🚀 go-pugleaf

In article <cscoging.66@unpcs1.cs.unp.ac.za> cscoging@unpcs1.cs.unp.ac.za (Chris Scogings) writes:
   > I am testing various optimization methods and I need some
   > problems to test them out on.  These problems must not be
   > too simple (I have already used Rosenbrock's function, etc.) ...
   > Ideally, I need a moderately complex function of 3 to 8
   > variables.  It is not necessary for the function to be
   > differentiable.

The objective function below appeared in the ACM Transactions
on Mathematical Software.  I find it remarkably difficult;
perhaps you will have better success.  The number of variables
to be optimized (the dimensionality of the domain) is
user selectable; I find it difficult for n=4 and incredibly
difficult for n=9.  The function is not differentiable.
Code is in the "C" language.  Good luck!






#define		VECTLEN	(50)	/* max dimensionality of function */


/* Objective function of Corana et al  ACM Trans on Mathematical */
/*                                     Software V13 No3 p272     */

/* Like the Chebyquad function, this one lets the user select    */
/* the dimensionality of the domain ("nvars").                   */
/* However, it is a very difficult function even when nvars=4.   */

/* Starting point is:  even numbered coordinates have x[j] = 999 */
/*                     odd numbered coordinates have x[j] = -999 */
/*                     { x[2i]=999 , x[2i+1]=-999 }              */

/* Minimum is at x[j] = 0.00 , for all j                         */
double	f(x,nvars)
	double	x[VECTLEN] ;
	int	nvars ;
{
	double	s[VECTLEN], t[VECTLEN], d[VECTLEN] ;
	double	term, summ, dj, c, deviate ;
	int	i, j, k;

	funevals++;

	for(i=0; i<VECTLEN; i++) { s[i]=0.2 ; t[i]=0.05; d[i]=10.0 ; }
	d[0] = 1.0 ;      d[1] = 1000.0 ;
	d[2] = 10.0 ;     d[3] = 100.0 ;
	d[4] = 1.0 ;      d[5] = 10.0 ;
	d[6] = 100.0 ;    d[7] = 1000.0 ;
	d[8] = 1.0 ;      d[9] = 10.0 ;
	c = 0.15 ;

	summ = 0.0;
	for(i=0; i<nvars; i++)
	{
		dj = floor(  fabs(x[i] / s[i]) + 0.49999999 ) ;
		if(x[i] < 0.0) dj = 0.0 - dj ;
		dj *= s[i] ;
		deviate = fabs(x[i] - dj) ;
		if( deviate < fabs(t[i]) )
		{
			term = 0.0 ;
			if(dj < 0.0) term = t[i] ;
			if(dj > 0.0) term = (0.0 - t[i]);
			term += dj ;
			term = term * term * c * d[i] ;
		}
		else term = d[i] * (x[i] * x[i]) ;
		summ += term ;
	}
	return(summ) ;
}

-------------------
  -- Mark Johnson

cscoging@unpcs1.cs.unp.ac.za (Chris Scogings) writes:

>I am testing various optimization methods and I need some problems to test 
>them out on.  These problems must not be too simple (I have already used 
>Rosenbrock's function, etc.) but must not be so complicated that I spend all 
>my time setting up the function and not optimising it.

>Ideally, I need a moderately complex function of 3 to 8 variables.  It is 
>not necessary for the function to be differentiable.  Results of the 
>optimization and comparisons between various methods will be posted if 
>anyone is interested.

If you are working on global optimization approaches, you should
check out the problem sets described in the following two books:

Aimo Torn, Antanas Zilinskas.
Global optimization 
Berlin ; New York : Springer-Verlag, c1989

C.A. Floudas, P.M. Pardalos.
A collection of test problems for constrained global optimization algorithms
Berlin ; New York : Springer-Verlag, 1990


--Bill

In article 66@unpcs1.cs.unp.ac.za, cscoging@unpcs1.cs.unp.ac.za (Chris Scogings) writes:
>I am testing various optimization methods and I need some problems to test 
>them out on.  These problems must not be too simple (I have already used 
>Rosenbrock's function, etc.) but must not be so complicated that I spend all 
>my time setting up the function and not optimising it.
>
>Ideally, I need a moderately complex function of 3 to 8 variables.  It is 
>not necessary for the function to be differentiable.  Results of the 
>optimization and comparisons between various methods will be posted if 
>anyone is interested.
>
>Thank you
>Chris

You should have a look at the following two books:

Hock, W. and Schittkowski, K. Test Examples for Nonlinear Programming Codes.
Springer-Verlag, Berlin, Heidelberg, New York 1981.

Schittkowski, K. Nonlinear Programming Codes (Information,Tests,Performance).
Springer-Verlag, Berlin, Heidelberg, New York 1980.

-- H. Boden