how I found W1,W2 ?

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ahlem sellami
ahlem sellami 2018-4-2
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!!

回答(2 个)

John D'Errico
John D'Errico 2018-4-2
编辑:John D'Errico 2018-4-2
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
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ahlem sellami
ahlem sellami 2018-4-2
my object is to maximize F1 and minimize F2 and formulating a single-objective optimization problem f more explanation please

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Walter Roberson
Walter Roberson 2018-4-2
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?
  11 个评论
Walter Roberson
Walter Roberson 2018-4-3
By the way if you can find analytic solutions for the above then you do not need to perform the optimization...
Walter Roberson
Walter Roberson 2018-4-3
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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