function?membership=paretoset（X）

%?PARETOSET??To?get?the?Pareto?set?from?a?given?set?of?points.
%?synopsis:???????????membership?=paretoset?（objectiveMatrix）
%?where:
%???objectiveMatrix:?[number?of?points?X?number?of?objectives]?array
%???membership:??????[number?of?points?X?1]?logical?vector?to?indicate?if?ith
%????????????????????point?belongs?to?the?Pareto?set?（true）?or?not?（false）.
%
%?by?Yi?Cao?Cranfield?University?02?June?2007
%?Revised?by?Yi?Cao?on?17?October?2007
%?Version?3?21?October?2007?new?sorting?scheme?to?improve?speed.
%?Bugfix?25?July?2008?devided?by?zero?error?is?fixed.
%
%?Examples:?see?paretoset_examples
%

m=size（X1）;
Xmin=min（X）;
X1=X-Xmin（ones（m1）:）;?????%make?sure?X1>=0;
Xmean=mean（X1）;?
%sort?X1?so?that?dominated?points?can?be?removed?quickly
[xchecklist]=sort（max（X1./（Xmean（ones（m1）:）+max（Xmean））[]2））;
Y=X（checklist:）;??????????????????
membership=false（m1）;
while?numel（checklist）>1
????k=checklist（1）;
????[membership（k）checklistY]=paretosub（Ychecklist）;
end
membership（checklist）=true;

function?[isparetonondominatedX]=paretosub（Xchecklist）

Z=X-X（ones（size（X1）1）:）;
nondominated=any（Z<02）;????????????????????%retain?nondominated?points?from?the?check?list?????????????????????????
ispareto=all（any（Z（nondominated:）>02））;???%check?if?current?point?belongs?to?pareto?set????
X=X（nondominated:）;
nondominated=checklist（nondominated）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????1444??2014-04-03?12:56??paretosetV5\paretoset.m
?????文件????????1249??2014-04-03?12:56??paretosetV5\paretoset_examples.m
?????文件????????1306??2014-04-03?12:56??license.txt