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This code is a part of coding a mutiobjective genetic algorithm, the algorithm for this code is the following:

- Initialization: Q=Ro; ND= ϕ, Ro is the initial population
- Randomly select a row x of Q, and set Q=Q-{x} [here I mean remove the row x from Q], RK= ϕ , R= ϕ
- while ( Q ≠ ϕ)

- for each y in Q do,
- if x dominates y, then remove y from Q and update Q {Q=Q-{y}}
- elseif, y dominates x then update x=y; and update Q by removing y from Q, Q=Q-{y}, RK=RK ∪ R then update R= ϕ [but since they are matrices so I use RK=[RK;R]; ]
- else, R= R ∪ {y} [I used R=[R;Y]; ], update Q by removing the row y from it
- end(if)
- end(do)

4. Take all the rows y in RK which are not dominated by x and put them in a matrix RKK

5.ND=[ND;x];

6.Q=[RKK;R];

7. If the number of rows in Q >1 then go to step 2, otherwise set ND=[ND;Q]; stop

in the code:

output=FD( x,y,Nvar,perci,Lb,Ub); is a function I wrote takes the rows/individuals x,y and returns 2 by Nvar*perci matrix named output, where the first row is the non-dominated individual and the second is the dominated one

Remark: In FD, 2 individuals/rows x,y has 3 outputs either x dominates y or y dominates x or no one dominates the other

in the first 2 cases FD returns: a matrix, 2 by Nvar*perci matrix named output, where the first row is the non-dominated individual and the second is the dominated one, in the third case it returns a matrix: output or 2 rows and Nvar*perci cols where each element in it is INF

I hope someone can help me because I am a beginner in MATLAB.

Thanks

Nind=100; %number of individuals to begin with

Nvar=1; %number of the decision variables

perci=10; %number of bits of every decision variable

Ro=crtbp(Nind,Nvar*perci); %random matrix of 0 and 1

%each element in it, is either 0 or 1

%crtbp is a function from GA toolbox

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function[Fronts,ranks]=IMPARENA(Nvar,perci,Ro,Lb,Ub)

iii=1; DOM=[]; ranks=[]; Lb=-100; Ub=100;

while ~isempty(Ro)

Q=Ro; carQ=size(Q,1);

ND=[];

while carQ>1

x=Q(1,:);

Q=Q(2:end,1:end); %remove x from Q

RK=[]; R=[]; RKK=[];

while ~isempty(Q) %while Q is not empty

y=Q(1,:); %let y be the first row in Q

output=FD( x,y,Nvar,perci,Lb,Ub); %check the dominance between y and x

if norm(x- output(1,1:end))==0 %if x dom y

%remove y from Q;

Q(all(Q==repmat(y,size(Q,1),1),2),:)=[];

elseif norm(y-output(1,1:end))==0 %if y dom x

x=y;

%remove y from Q

Q(all(Q==repmat(y,size(Q,1),1),2),:)=[];

RK=[RK;R]; R=[];

else

R=[R;y];

%remove y from Q

Q(all(Q==repmat(y,size(Q,1),1),2),:)=[];

end

if ~isempty(RK)

for j=1:size(RK,1)

rr=RK(j,1:end);

output=FD(x,rr,Nvar,perci,Lb,Ub);

if norm(x-output(1,1:end))~=0 %x~=output(1,1:end)

RKK=[RKK;rr];

else

j=j+1;

end

end

end

ND=[ND;x];

QSS=[RKK;R]; %%the code gets stuck here%%%

Q=QSS;

carQ=size(Q,1);

if carQ>1

break;

end

end

end

ND=[ND;Q];

%%%%%%%%%%%%%%%%%%%%%%%%%

UND=unique(ND, 'rows', 'stable');

ND=UND;

%%%%%%%%%%%

DOM=[DOM;ND];

%%%%%%

%assigning ranks

rD=iii*ones(size(ND,1),1);

ranks=[ranks;rD];

iii=iii+1;

%%%%%%%%%%%%%%%

C=setdiff(Ro,ND,'rows');

Ro=C;

end

%%%%%%%%%END%%%%%%%%%%%%

Fronts=[DOM];

ranks;

end

Matlab tell me that the error at the line I referred to but I don't understand why it tells me:

QSS is 1x10 double, RKK 0X0 empty double and R is 2x10 double

and that Q is empty 0x10 double!

Why? and what does it mean?

EDIT: The code sometimes work and sometimes it gets stuck, so maybe there is something computational that happens

because every time crtbp generates a different random binary matrix Ro

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