Amarjeet Kumar
2021-Dec-23 15:39 UTC
[R] Request for help in solving an optimization problem
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]]
1. This ia a plain text list. No html. 2. Looks like homework. We don't do homework here. 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 <kamarjeet21 at 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 at 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.