R help - Feb 2012 - Schwefel Function Optimization

All,

I am looking for an optimization library that does well on something as chaotic
as the Schwefel function:

schwefel <- function(x) sum(-x * sin(sqrt(abs(x))))

With these guys, not much luck:
> optim(c(1,1), schwefel)$value
[1] -7.890603
> optim(c(1,1), schwefel, method="SANN",
control=list(maxit=10000))$value
[1] -28.02825
> optim(c(1,1), schwefel, lower=c(-500,-500), upper=c(500,500),
method="L-BFGS-B")$value
[1] -7.890603
> optim(c(1,1), schwefel, method="BFGS")$value
[1] -7.890603
> optim(c(1,1), schwefel, method="CG")$value
[1] -7.890603

All trapped in local minima. I get the right answer when I pick a starting point
that's close:
> optim(c(400,400), schwefel, lower=c(-500,-500), upper=c(500,500),
method="L-BFGS-B")$value
[1] -837.9658

Of course I can always roll my own:

r <- vector()
for(i in 1:1000) {
  x <- runif(2, -500,500)
  m <- optim(x, schwefel, lower=c(-500,-500), upper=c(500,500),
method="L-BFGS-B")
  r <- rbind(r, c(m$par, m$value))
}

And this does fine. I'm just wondering if this is the right approach, or if
there is some other package that wraps this kind of multi-start up so that the
user doesn't have to think about it.

Best,

Ara

Vartanian, Ara <aravart <at> indiana.edu> writes:
> All,
> 
> I am looking for an optimization library that does well on something as
>  chaotic as the Schwefel function:
> 
> schwefel <- function(x) sum(-x * sin(sqrt(abs(x))))
> 
> With these guys, not much luck:
> 
> > optim(c(1,1), schwefel)$value
> [1] -7.890603
> > optim(c(1,1), schwefel, method="SANN",
control=list(maxit=10000))$value
> [1] -28.02825
> > optim(c(1,1), schwefel, lower=c(-500,-500), upper=c(500,500), 
>                         method="L-BFGS-B")$value
> [1] -7.890603
> > optim(c(1,1), schwefel, method="BFGS")$value
> [1] -7.890603
> > optim(c(1,1), schwefel, method="CG")$value
> [1] -7.890603
Why is it necessary over and over again to point to the Optimization Task
View? This is a question about a global optimization problem, and the task
view tells you to look at packages like 'NLoptim' with specialized
routines,
or use one of the packages with evolutionary algorithms, such as
'DEoptim'
or'pso'.

    library(DEoptim)
    schwefel <- function(x) sum(-x * sin(sqrt(abs(x))))
    de <- DEoptim(schwefel, lower = c(-500,-500), upper = c(500,500),
                         control = list(trace = FALSE))
    de$optim$bestmem
    #     par1     par2 
    # 420.9687 420.9687 
    de$optim$bestval
    # [1] -837.9658
> All trapped in local minima. I get the right answer when I pick a starting 
> point that's close:
> 
> > optim(c(400,400), schwefel, lower=c(-500,-500), upper=c(500,500),
> >                             method="L-BFGS-B")$value
> [1] -837.9658
> 
> Of course I can always roll my own:
> 
> r <- vector()
> for(i in 1:1000) {
>   x <- runif(2, -500,500)
>   m <- optim(x, schwefel, lower=c(-500,-500), upper=c(500,500),
>                 method="L-BFGS-B")
>   r <- rbind(r, c(m$par, m$value))
> }
> 
> And this does fine. I'm just wondering if this is the right approach,
> or if there is some other package that wraps this kind of multi-start
> up so that the user doesn't have to think about it.
> 
> Best,
> 
> Ara

On 11/02/2012 08:25, Hans W Borchers wrote:
> Vartanian, Ara<aravart<at>  indiana.edu>  writes:
>
>> All,
>>
>> I am looking for
...
>>
>
> Why is it necessary over and over again to point to the Optimization Task
> View?
...

Now it could be that people are not trying
very hard to solve their own problems, but
to be fair it is a pretty gruelling process
to find the Task Views.

May I suggest that there be a "Task Views" item
on the left sidebar of the R website in the
Documentation section?

-- 
Patrick Burns
pburns at pburns.seanet.com
twitter: @portfolioprobe
http://www.portfolioprobe.com/blog
http://www.burns-stat.com
(home of 'Some hints for the R beginner'
and 'The R Inferno')

On 12-02-11 01:10 PM, Uwe Ligges wrote:
> On 11.02.2012 18:55, Patrick Burns wrote:
>>
>> On 11/02/2012 08:25, Hans W Borchers wrote:
>>> Vartanian, Ara<aravart<at> indiana.edu> writes:
>>>
>>>> All,
>>>>
>>>> I am looking for
>> ...
>>> Why is it necessary over and over again to point to the
Optimization
>>> Task
>>> View?
>> ...
>> Now it could be that people are not trying
>> very hard to solve their own problems, but
>> to be fair it is a pretty gruelling process
>> to find the Task Views.
>>
>> May I suggest that there be a "Task Views" item
>> on the left sidebar of the R website in the
>> Documentation section?
>>
> It is in the left side bar of CRAN already.
>
> Uwe
Yes, on CRAN but not on the R Homepage. I do agree with Hans that people 
do not seem to find it easily. One reason may be the term "Task Views"
is fine once you know what it is, but it is not completely self 
explanatory, so you have to look to see what it is. Thus, a bit like 
reading documentation, people do not always do it. Perhaps a bullet in 
"Getting Started" would help?

Paul