R help - May 2007 - Increasing precision of rgenoud solutions

Dear All

I am using rgenoud to solve the following maximization problem:

myfunc <- function(x) {
  x1 <- x[1]
  x2 <- x[2]
  if (x1^2+x2^2 > 1)
    return(-9999999)
  else x1+x2
}

genoud(myfunc, nvars=2,
Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2,solution.tolerance=0.000001)

How can one increase the precision of the solution

$par
[1] 0.7072442 0.7069694

?

I have tried solution.tolerance but without a significant improvement.

Any ideas?

Thanks in advance,

Paul

Hi Paul,

Solution.tolerance is the right way to increase precision.  In your
example, extra precision *is* being obtained, but it is just not
displayed because the number of digits which get printed is controlled
by the options("digits") variable.  But the requested solution
precision is in the object returned by genoud().

For example, if I run

a <- genoud(myfunc, nvars=2,
    
Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2,solution.tolerance=0.000001)

I get
> a$par
[1] 0.7062930 0.7079196

But if I set options("digits"=12), and without rerunning anything I
check
a$par again, I observe that:
> a$par
[1] 0.706293049455 0.707919577559

Cheers,
Jas.

======================================Jasjeet S. Sekhon                     
                                      
Associate Professor             
Survey Research Center          
UC Berkeley                     

http://sekhon.berkeley.edu/
V: 510-642-9974  F: 617-507-5524
======================================

Paul Smith writes:
 > Dear All
 > 
 > I am using rgenoud to solve the following maximization problem:
 > 
 > myfunc <- function(x) {
 >   x1 <- x[1]
 >   x2 <- x[2]
 >   if (x1^2+x2^2 > 1)
 >     return(-9999999)
 >   else x1+x2
 > }
 > 
 > genoud(myfunc, nvars=2,
 >
Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2,solution.tolerance=0.000001)
 > 
 > How can one increase the precision of the solution
 > 
 > $par
 > [1] 0.7072442 0.7069694
 > 
 > ?
 > 
 > I have tried solution.tolerance but without a significant improvement.
 > 
 > Any ideas?
 > 
 > Thanks in advance,
 > 
 > Paul
 > 
 >

Thanks, Jasjeet, for your reply, but maybe I was not enough clear.

The analytical solution for the optimization problem is the pair

(sqrt(2)/2,sqrt(2)/2),

which, approximately, is

(0.707106781186548,0.707106781186548).

The solution provided by rgenoud, with

solution.tolerance=0.000000001

was

$par
[1] 0.7090278 0.7051806

which is not very precise comparing with the values of the
(analytical) solution. Is it possible to increase the degree of
closeness of the rgenoud solutions with the analytical ones?

Paul


On 5/10/07, Jasjeet Singh Sekhon <sekhon at berkeley.edu>
wrote:
>
> Hi Paul,
>
> Solution.tolerance is the right way to increase precision.  In your
> example, extra precision *is* being obtained, but it is just not
> displayed because the number of digits which get printed is controlled
> by the options("digits") variable.  But the requested solution
> precision is in the object returned by genoud().
>
> For example, if I run
>
> a <- genoud(myfunc, nvars=2,
>     
Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2,solution.tolerance=0.000001)
>
> I get
>
> > a$par
> [1] 0.7062930 0.7079196
>
> But if I set options("digits"=12), and without rerunning anything
I check
> a$par again, I observe that:
>
> > a$par
> [1] 0.706293049455 0.707919577559
>
> Cheers,
> Jas.
>
> ======================================> Jasjeet S. Sekhon
>
> Associate Professor
> Survey Research Center
> UC Berkeley
>
> http://sekhon.berkeley.edu/
> V: 510-642-9974  F: 617-507-5524
> ======================================>
>
> Paul Smith writes:
>  > Dear All
>  >
>  > I am using rgenoud to solve the following maximization problem:
>  >
>  > myfunc <- function(x) {
>  >   x1 <- x[1]
>  >   x2 <- x[2]
>  >   if (x1^2+x2^2 > 1)
>  >     return(-9999999)
>  >   else x1+x2
>  > }
>  >
>  > genoud(myfunc, nvars=2,
>  >
Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2,solution.tolerance=0.000001)
>  >
>  > How can one increase the precision of the solution
>  >
>  > $par
>  > [1] 0.7072442 0.7069694
>  >
>  > ?
>  >
>  > I have tried solution.tolerance but without a significant
improvement.
>  >
>  > Any ideas?
>  >
>  > Thanks in advance,
>  >
>  > Paul
>  >
>  >
>

Hi Paul,

I see.  You want to increase the population size (pop.size)
option---of lesser importance are the max.generations,
wait.generations and P9 options.  For more details, see
http://sekhon.berkeley.edu/papers/rgenoudJSS.pdf.

For example, if I run

a <- genoud(myfunc, nvars=2,
           
Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2,solution.tolerance=0.0000001,
            pop.size=6000, P9=50)

options("digits"=12)

I obtain:

#approx analytical solution
sum(c(0.707106781186548,0.707106781186548))
[1] 1.41421356237

#genoud solution
#a$value
[1] 1.41421344205

#difference
a$value-sum(c(0.707106781186548,0.707106781186548))

[1] -2.91195978441e-09

If that's not enough precision, increase the options (and the
run-time).  This would be faster with analytical derivatives.

Cheers,
Jas.

======================================Jasjeet S. Sekhon                     
                                      
Associate Professor             
Travers Department of Political Science
Survey Research Center          
UC Berkeley                     

http://sekhon.berkeley.edu/
V: 510-642-9974  F: 617-507-5524
======================================


Paul Smith writes:
>Thanks, Jasjeet, for your reply, but maybe I was not enough clear.
>
>The analytical solution for the optimization problem is the pair
>
>(sqrt(2)/2,sqrt(2)/2),
>
>which, approximately, is
>
>(0.707106781186548,0.707106781186548).
>
>The solution provided by rgenoud, with
>
>solution.tolerance=0.000000001
>
>was
>
>$par
>[1] 0.7090278 0.7051806
>
>which is not very precise comparing with the values of the
>(analytical) solution. Is it possible to increase the degree of
>closeness of the rgenoud solutions with the analytical ones?
>
>Paul
>
>Paul Smith writes:
> > Dear All
> > 
> > I am using rgenoud to solve the following maximization problem:
> > 
> > myfunc <- function(x) {
> >   x1 <- x[1]
> >   x2 <- x[2]
> >   if (x1^2+x2^2 > 1)
> >     return(-9999999)
> >   else x1+x2
> > }
> > 
> > genoud(myfunc, nvars=2,
> >
Domains=rbind(c(0,1),c(0,1)),max=TRUE,boundary.enforcement=2,solution.tolerance=0.000001)
> > 
> > How can one increase the precision of the solution
> > 
> > $par
> > [1] 0.7072442 0.7069694
> > 
> > ?
> > 
> > I have tried solution.tolerance but without a significant improvement.
> > 
> > Any ideas?
> > 
> > Thanks in advance,
> > 
> > Paul
> > 
> > 
>