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
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