[R] Constrined dependent optimization.

Paul Smith phhs80 at gmail.com
Mon Mar 30 20:51:19 CEST 2009

```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
>>
>> 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
>>>
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>>
>> --
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>>
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