function?nsga_2（）
%%?Main?Function
%?Main?program?to?run?the?NSGA-II?MOEA.
%?Read?the?corresponding?documentation?to?learn?more?about?multiobjective
%?optimization?using?evolutionary?algorithms.
%?initialize_variables?has?two?arguments;?First?being?the?population?size
%?and?the?second?the?problem?number.?‘1‘?corresponds?to?MOP1?and?‘2‘
%?corresponds?to?MOP2.

%%?Initialize?the?variables
%?Declare?the?variables?and?initialize?their?values
%?pop?-?population
%?gen?-?generations
%?pro?-?problem?number

pop?=?200;
gen?=?1000;
pro?=?1;

switch?pro
????case?1
????????%?M?is?the?number?of?objectives.
????????M?=?2;
????????%?V?is?the?number?of?decision?variables.?In?this?case?it?is
????????%?difficult?to?visualize?the?decision?variables?space?while?the
????????%?objective?space?is?just?two?dimensional.
????????V?=?6;
????case?2
????????M?=?3;
????????V?=?12;
end

%?Initialize?the?population
chromosome?=?initialize_variables（poppro）;


%%?Sort?the?initialized?population
%?Sort?the?population?using?non-domination-sort.?This?returns?two?columns
%?for?each?individual?which?are?the?rank?and?the?crowding?distance
%?corresponding?to?their?position?in?the?front?they?belong.?
chromosome?=?non_domination_sort_mod（chromosomepro）;

%%?Start?the?evolution?process

%?The?following?are?performed?in?each?generation
%?Select?the?parents
%?Perfrom?crossover?and?Mutation?operator
%?Perform?Selection

for?i?=?1?:?gen
????%?Select?the?parents
????%?Parents?are?selected?for?reproduction?to?generate?offspring.?The
????%?original?NSGA-II?uses?a?binary?tournament?selection?based?on?the
????%?crowded-comparision?operator.?The?arguments?are?
????%?pool?-?size?of?the?mating?pool.?It?is?common?to?have?this?to?be?half?the
????%????????population?size.
????%?tour?-?Tournament?size.?Original?NSGA-II?uses?a?binary?tournament
????%????????selection?but?to?see?the?effect?of?tournament?size?this?is?kept
????%????????arbitary?to?be?choosen?by?the?user.
????pool?=?round（pop/2）;
????tour?=?2;
????parent_chromosome?=?tournament_selection（chromosomepooltour）;

????%?Perfrom?crossover?and?Mutation?operator
????%?The?original?NSGA-II?algorithm?uses?Simulated?Binary?Crossover?（SBX）?and
????%?Polynomial?crossover.?Crossover?probability?pc?=?0.9?and?mutation
????%?probability?is?pm?=?1/n?where?n?is?the?number?of?decision?variables.
????%?Both?real-coded?GA?and?binary-coded?GA?are?implemented?in?the?original
????%?algorithm?while?in?this?program?only?the?real-coded?GA?is?considered.
????%?The?distribution?indeices?for?crossover?and?mutation?operators?as?mu?=?20
????%?and?mum?=?20?respectively.
????mu?=?20;
????mum?=?20;
????offspring_chromosome?=?genetic_operator（parent_chromosomepromumum）;

????%?Intermediate?population
????%?Intermediate?population?is?the?combined?population?of?parents?and
????%?offsprings?of?the?current?generation.?The?population?size?is?almost?1?and
????%?half?times?the?initial?population.

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----

?????文件???????4670??2006-03-07?16:48??nsga_2.m

-----------?---------??----------?-----??----

?????????????????4888????????????????????2