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DISCS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DISCS
* Problem :
* *********
* The problem is to replace the nodes of a planar graph by discs
* such that adjacent nodes have touching discs and non adjacent nodes
* disjoint discs. The smallest disc is constrained to have radius equal to
* one and is centered at the origin. The second discs is also
* constrained to have its Y = 0.0, in order to cancel invariance under
* rotation.
* Source:
* W. Pulleyblank,
* private communication, 1991.
* classification LQR2-MY-36-66
* SIF input: A.R. Conn and Ph. Toint, April 1991.
* Number of nodes
IE NNODES 12
* Separation threshold
RE EPSIL 0.0001
* Constants
IE 1 1
IE 2 2
* Construct of adjacency matrix
DO I 1 NNODES
IA I-1 I -1
DO J 1 I-1
AE A(J,I) 0.0
ND
* Annihilate elements of A corresponding to arcs of the graph
RE A1,2 1.01
RE A1,7 1.01
RE A2,3 1.01
RE A2,4 1.01
RE A3,4 1.01
RE A4,5 1.01
RE A4,6 1.01
RE A5,6 1.01
RE A5,11 1.01
RE A6,7 1.01
RE A7,8 1.01
RE A7,9 1.01
RE A8,9 1.01
RE A8,10 1.01
RE A9,10 1.01
RE A10,11 1.01
RE A10,12 1.01
RE A11,12 1.01
* Lower bound on the objective function
RI RNODES NNODES
VARIABLES
DO I 1 NNODES
X X(I)
X Y(I)
X R(I)
ND
GROUPS
* Objective function
DO I 1 NNODES
XN OBJ R(I) 1.0
ND
* Separation constraints
DO I 2 NNODES
IA I-1 I -1
DO J 1 I-1
A= RAIJ A(J,I)
IR AIJ RAIJ
DO K 1 AIJ
XE S(J,I)
OD K
IA AIJ-1 AIJ -1
IM NAIJ AIJ-1 -1
DO K 1 NAIJ
XL S(J,I)
ND
CONSTANTS
RM -EPSIL EPSIL -1.0
DO I 1 NNODES
IA I-1 I -1
DO J 1 I-1
A= RAIJ A(J,I)
IR AIJ RAIJ
IA AIJ-1 AIJ -1
IM NAIJ AIJ-1 -1
DO K 1 NAIJ
Z DISCS S(J,I) -EPSIL
ND
BOUNDS
FR DISCS 'DEFAULT'
DO I 1 NNODES
XL DISCS R(I) 1.0
ND
XX DISCS X(1) 0.0
XX DISCS Y(1) 0.0
XX DISCS Y(2) 0.0
START POINT
DO I 1 NNODES
RI RI I
RM RM RI 0.03
RM RP RI 0.0055555
ZV DISCS R(I) RI
ZV DISCS X(I) RM
ZV DISCS Y(I) RP
ND
ELEMENT TYPE
EV IPSQ X Y
IV IPSQ U
EV IMSQ X Y
IV IMSQ U
ELEMENT USES
DO I 2 NNODES
IA I-1 I -1
DO J 1 I-1
XT DR(J,I) IPSQ
ZV DR(J,I) X R(I)
ZV DR(J,I) Y R(J)
XT DX(J,I) IMSQ
ZV DX(J,I) X X(I)
ZV DX(J,I) Y X(J)
XT DY(J,I) IMSQ
ZV DY(J,I) X Y(I)
ZV DY(J,I) Y Y(J)
ND
GROUP USES
DO I 2 NNODES
IA I-1 I -1
DO J 1 I-1
XE S(J,I) DR(J,I)
XE S(J,I) DX(J,I) -1.0 DY(J,I) -1.0
ND
OBJECT BOUND
*ZL DISCS RNODES
* Solution
*LO SOLTN(12) 20.46122911
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DISCS
INDIVIDUALS
T IPSQ
R U X 1.0 Y 1.0
F U * U
G U U + U
H U U 2.0
T IMSQ
R U X 1.0 Y -1.0
F U * U
G U U + U
H U U 2.0
ENDATA