# help pareto front?

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JL555 on 21 Apr 2016
Commented: Brendan Hamm on 21 May 2016
what does the 3rd line in 2nd function 'pickindex' mean? and what is 'k'?

Brendan Hamm on 21 Apr 2016
The function simple_mult contains two objective functions and returns the objective function evaluation of both of these objectives. That is
f(1) = sqrt(1+x.^2);
f(2) = 4 + 2*sqrt(1+(x-1).^2);
Since these functions will have different minimums we want to run the optimization on each of them separately. To do this we call this function inside of pickindex and then return only one of the solutions. So if k = 1, we are returned the sqrt(1+x.^2) evaluated at x and if k = 2, we get 4 + 2*sqrt(1+(x-1).^2) evaluated at x. Since the return depends on k, when we run the minimization fminbnd with a specified value of k we are minimizing the corresponding objective function from simple_mult.
JL555 on 21 Apr 2016
I tried implementing that for different objective functions but the error always pointed out to that 3rd line with "not enough input arguments"

Brendan Hamm on 21 Apr 2016
Edited: Brendan Hamm on 21 Apr 2016
1. Do your objective functions take exactly one input argument? I assume you have more based upon this error. 2. I can't really point out what the issue is with your objective functions without seeing your code. Please place your code in a comment and make sure to format it with the { } Code button (located at the top of the text box where you type your comments).
You can see that the code works with the following example. Try this create a function file called runPareto.m and define the file to look exactly as below:
function goal = runPareto
k = 1;
[min1,minfn1] = fminbnd(@(x)pickindex(x,k),-1,2);
k = 2;
[min2,minfn2] = fminbnd(@(x)pickindex(x,k),-1,2);
goal = [min1,min2];
end
function f = simple_mult(x)
f(:,1) = sqrt(1+x.^2);
f(:,2) = 4 + 2*sqrt(1+(x-1).^2);
end
function z = pickindex(x,k)
z = simple_mult(x); % evaluate both objectives
z = z(k); % return objective k
end
Now at the command line you can run:
goal = runPareto
and this should return to you the vector [0,1] (i.e. the x that minimizes each function).
JL555 on 20 May 2016
Sir,where are you?
Brendan Hamm on 21 May 2016
So, what exactly is the code you sent. There seem to be several files which somebody else wrote and one file which is un-commented. I am not sure how you intended these files to be called or what the relation is to your original problem which you posted. I am not going to pour through hundreds of lines of code searching for a similarity to the pareto front problem you mentioned. Provide some information if you would like me to spend any of my time on this.