Image you want to minimize the following linear function f <- function(x) sum( c(1:50, 50:1) * x / (50*51) )
on the set of all permutations of the numbers 1,..., 100. I wonder how will you do that with lpSolve? I would simply order the coefficients and then sort the numbers 1,...,100 accordingly. I am also wondering how optim with "SANN" could be applied here. As this is a problem in the area of discrete optimization resp. constraint programming, I propose to use an appropriate program here such as the free software Bprolog. I would be interested to learn what others propose. Of course, if we don't know anything about the function f then it amounts to an exhaustive search on the 100! permutations -- probably not a feasible job. Regards, Hans Werner Paul Smith wrote: > > On Sun, Mar 29, 2009 at 9:45 PM, <rkevinbur...@charter.net> wrote: >> I have an optimization question that I was hoping to get some suggestions >> on how best to go about sovling it. I would think there is probably a >> package that addresses this problem. >> >> This is an ordering optimzation problem. Best to describe it with a >> simple example. Say I have 100 "bins" each with a ball in it numbered >> from 1 to 100. Each bin can only hold one ball. This optimization is that >> I have a function 'f' that this array of bins and returns a number. The >> number returned from f(1,2,3,4....) would return a different number from >> that of f(2,1,3,4....). The optimization is finding the optimum order of >> these balls so as to produce a minimum value from 'f'.I cannot use the >> regular 'optim' algorithms because a) the values are discrete, and b) the >> values are dependent ie. when the "variable" representing the bin >> location is changed (in this example a new ball is put there) the >> existing ball will need to be moved to another bin (probably swapping >> positions), and c) each "variable" is constrained, in the example above >> the only allowable values are integers from 1-100. So the problem becomes >> finding the optimum order of the "balls". >> >> Any suggestions? > > If your function f is linear, then you can use lpSolve. > > Paul > > ______________________________________________ > R-help@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. > > -- View this message in context: http://www.nabble.com/Constrined-dependent-optimization.-tp22772520p22782922.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@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.