3-objective optimization weights

I need a weight function for 3-objective optimization that will look like weights proposed in attachment. Is there a way to present this matrix as a function? Thank you for your help.

Jasmina

[Alan Weiss]

Sorry, I have no idea what you are asking. You need a "weight function for a 3-objective optimization" where the weights add up to one and are positive. What does that mean? You want a function that gives three weights that are positive and add to one, and what else? For example, here is a function: f(x) = [1/3,1/3,1/3]. What is wrong with that? If you can say what you want, then we might be able to help you.

Alan Weiss

MATLAB mathematical toolbox documentation

[Jasmina Burek]

Hi Alan, Thank you for your reply. I attached a figure in my original post how the weights should look like, but more gradual. For example, for two-objective optimization problem I used weight=[t(1,r),1-(t(1,r))]; t = linspace(0,1,N); I want to avoid listing all the weights as a matrix. Thank you for your help.

[Alan Weiss]

Again, I do not understand what you want. For three-objective optimization, based on your latest comment, I would use

t = linspace(0,1,N)';
w1 = [t,(1-t)/2,(1-t)/2];
w2 = [(1-t)/2,t,(1-t)/2];
w3 = [(1-t)/2,(1-t)/2,t];

The rows of w1, w2, or w3 seem to me to satisfy your requirement. But I believe that you know this already, so again do not understand what you want.

Alan Weiss

MATLAB mathematical toolbox documentation