[R] Optimizing

Sat Nov 17 15:22:49 CET 2012

On Thu, Nov 15, 2012 at 7:49 PM, Sam Asin <asin.sam at gmail.com> wrote:
> Hey,
>
> It's actually not homework, what gave you that impression?

Real data sets don't usually have people named A,B,C with wages 3,4,5. ;-)

To your question at hand, it's close to a classic problem in
combinatorial optimization known as the knapsack problem, but there
are some small differences. That's a difficult (in a technical sense)
problem but well-studied so there are lots of good "almost solutions."
I'd look into that and see if you can transform it to fit that
framework, for which there is almost surely a CRAN-tested
implementation available.

> I graduated in
> May and studied Math, economics, and international relations, so I don't
> have much of a programming background.  This is a project that I'm working
> on out of personal interest.
>
> Obviously, I've tried doing some homework, but after 45 minutes of digging
> around without even really having any leads I figured I would post here.
>
> The optimization problems I see more generally seem tailored towards
> maximizing a function subject to some constraint on that function.  For
> example, maximizing U(x,y)=2x^2+4y s.t. x+y=3.  I don't really see a way to
> frame my current maximization like that at all.  We aren't choosing one
> observation in our dataset, we are choosing a group.  And, the constraints
> aren't something like the types sum to a number, but rather that our choice
> of observations meet some specific condition.
>
> Sorry if I'm being clueless here, but when I look at
> http://cran.r-project.org/web/views/Optimization.html I just see a giant
> list of packages, most of which I believe are optimizing a function subject
> to constraints.  Maybe my problem actually is a common one, there is some
> package out there that would do it, and I just need to find it.  If so, my
> googling and looking on the help pages has been so far unsuccessful. I
> apologize if the answer really is sitting there on some help page, but I
> really haven't found it.  If this were some homework problem, then I would
> know that it's probably a common, normal thing, and feel more confident
> looking on the Cran page.  But, since it isn't, I wasn't even sure if the
> answer was out there and my searching had so far been fruitless.  That's
> why I wanted to know if there would be some function that would do this
> sort of thing or if it's the sort of thing that I just need to manually
> work through.
>
> The help pages are over my head in so far as the help pages are highly
> technical and focused on methods.  They assume a knowledge about the basic
> type of optimization problem that I don't have, and I think that's because
> there is a standard type of optimization that is most common.
>
> Anyways, I am thinking I might just try to manually do the calculation
> because I can't follow the optimize commands.  The general strategy I think
> is to somehow make a dataset that has all combinations of 6 people as rows.
>  Then, for each row, make a vector that is just all the types of the people
> in that row, a vector for the sum of the values, and a vector for the sum
> of the wages.  Then, keep only those rows which have the correct types and
> wages under the max.  Then, sort by the sum of the values.  Let me know if
> you have any better ideas!
>
> Sam
>
>
> On Wed, Nov 14, 2012 at 7:35 PM, Bert Gunter <gunter.berton at gene.com> wrote:
>
>> Sam:
>>
>> 1. Homework? R has a no homework policy.
>>
>> 2. But in any case, check out the Optimization task view on CRAN. You
>> should be able to find something there that meets your needs.
>>
>> Of course, if something is "a little over your head," that's not an
>> excuse, but rather an admission that you have to do some "homework" on
>> your own.
>>
>> Cheers,
>> Bert
>>
>> On Wed, Nov 14, 2012 at 5:23 PM, Sam Asin <asin.sam at gmail.com> wrote:
>> > Hello,
>> >
>> > I am fairly new with R and am having trouble finding an optimal group.  I
>> > checked the help functions for the various optimize commands and it was a
>> > little over my head.
>> >
>> > I have a dataset with 4 columns, name, type, value, and cost.  The set
>> > consists of a list of people, which have 3 types.  I want to choose 6
>> > people, two of each type, and maximize the sum of their values.  However,
>> > I'm subject to the constraint that the wage of the three people has to
>> sum
>> > to less than 20 dollars.  Here is some sample data.
>> >
>> > people <- c("A", "B", "C", "D", "E", "F", "G", "H", "I")
>> > type<- c(1, 1, 1, 1, 2, 2, 3, 3, 3)
>> > value<-c(25.20, 24, 38, 20, 14, 20, 31, 11, 8)
>> > wage<- c(4, 3.8, 5.1, 3.5, 2.4, 3, 6, 2.4, 2)
>> >
>> > data<- data.frame(people, type, value, wage)
>> >
>> > With this small dataset the question isn't very interesting, but the
>> answer
>> > would be something like person C, D, E, F, G, and I (I didn't check to
>> see
>> > that those prices sum to less than $20).
>> >
>> > How can I write a program that will do this?  Can I just use the optimize
>> > command?  Do I have to transform my dataset into something that is easier
>> > to use the optimize command on?  Or should I write my own code that does
>> > the process?
>> >
>> > Thanks,
>> >
>> > Sam
>> >
>> >         [[alternative HTML version deleted]]
>> >
>> > ______________________________________________
>> > R-help at r-project.org mailing list
>> > 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.
>>
>>
>>
>> --
>>
>> Bert Gunter
>> Genentech Nonclinical Biostatistics
>>
>> Internal Contact Info:
>> Phone: 467-7374
>> Website:
>>
>> http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm
>>
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> 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.