[R] Constrined dependent optimization.

rkevinburton at charter.net rkevinburton at charter.net
Thu Apr 2 16:49:45 CEST 2009


Sorry I sent a description of the function I was trying to minimize but I must not have sent it to this group (and you). Hopefully with this clearer description of my problem you might have some suggestions. 

It is basically a warehouse placement problem. You have a warehouse that has many items each placed in a certain bin (the "real" warehouse has about 20,000 of these bins, hence the large number of variables that I want to input to optimize). Now assume that an order comes in for three items A, B, and C. In the worst case A will be on one end of the warehouse, B in the middle and C on the other end of the warehouse. The "work" involved in getting these items to fulfill this order is roughly proportional to the distance from A to B plus the distance from B to C (assuming the absolute positions are sorted). So the cost for fulfilling this order is this distance. In the ideal world A, B, and C would be right next to each other and the cost/distance would be minimized. So the function I want to minimize would be placing these 20,000 items in such a way so that the minimum "work" is involved in fulfilling the orders for the past month or two. Clearer? 

I can see that I may need to cut back on the variables 20,000 is probably too many. Maybe I can take the top 1,000 or so. I just am not sure of the packages available what to reasonably expect. I would like this optimization to complete in a reasonable amount of time (less than a few days). I have heard that SANN is slower than other optimization methods but it does have the feature of supplying a "gradient" as you pointed out. Are there other packages out there that might be better suited to such a large scale optimizaiton?

Thanks again.

Kevin
---- Paul Smith <phhs80 at gmail.com> wrote: 
> As I told you before, without knowing the definition of your function
> f, one cannot help much.
> 
> Paul
> 
> 
> On Wed, Apr 1, 2009 at 3:15 PM,  <rkevinburton at charter.net> wrote:
> > Thank you I had not considered using "gradient" in this fashion. Now as an add on question. You (an others) have suggested using SANN. Does your answer change if instead of 100 "variables" or bins there are 20,000? From the documentation L-BFGS-B is designed for a large number of variables. But maybe SANN can handle this as well.
> >
> > Kevin
> >
> > ---- Paul Smith <phhs80 at gmail.com> wrote:
> >> Apparently, the convergence is faster if one uses this new swap function:
> >>
> >> swapfun <- function(x,N=100) {
> >>  loc <- c(sample(1:(N/2),size=1,replace=FALSE),sample((N/2):100,1))
> >>  tmp <- x[loc[1]]
> >>  x[loc[1]] <- x[loc[2]]
> >>  x[loc[2]] <- tmp
> >>  x
> >> }
> >>
> >> It seems that within 20 millions of iterations, one gets the exact
> >> optimal solution, which does not take too long.
> >>
> >> Paul
> >>
> >>
> >> On Mon, Mar 30, 2009 at 5:11 PM, Paul Smith <phhs80 at gmail.com> wrote:
> >> > Optim with SANN also solves your example:
> >> >
> >> > -------------------------------------------
> >> >
> >> > f <- function(x) sum(c(1:50,50:1)*x)
> >> >
> >> > swapfun <- function(x,N=100) {
> >> >  loc <- sample(N,size=2,replace=FALSE)
> >> >  tmp <- x[loc[1]]
> >> >  x[loc[1]] <- x[loc[2]]
> >> >  x[loc[2]] <- tmp
> >> >  x
> >> > }
> >> >
> >> > N <- 100
> >> >
> >> > opt1 <- optim(fn=f,par=sample(1:N,N),gr=swapfun,method="SANN",control=list(maxit=50000,fnscale=-1,trace=10))
> >> > opt1$par
> >> > opt1$value
> >> >
> >> > -------------------------------------------
> >> >
> >> > We need to specify a large number of iterations to get the optimal
> >> > solution. The objective function at the optimum is 170425, and one
> >> > gets a close value with optim and SANN.
> >> >
> >> > Paul
> >> >
> >> >
> >> > On Mon, Mar 30, 2009 at 2:22 PM, Hans W. Borchers
> >> > <hwborchers at googlemail.com> wrote:
> >> >>
> >> >> 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,  <rkevinburton at 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 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.
> >> >>>
> >> >>>
> >> >>
> >> >> --
> >> >> 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 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.
> >> >>
> >> >
> >>
> >> ______________________________________________
> >> 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.
> >
> >
> 
> ______________________________________________
> 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.



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