How can I find a Pareto optimal using weighted sum method in Multi objective optimization ?

Hi All,

I am new to the MOOP problem. I would like to find out pareto optimal front using weighted sum method. So I tried the following code,

objective1=x3+y2;

objective2=y2-4x;

x0=[1,1];

w1=linspace(0,1,N);

w2=1-w1;

sol=nan(3,N);

for i=1:N

FWS=@(x) w1(i)* (x).^3 +(y).^2 + w2(i)* (y).^2 - 4x;

%sol(:,i)=fminunc(FWS,x0(:));

[x,fval] = fminunc(FWS,x0);

end

Finally I got the error like,

Error using fminunc (line 368)

Supplied objective function must return a scalar value.

Can anyone help me to clear this problem really appreciated?

Thanks

Answer 1

[Alan Weiss]

There are several approaches to finding Pareto fronts. This example uses fgoalattain, but you can easily modify it to use fminunc.

Alan Weiss

MATLAB mathematical toolbox documentation