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GENHUMPS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME GENHUMPS
* Problem :
* *********
* A multi-dimensional variant of HUMPS, a two dimensional function
* with a lot of humps. The density of humps increases with the
* parameter ZETA, making the problem more difficult.
* The problem is nonconvex.
* Source:
* Ph. Toint, private communication, 1997.
* SDIF input: N. Gould and Ph. Toint, November 1997.
* classification SUR2-AN-V-0
* Number of variables
*IE N 5 $-PARAMETER
*IE N 10 $-PARAMETER
*IE N 100 $-PARAMETER
*IE N 500 $-PARAMETER
*IE N 1000 $-PARAMETER original value
IE N 5000 $-PARAMETER
* Density of humps
*RE ZETA 2.0 $-PARAMETER
RE ZETA 20.0 $-PARAMETER
* other parameter definitions
IE 1 1
IA N-1 N -1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
N OBJ
BOUNDS
FR GENHUMPS 'DEFAULT'
START POINT
V GENHUMPS 'DEFAULT' -506.2
XV GENHUMPS X(1) -506.0
ELEMENT TYPE
EV HMP X Y
EP HMP A
EV SQ X
ELEMENT USES
DO I 1 N-1
IA I+1 I 1
XT Q(I) HMP
ZV Q(I) X X(I)
ZV Q(I) Y X(I+1)
ZP Q(I) A ZETA
XT SX(I) SQ
ZV SX(I) X X(I)
XT SY(I) SQ
ZV SY(I) X X(I+1)
ND
GROUP USES
DO I 1 N-1
XE OBJ Q(I) 1.0
XE OBJ SX(I) 0.05 SY(I) 0.05
ND
OBJECT BOUND
LO GENHUMPS 0.0
*LO SOLTN 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS GENHUMPS
TEMPORARIES
R AA
R AAA
R SAX
R SAY
R CAX
R CAY
M SIN
M COS
INDIVIDUALS
T HMP
A SAX SIN( A * X )
A SAY SIN( A * Y )
A CAX COS( A * X )
A CAY COS( A * Y )
A AA A + A
A AAA A * AA
F ( SAX * SAY )**2
G X AA * SAX * CAX * SAY**2
G Y AA * SAX**2 * CAY * SAY
H X X AAA * SAY**2 * ( CAX**2 - SAX**2 )
H X Y AA * AA * SAX * CAX * SAY * CAY
H Y Y AAA * SAX**2 * ( CAY**2 - SAY**2 )
T SQ
F X**2
G X X + X
H X X 2.0
ENDATA