3-objective optimization weights

2018 6 15
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更新时间：2018 6 19
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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

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Alan Weiss
Alan Weiss 2018-6-18
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
Jasmina Burek 2018-6-18
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
Alan Weiss 2018-6-19
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

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