[R] Request for help in solving an optimization problem

[Bert Gunter]

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Bert Gunter

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On Thu, Dec 23, 2021 at 10:31 AM Amarjeet Kumar <kamarjeet21 using gmail.com> wrote:
>
> Dear All.
>
> Warm greetings to you. I need help in solving an optimization formulation
> in R software. I tried to solve it in excel solver but it was going up to
> local minimum using GRG nonlinear solving method. I thought R can help in
> solving this problem so I am explaining the problem in few sentences below:
>
> The optimization problem is to determine weights for ranking six
> alternatives(j) based on two attributes(i).
>
> Y1 Y2
>
> 2 4
>
> 4 5
>
> 4 4
>
> 5 3
>
> 5 2
>
> An aggregate performance function Pj is used to calculate jth alternative
> performance to the ideal.
>
> [image: enter image description here] <https://i.stack.imgur.com/JoM3B.png>
>
> Pj is the aggregate performance of the jth alternative relative to the
> ideal.
>
> Sj is the relative distance between the jth alternative and the ideal in
> terms of the aggregate performance given by
>
> Sj = 1 – Pj
>
> The problem is transformed to finding the set of weights Wi, i = 1, . . . ,
> m, which produce the smallest total squared difference between the relative
> performance of the alternative and that of the ideal.
>
> Here the maximum value of each attribute is taken as the ideal (Y*). Ideal
> for our data is (Y1*,Y2*)=(5,5)
>
> Objective function :
>
> [image: enter image description here] <https://i.stack.imgur.com/Yymud.png>
>
> e is a small value greater than zero so that weights are not zero
>
> After the optimal weights Wi , i = 1, . . . , m, are obtained, the relative
> performance of the jth alternative is calculated as [image: enter image
> description here] <https://i.stack.imgur.com/AqEqx.png>
>
> The relative distance to the ideal is[image: enter image description here]
> <https://i.stack.imgur.com/z3YlD.png> which is the basis of ranking. The
> higher value means the alternative is away from ideal and hence ranks low.
>
> I know that R has better capabilities to find solutions for this
> optimization problem but, as I have no experience in R, I am unable to move
> a step further. If you can find some time to help me in this regard I would
> be very thankful to you for this timely help.
>
> Thank you in advance for your help.
>
>
> Kind Regards,
> *Amarjeet Kumar*
> Research scholar,
>
>         [[alternative HTML version deleted]]
>
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