori=1:
M
forj=2:
num-1
distance（j）.individual=distance（j）.individual+...
（sorted（i）.individual（j+1）-sorted（i）.individual（j-1））/...
objective（i）.range;
y（sorted（i）.index（j）,M+V+2）=distance（j）.individual;
end
end
PublishedwithMATLAB®7.0
functionf=genetic_operator（parent_chromosome,pro,mu,mum）;
%Thisfunctionisutilizedtoproduceoffspringsfromparentchromosomes.
%Thegeneticoperatorscorssoverandmutationwhicharecarriedoutwith
%slightmodificationsfromtheoriginaldesign.Formoreinformationread
%thedocumentenclosed.
[N,M]=size（parent_chromosome）;
switchpro
case1
M=2;
V=6;
case2
M=3;
V=12;
end
p=1;
was_crossover=0;
was_mutation=0;
l_limit=0;
u_limit=1;
fori=1:
N
ifrand
（1）<0.9
child_1=[];
child_2=[];
parent_1=round（N*rand
（1））;
ifparent_1<1
parent_1=1;
end
parent_2=round（N*rand
（1））;
ifparent_2<1
parent_2=1;
end
whileisequal（parent_chromosome（parent_1,:
）,parent_chromosome（parent_2,:
））
parent_2=round（N*rand
（1））;
ifparent_2<1
parent_2=1;
end
end
parent_1=parent_chromosome（parent_1,:
）;
parent_2=parent_chromosome（parent_2,:
）;
forj=1:
V
%SBX（SimulatedBinaryCrossover）
%Generatearandomnumber
u（j）=rand
（1）;
ifu（j）<=0.5
bq（j）=（2*u（j））^（1/（mu+1））;
else
bq（j）=（1/（2*（1-u（j））））^（1/（mu+1））;
end
child_1（j）=...
0.5*（（（1+bq（j））*parent_1（j））+（1-bq（j））*parent_2（j））;
child_2（j）=...
0.5*（（（1-bq（j））*parent_1（j））+（1+bq（j））*parent_2（j））;
ifchild_1（j）>u_limit
child_1（j）=u_limit;
elseifchild_1（j）child_1（j）=l_limit;
end
ifchild_2（j）>u_limit
child_2（j）=u_limit;
elseifchild_2（j）child_2（j）=l_limit;
end
end
child_1（:
V+1:
M+V）=evaluate_objective（child_1,pro）;
child_2（:
V+1:
M+V）=evaluate_objective（child_2,pro）;
was_crossover=1;
was_mutation=0;
else
parent_3=round（N*rand
（1））;
ifparent_3<1
parent_3=1;
end
%Makesurethatthemutationdoesnotresultinvariablesoutof
%thesearchspace.ForboththeMOP'stherangefordecisionspace
%is[0,1].Incasedifferentvariableshavedifferentdecision
%spaceeachvariablecanbeassignedarange.
child_3=parent_chromosome（parent_3,:
）;
forj=1:
V
r（j）=rand
（1）;
ifr（j）<0.5
delta（j）=（2*r（j））^（1/（mum+1））-1;
else
delta（j）=1-（2*（1-r（j）））^（1/（mum+1））;
end
child_3（j）=child_3（j）+delta（j）;
ifchild_3（j）>u_limit
child_3（j）=u_limit;
elseifchild_3（j）child_3（j）=l_limit;
end
end
child_3（:
V+1:
M+V）=evaluate_objective（child_3,pro）;
was_mutation=1;
was_crossover=0;
end
ifwas_crossover
child（p,:
）=child_1;
child（p+1,:
）=child_2;
was_cossover=0;
p=p+2;
elseifwas_mutation
child（p,:
）=child_3（1,1:
M+V）;
was_mutation=0;
p=p+1;
end
end
f=child;
PublishedwithMATLAB®7.0
functionf=initialize_variables（N,problem）
%functionf=initialize_variables（N,problem）
%N-Populationsize
%problem-takesintegervalues1and2where,
%'1'forMOP1
%'2'forMOP2
%
%ThisfunctioninitializesthepopulationwithNindividualsandeach
%individualhavingMdecisionvariablesbasedontheselectedproblem.
%M=6forproblemMOP1andM=12forproblemMOP2.Theobjectivespace
%forMOP1is2dimensionalwhileforMOP2is3dimensional.
%BoththeMOP'shas0to1asitsrangeforallthedecisionvariables.
min=0;
max=1;
switchproblem
case1
M=6;
K=8;
case2
M=12;
K=15;
end
fori=1:
N
%Initializethedecisionvariables
forj=1:
M
f（i,j）=rand
（1）;%i.ef（i,j）=min+（max-min）*rand
（1）;
end
%Evaluatetheobjectivefunction
f（i,M+1:
K）=evaluate_objective（f（i,:
）,problem）;
end
PublishedwithMATLAB®7.0
Non-DonimationSort
Thisfunctionsortthecurrentpopultionbasedonnon-domination.Alltheindividualsinthefirstfrontaregivenarankof1,thesecondfrontindividualsareassignedrank2andsoon.Afterassigningtherankthecrowdingineachfrontiscalculated.
[N,M]=size（x）;
switchproblem
case1
M=2;
V=6;
case2
M=3;
V=12;
end
front=1;
%Thereisnothingtothisassignment,usedonlytomanipulateeasilyin
%MATLAB.
F（front）.f=[];
individual=[];
fori=1:
N
%Numberofindividualsthatdominatethisindividual
individual（i）.n=0;
%Individualswhichthisindividualdominate
individual（i）.p=[];
forj=1:
N
dom_less=0;
dom_equal=0;
dom_more=0;
fork=1:
M
if（x（i,V+k）dom_less=dom_less+1;
elseif（x（i,V+k）==x（j,V+k））
dom_equal=dom_equal+1;
else
dom_more=dom_more+1;
end
end
ifdom_less==0&dom_equal~=M
individual（i）.n=individual（i）.n+1;
elseifdom_more==0&dom_equal~=M
individual（i）.p=[individual（i）.pj];
end
end
ifindividual（i）.n==0
x（i,M+V+1）=1;
F（front）.f=[F（front）.fi];
end
end
%Findthesubsequentfronts
while~isempty（F（front）.f）
Q=[];
fori=1:
length（F（front）.f）
if~isempty（individual（F（front）.f（i））.p）
forj=1:
length（individual（F（front）.f（i））.p）
individual（individual（F（front）.f（i））.p（j））.n=...
individual（individual（F（front）.f（i））.p（j））.n-1;
ifindividual（individual（F（front）.f（i））.p（j））.n==0
x（individual（F（front）.f（i））.p（j）,M+V+1）=...
front+1;
Q=[Qindividual（F（front）.f（i））.p（j）];
end
end
end
end
front=front+1;
F（front）.f=Q;
end
[temp,index_of_fronts]=sort（x（:
M+V+1））;
fori=1:
length（index_of_fronts）
sorted_based_on_front（i,:
）=x（index_of_fronts（i）,:
）;
end
current_index=0;
%Findthecrowdingdistanceforeachindividualineachfront
forfront=1:
（length（F）-1）
objective=[];
distance=0;
y=[];
previous_index=current_index+1;
fori=1:
length（F（front）.f）
y（i,:
）=sorted_based_on_front（current_index+i,:
）;
end
current_index=current_index+i;
%Sorteachindividualbasedontheobjective
sorted_based_on_objective=[];
fori=1:
M
[sorted_based_on_objective,index_of_objectives]=...
sort（y（:
V+i））;
sorted_based_on_objective=[];
forj=1:
length（index_of_objectives）
sorted_based_on_objective（j,:
）=y（index_of_objectives（j）,:
）;
end
f_max=...
sorted_based_on_objective（length（index_of_objectives）,V+i）;
f_min=sorted_based_on_objective（1,V+i）;
y（index_of_objectives（length（index_of_objectives））,M+V+1+i）...
=Inf;
y（index_of_objectives
（1）,M+V+1+i）=Inf;
forj=2:
length（index_of_objectives）-1
next_obj=sorted_based_on_objective（j+1,V+i）;
previous_obj=sorted_based_on_objective（j-1,V+i）;
if（f_max-f_min==0）
y（index_of_objectives（j）,M+V+1+i）=Inf;
else
y（index_of_objectives（j）,M+V+1+i）=...
（next_obj-previous_obj）/（f_max-f_min）;
end
end
end
distance=[];
distance（:
1）=zeros（length（F（front）.f）,1）;
fori=1:
M
distance（:
1）=distance（:
1）+y（:
M+V+1+i）;
end
y（:
M+V+2）=distance;
y=y（:
1:
M+V+2）;
z（previous_index:
current_index,:
）=y;
end
f=z（）;
PublishedwithMATLAB®7.0
MainFunction
MainprogramtoruntheNSGA-IIMOEA.Readthecorrespondingdocumentationtolearnmoreaboutmultiobjectiveoptimizationusingevolutionaryalgorithms.initialize_variableshastwoarguments;Firstbeingthepopulationsizeandthesecondtheproblemnumber.'1'correspondstoMOP1and'2'correspondstoMOP2.
Contents
∙Initializethevariables
∙Sorttheinitializedpopulation
∙Starttheevolutionprocess
∙Result
∙Visualize
Initializethevariables
Declarethevariablesandinitializetheirvaluespop-populationgen-generationspro-problemnumber
pop=200;
gen=1;
pro=1;
switchpro
case1
%Misthenumberofobjectives.
M=2;
%Visthenumberofdecisionvariables.Inthiscaseitis
%difficulttovisualizethedecisionvariablesspacewhilethe
%objectivespaceisjusttwodimensional.
V=6;
case2
M=3;
V=12;
end
%Initializethepopulation
chromosome=initialize_variables（pop,pro）;
Sorttheinitializedpopulation
Sortthepopulationusingnon-domination-sort.Thisreturnstwocolumnsforeachindividualwhicharetherankandthecrowdingdistancecorrespondingtotheirpositioninthefronttheybelong.
chromosome=non_domination_sort_mod（chromosome,pro）;
Starttheevolutionprocess
%Thefollowingareperformedineachgeneration
%Selecttheparents
%PerfromcrossoverandMutationoperator
%PerformSelection
fori=1:
gen
%Selecttheparents
%Parentsareselectedforreproductiontogenerateoffspring.The
%originalNSGA-IIusesabinarytournamentselectionbasedonthe
%crowded-comparisionoperator.Theargumentsare
%pool-sizeofthematingpool.Itiscommontohavethistobehalfthe
%populationsize.
%tour-Tournamentsiz
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