Dear Respected Researchers,
I hope this question finds you well.
The weighted sum objective function is one of the techniques used to solve multi-objective models. This weighted sum objective function: minimize ∑ _(i∈P)∑ _(t=1)^T〖w_i (t-1) X_it+∑ _(t=1)^T〖v C_t 〗〗
subject to
{set of constraints}
Where, X_it and C_t are binary variable and continuous variable, respectively, and the weights are w_i and v.
If the set P={P1, P2, P3} and T=4
My question is: Is it right to choose the weights w_i={10, 20, 30} and v=30?
or, I have to choose w_i=0.5 for all i, and v=0.5 or any combination guarantees that w_i +v=1?
Any answer is appreciated.
Best Regards,
Mahmoud
Hi Mahmoud
Actually there is no hard and fast rule for the same.
But looking at the computation angle, you will require normalization at some point of time. And also you may need to compare the weights or scoes of entities.
If it is 100% it gives ease in computation throughout. Thats all.
you are free to chose the upper cap.
When you evaluate the weighst of some variables-and if you dont have the upper cap-then it may lead to computational imbalance in real world scenario problems.
Cheers
Dr.Indrajit
Dear Dr Mandal,
Thank you very much, I really appreciate your answer.
Best Regards,
Mahmoud
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