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3. Please read the posting guide. This is R-Help, not "R we do your work for you." We expect posters to show us their efforts to solve their problems. (In R, not Excel of course). 4. See here for R optimization resources: https://cran.r-project.org/web/views/Optimization.html Bert Gunter "The trouble with having an open mind is that people keep coming along and sticking things into it." -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip ) On Thu, Dec 23, 2021 at 10:31 AM Amarjeet Kumar <kamarjee...@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]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
