how I found W1,W2 ?
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f= w1 F1(x) + w2 F2(x)
Consider the problem for minimize F1(x)and maximize F2(x)
Wi = weight value
how I found W1,W2 ? help me please!!
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Answers (2)
John D'Errico
on 2 Apr 2018
Edited: John D'Errico
on 2 Apr 2018
Huh?
First, you would simply minimize
f = w1*F1(x) - w2*F2(x)
for some choice of positive w1 and w2.
But ONLY YOU can choose the values of w1 and w2. They would represent the relative importance of these two functions, as well as the relative scaling of the two functions, to make them both of roughly the same size.
Completely your choice though.
You might want to do some reading here:
https://en.wikipedia.org/wiki/Multi-objective_optimization
https://en.wikipedia.org/wiki/Pareto_efficiency
Walter Roberson
on 2 Apr 2018
F1(x) and F2(x) are whatever they are. Changing w1 and w2 will not change them.
Is f a fixed value and is the question to fit a bunch of known points? You can use the \ operator for fitting. But that will not have anything to do with minimizing or maximizing.
Are there bounds on the weights or on their sum?
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Walter Roberson
on 3 Apr 2018
By the way if you can find analytic solutions for the above then you do not need to perform the optimization...
Walter Roberson
on 3 Apr 2018
Also remember that solve(diff(w1*f1(x) + w2*f2(x), x)==0, x) might be solving for a maxima rather than a minima.
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