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Vectorized fitness function for ga

Asked by Emiliano Rosso on 3 Sep 2015
Latest activity Edited by Alan Weiss
on 4 Sep 2015
I'm not very experienced in vectorization and I have not found something of interesting on internet.I've built a fitness function for genetic algorithm but I did not understand very well if I have to vectorize all components (as in the second code) or if it's sufficient to vectorize function's input "variables".(variables is composed by 8200 integer variables).Initial population is composed by 100 components. In both cases I have errors:
for code 1 :
Subscripted assignment dimension mismatch.
Error in GeneticPattern (line 27) tempvariables(i,j)=variables(:,j+(82.*(i-1)));
code 1
function my_y=GeneticPattern(variables)
global inputs;global fval;global Nvar;global LB;global UB;global IntCon;global option;
global final_pop;global exitflag;global GAoutput;global indicatorrange;global inputrange;
global tempvariables;global inputstemp;global classi;global Nneuron;global targets; global tr;
global GAfilter;global GAPOP;
[m,n]=size(inputs);
nimp=1:n;
nset=1:100;
nvar=1:82;
nindy=1:5;
nforex=1:6;
nprice=1:11;
npart=1:33;
tempvariables(nset,nvar)=0;
inputstemp(nset,npart,nimp)=0;
classi(nset,nindy,nimp)=0;
cutindy=[20,15,10,5,3,1];
%tempvariables(:,nset,nvar)=variables(:,nvar+(82.*(nset-1)));
for i=1:numel(nset)
for j=1:numel(nvar)
tempvariables(i,j)=variables(:,j+(82.*(i-1))); %line 27
end
end
if tempvariables(nset,2+(nindy-1).*3)==1
if inputs(33.*6+nindy,nimp)<=indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(nset,1+(nindy-1).*3)
classi(nset,nindy,nimp)=1;
end
end
if tempvariables(nset,2+(nindy-1).*3)==2
if inputs(33.*6+nindy,nimp)>=indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(nset,1+(nindy-1).*3)
classi(nset,nindy,nimp)=1;
end
end
if tempvariables(nset,2+(nindy-1).*3)==3 & tempvariables(nset,3+(nindy-1).*3)~=5
if inputs(33.*6+nindy,nimp)>=indicatorrange(1+(nindy-1).*2) && inputs(33.*6+nindy,nimp)<=indicatorrange(2+(nindy-1).*2)
if inputs(33.*6+nindy,nimp)>=indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(nset,1+(nindy-1).*3)...
-((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(nset,3+(nindy-1).*3)))./2 && ...
inputs(33.*6+nindy,nimp)<indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(nset,1+(nindy-1).*3)...
+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(nset,3+(nindy-1).*3)))./2
classi(nset,nindy,nimp)=1;
end
end
if inputs(33.*6+nindy,nimp)<indicatorrange(1+(nindy-1).*2) && ...
indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(nset,1+(nindy-1).*3)...
-((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(nset,3+(nindy-1).*3)))./2 ...
<indicatorrange(1+(nindy-1).*2)
classi(nset,nindy,nimp)=1;
end
if inputs(33.*6+nindy,nimp)>indicatorrange(2+(nindy-1).*2) && ...
indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(nset,1+(nindy-1).*3)...
+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(nset,3+(nindy-1).*3)))./2 ...
>indicatorrange(2+(nindy-1).*2)
classi(nset,nindy,nimp)=1;
end
end
if tempvariables(nset,2+(nindy-1).*3)==3 & tempvariables(nset,3+(nindy-1).*3)==5
classi(nset,nindy,nimp)=1;
end
if classi(nset,1,nimp)==1 & classi(nset,2,nimp)==1 & classi(nset,3,nimp)==1 & classi(nset,4,nimp)==1 & classi(nset,5,nimp)==1
if tempvariables(nset,18+(npart-1).*2)~=5
if inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)<=inputrange(npart+(33.*tempvariables(nset,16)-1),2) && ...
inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)>=inputrange(npart+(33.*tempvariables(nset,16)-1),1)
if inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)<inputrange(npart+(33.*tempvariables(nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./11.*tempvariables(nset,17+(npart-1).*2)...
+ (inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./cutindy(tempvariables(nset,18+(npart-1).*2))./2 &&...
inputs(npart+(33.*tempvariables(nset,16)-1),nimp)>=inputrange(npart+(33.*tempvariables(nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./11.*tempvariables(nset,17+(npart-1).*2)...
-(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./cutindy(tempvariables(nset,18+(npart-1).*2))./2
inputstemp(nset,npart,nimp)=1-(abs(inputs(npart+(33.*tempvariables(nset,16)-1),nimp)-(inputrange(npart+(33.*tempvariables(nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./11.*tempvariables(nset,17+(npart-1).*2))))...
./((inputrange(npart+(33.*tempvariables(nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./11.*tempvariables(nset,17+(npart-1).*2))...
-abs((inputrange(npart+(33.*tempvariables(nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./11.*tempvariables(nset,17+(npart-1).*2))-(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./cutindy(tempvariables(nset,18+(npart-1).*2))./2));
end
end
if inputs(npart+(33.*tempvariables(nset,16)-1),nimp)<inputrange(npart+(33.*tempvariables(nset,16)-1),1) && ...
inputrange(npart+(33.*tempvariables(nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(nset,17+(npart-1).*2)...
-(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./cutindy(tempvariables(nset,18+(npart-1).*2))./2 ...
<inputrange(npart+(33.*tempvariables(nset,16)-1),1)
inputstemp(nset,npart,nimp)=1;
end
if inputs(npart+(33.*tempvariables(nset,16)-1),nimp)>inputrange(npart+(33.*tempvariables(nset,16)-1),2) && ...
inputrange(npart+(33.*tempvariables(nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./11.*tempvariables(nset,17+(npart-1).*2)...
+ (inputrange(npart+(33.*tempvariables(nset,16)-1),2)-inputrange(npart+(33.*tempvariables(nset,16)-1),1))./cutindy(tempvariables(nset,18+(npart-1).*2))./2 ...
>inputrange(npart+(33.*tempvariables(nset,16)-1),2)
inputstemp(nset,npart,nimp)=1;
end
else
inputstemp(nset,npart,nimp)=1;
end
end
STDinputs(nset,nimp)=0;
AVinputs(nset,nimp)=0;
STDinputs(nset,nimp)=std(inputstemp,0,2);
AVinputs(nset,nimp)=mean(inputstemp,2);
inputstemp2(nset,nimp)=0;
inputstemp2(nset,nimp)=AVinputs(nset,nimp)-STDinputs(nset,nimp);
if GAfilter{1,1}(1,1)~=0
if inputstemp2(nset,nimp)<GAfilter{1,1}(1,1)
inputstemp2(nset,nimp)=0;
end
end
clear('l','k','i','j','n','m','nimp','nset','nvar','nindy','nforex','nprice','npart','cutindy','mycut','STDinputs','AVinputs');
myneuron=double(Nneuron{1,1}(1,1));
mynet=fitnet(myneuron(1,1));
mynet.trainFcn= 'trainlm';
mynet.biasConnect = [1;1];
mynet.inputs{1}.processFcns = {};
mynet.outputs{2}.processFcns = {};
mynet.divideFcn = 'divideblock';
mynet.divideParam.trainRatio = 80/100;
mynet.divideParam.valRatio = 10/100;
mynet.divideParam.testRatio = 10/100;
mynet.trainParam.showWindow = false;
mynet.trainParam.showCommandLine = false;
mynet.trainParam.epochs=100;
mynet.layers{1}.transferFcn = 'tansig';
mynet.layers{2}.transferFcn = 'tansig';
mynet.efficiency.memoryReduction=1;
[mynet,tr]=train(mynet,inputstemp2,targets);
if tr.best_vperf>=tr.best_tperf
my_y=tr.best_vperf;
else
my_y=tr.best_tperf;
end
clear('myneuron','inputstemp2','mynet');
end
for code 2:
Assignment has more non-singleton rhs dimensions than non-singleton subscripts
Error in GeneticPattern (line 29) tempvariables(:,i,j)=variables(:,j+(82.*(i-1)));
code 2
function my_y=GeneticPattern(variables)
global inputs;global fval;global Nvar;global LB;global UB;global IntCon;global option;
global final_pop;global exitflag;global GAoutput;global indicatorrange;global inputrange;
global tempvariables;global inputstemp;global classi;global Nneuron;global targets; global tr;
global GAfilter;global GAPOP;global myvariables;
[m,n]=size(inputs);
nimp1=1:n;
nset1=1:100;
nvar=1:82;
nindy1=1:5;
nforex=1:6;
nprice=1:11;
npart1=1:33;
tempvariables(:,nset1,nvar)=0;
inputstemp(:,nset1,npart1,nimp1)=0;
classi(:,nset1,nindy1,nimp1)=0;
cutindy=[20,15,10,5,3,1];
%tempvariables(:,nset,nvar)=variables(:,nvar+(82.*(nset-1)));
%myvariables=variables;
for i=1:numel(nset1)
for j=1:numel(nvar)
tempvariables(:,i,j)=variables(:,j+(82.*(i-1))); %line 29
end
end
for nset=1:100
for nindy=1:5
for nimp=1:n
if tempvariables(:,nset,2+(nindy-1).*3)==1
if inputs(33.*6+nindy,nimp)<=indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(:,nset,1+(nindy-1).*3)
classi(:,nset,nindy,nimp)=1;
end
end
if tempvariables(:,nset,2+(nindy-1).*3)==2
if inputs(33.*6+nindy,nimp)>=indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(:,nset,1+(nindy-1).*3)
classi(:,nset,nindy,nimp)=1;
end
end
if tempvariables(:,nset,2+(nindy-1).*3)==3 & tempvariables(:,nset,3+(nindy-1).*3)~=5
if inputs(33.*6+nindy,nimp)>=indicatorrange(1+(nindy-1).*2) && inputs(33.*6+nindy,nimp)<=indicatorrange(2+(nindy-1).*2)
if inputs(33.*6+nindy,nimp)>=indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(:,nset,1+(nindy-1).*3)...
-((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(:,nset,3+(nindy-1).*3)))./2 && ...
inputs(33.*6+nindy,nimp)<indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(:,nset,1+(nindy-1).*3)...
+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(:,nset,3+(nindy-1).*3)))./2
classi(:,nset,nindy,nimp)=1;
end
end
if inputs(33.*6+nindy,nimp)<indicatorrange(1+(nindy-1).*2) && ...
indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(:,nset,1+(nindy-1).*3)...
-((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(:,nset,3+(nindy-1).*3)))./2 ...
<indicatorrange(1+(nindy-1).*2)
classi(:,nset,nindy,nimp)=1;
end
if inputs(33.*6+nindy,nimp)>indicatorrange(2+(nindy-1).*2) && ...
indicatorrange(1+(nindy-1).*2)+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./11).*tempvariables(:,nset,1+(nindy-1).*3)...
+((indicatorrange(2+(nindy-1).*2)-indicatorrange(1+(nindy-1).*2))./cutindy(tempvariables(:,nset,3+(nindy-1).*3)))./2 ...
>indicatorrange(2+(nindy-1).*2)
classi(:,nset,nindy,nimp)=1;
end
end
if tempvariables(:,nset,2+(nindy-1).*3)==3 & tempvariables(:,nset,3+(nindy-1).*3)==5
classi(:,nset,nindy,nimp)=1;
end
end
end
end
for nset=1:100
for npart=1:33
for nimp=1:n
if classi(:,nset,1,nimp)==1 & classi(:,nset,2,nimp)==1 & classi(:,nset,3,nimp)==1 & classi(:,nset,4,nimp)==1 & classi(:,nset,5,nimp)==1
if tempvariables(:,nset,18+(npart-1).*2)~=5
if inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)<=inputrange(npart+(33.*tempvariables(:,nset,16)-1),2) && ...
inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)>=inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)
if inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)<inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(:,nset,17+(npart-1).*2)...
+ (inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./cutindy(tempvariables(:,nset,18+(npart-1).*2))./2 &&...
inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)>=inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(:,nset,17+(npart-1).*2)...
-(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./cutindy(tempvariables(:,nset,18+(npart-1).*2))./2
inputstemp(:,nset,npart,nimp)=1-(abs(inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)-(inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(:,nset,17+(npart-1).*2))))...
./((inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(:,nset,17+(npart-1).*2))...
-abs((inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(:,nset,17+(npart-1).*2))-(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./cutindy(tempvariables(:,nset,18+(npart-1).*2))./2));
end
end
if inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)<inputrange(npart+(33.*tempvariables(:,nset,16)-1),1) && ...
inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(:,nset,17+(npart-1).*2)...
-(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./cutindy(tempvariables(:,nset,18+(npart-1).*2))./2 ...
<inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)
inputstemp(:,nset,npart,nimp)=1;
end
if inputs(npart+(33.*tempvariables(:,nset,16)-1),nimp)>inputrange(npart+(33.*tempvariables(:,nset,16)-1),2) && ...
inputrange(npart+(33.*tempvariables(:,nset,16)-1),1)+(inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./11.*tempvariables(:,nset,17+(npart-1).*2)...
+ (inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)-inputrange(npart+(33.*tempvariables(:,nset,16)-1),1))./cutindy(tempvariables(:,nset,18+(npart-1).*2))./2 ...
>inputrange(npart+(33.*tempvariables(:,nset,16)-1),2)
inputstemp(:,nset,npart,nimp)=1;
end
else
inputstemp(:,nset,npart,nimp)=1;
end
end
end
end
end
STDinputs(:,nset1,nimp1)=0;
AVinputs(:,nset1,nimp1)=0;
STDinputs(:,nset1,nimp1)=std(inputstemp,0,3);
AVinputs(:,nset1,nimp1)=mean(inputstemp,3);
inputstemp2(:,nset1,nimp1)=0;
inputstemp2(:,nset1,nimp1)=AVinputs(:,nset1,nimp1)-STDinputs(:,nset1,nimp1);
if GAfilter{1,1}(1,1)~=0
if inputstemp2(:,nset1,nimp1)<GAfilter{1,1}(1,1)
inputstemp2(:,nset1,nimp1)=0;
end
end
for i=1:100
for l=1:n
myinputsvect(:).myinputs(i,l)= inputstemp2(:,i,l);
end
end
clear('l','k','i','j','n','m','nimp','nset','nvar','nindy','nforex','nprice','npart','cutindy','mycut','STDinputs','AVinputs');
clear('nset1','nindy1','nimp1','npart1','inputstemp2');
myneuron=double(Nneuron{1,1}(1,1));
myvect(:).mynet=fitnet(myneuron(1,1));
myvect(:).mynet.trainFcn= 'trainlm';
myvect(:).mynet.biasConnect = [1;1];
myvect(:).mynet.inputs{1}.processFcns = {};
myvect(:).mynet.outputs{2}.processFcns = {};
myvect(:).mynet.divideFcn = 'divideblock';
myvect(:).mynet.divideParam.trainRatio = 80/100;
myvect(:).mynet.divideParam.valRatio = 10/100;
myvect(:).mynet.divideParam.testRatio = 10/100;
myvect(:).mynet.trainParam.showWindow = false;
myvect(:).mynet.trainParam.showCommandLine = false;
myvect(:).mynet.trainParam.epochs=100;
myvect(:).mynet.layers{1}.transferFcn = 'tansig';
myvect(:).mynet.layers{2}.transferFcn = 'tansig';
myvect(:).mynet.efficiency.memoryReduction=1;
[myvect(:).mynet,mytr(:).tr]=train(myvect(:).mynet,myinputsvect(:).myinputs,targets);
if mytr(:).tr.best_vperf>=mytr(:).tr.best_tperf
my_y=mytr(:).tr.best_vperf;
else
my_y=mytr(:).tr.best_tperf;
end
clear('myneuron');
end
Somebody can explain me what's wrong? Thanks

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1 Answer

Answer by Alan Weiss
on 3 Sep 2015
 Accepted Answer

It is difficult to look at your code and figure out what you are trying to do. In "code 1" you have the line
tempvariables(i,j)=variables(:,j+(82.*(i-1))); %line 27
What do you think that tempvariables(i,j) should be here? i and j have particular values, so tempvariables(i,j) should have just one value.
If you are trying to set a whole piece of a matrix at once, you have to index that piece properly, and ensure that the left and right sides of the assignment statement have the same number of elements and orientation.
For example, if you have a matrix A and a matrix B, and you want to set column 5 of matrix A to equal column 4 of matrix B plus 6 times column 7 of matrix B, you could write
A(:,5) = B(:,4) + 6*B(:,7);
Similarly, if you want to do the same with rows of the matrices, you would write
A(5,:) = B(4,:) + 6*B(7,:);
I hope that this helps. For more information, see the colon operator reference page.
Alan Weiss
MATLAB mathematical toolbox documentation

  2 Comments

variables is 1X8200 , vectorization uses it ":" times.When I build tempvariables I want to create an array of dimension 100X82 for better use in my code.I don't know if vectorization uses the objective function ":" times and every time I need to assign tempvariables to the ":" line of variables or if tempvariables must contain all ":" lines to calculate all function's output at once.In the first case I must vectorize only "variables" as it seems looking Matlab manuals,in the second I must vectorize all the function 's component.I tried both but I have different errors,
I am not sure that I understand your problem. As the documentation states, for ga you vectorize the fitness function by having it accept a matrix with an arbitrary number of rows, and return a column vector giving the fitness function for each row. Each row represents one individual, and the matrix represents the entire population.
Generally, you use the colon operator : to represent the list of rows (individuals) in the matrix (population). For example,
fun = x(:,1).^2 - x(:,2).^3
is a vectorized form of the fitness function x(1)^2 - x(2)^3.
Alan Weiss
MATLAB mathematical toolbox documentation

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