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DISC2.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DISC2
* Problem :
* *********
* The problem is to find the minimum disc radius subject to polygon
* determined by boundary discs intersecting all interior discs.
* Source:
* W. Pulleyblank,
* private communication, 1991.
* SIF input: A.R. Conn, November 1991.
* classification LQR2-MY-29-23
* Number of nodes
IE NNODES 11
* Number of sides to the polygon
IE NLINES 6
* Constants
IE 0 0
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
IE 6 6
IE 7 7
IE 8 8
IE 10 10
IE 12 12
RE X1 0.0
RE X2 8.0
RE X3 12.0
RE X4 8.0
RE X5 0.0
RE X6 4.0
RE X7 8.0
RE X8 8.0
RE X9 4.0
RE X10 2.0
RE X11 2.0
RE Y1 10.0
RE Y2 10.0
RE Y3 5.0
RE Y4 0.0
RE Y5 0.0
RE Y6 8.0
RE Y7 7.0
RE Y8 3.0
RE Y9 1.0
RE Y10 3.0
RE Y11 6.0
* Lower bound on the objective function
RI RNODES NNODES
VARIABLES
EPSILON
DO I 1 NNODES
X U(I)
X V(I)
ND
DO I 1 NLINES
X ALPHA(I)
ND
GROUPS
* Objective function
N OBJ EPSILON 1.0
* Boundary constraints
DO I 1 5
XE B(I)
ND
DO I 6 NNODES
XL B(I)
ND
* Collinearity constraints
XE B162 U6 1.0 U1 -1.0
XE C162 V6 1.0 V1 -1.0
XE B273 U7 1.0 U2 -1.0
XE C273 V7 1.0 V2 -1.0
XE B384 U8 1.0 U3 -1.0
XE C384 V8 1.0 V3 -1.0
XE B495 U9 1.0 U4 -1.0
XE C495 V9 1.0 V4 -1.0
XE B5101 U10 1.0 U5 -1.0
XE C5101 V10 1.0 V5 -1.0
XE B5111 U11 1.0 U5 -1.0
XE C5111 V11 1.0 V5 -1.0
BOUNDS
FR DISC2 'DEFAULT'
DO I 1 NLINES
XU DISC2 ALPHA(I) 1.0
XL DISC2 ALPHA(I) 0.0
ND
LO DISC2 EPSILON 0.0
UP DISC2 EPSILON 3.0
START POINT
DO I 1 NNODES
XV START U(I) 5.0
XV START V(I) 5.0
ND
START EPSILON 0.5
ELEMENT TYPE
EV CIRCLE X Y
EV CIRCLE Z
EP CIRCLE P1 P2
EV LINE X Y
EV LINE Z
IV LINE U V
ELEMENT USES
T b162 LINE
V b162 X U2
V b162 Y U1
V b162 Z ALPHA1
T c162 LINE
V c162 X V2
V c162 Y V1
V c162 Z ALPHA1
T b273 LINE
V b273 X U3
V b273 Y U2
V b273 Z ALPHA2
T c273 LINE
V c273 X V3
V c273 Y V2
V c273 Z ALPHA2
T b384 LINE
V b384 X U4
V b384 Y U3
V b384 Z ALPHA3
T c384 LINE
V c384 X V4
V c384 Y V3
V c384 Z ALPHA3
T b495 LINE
V b495 X U5
V b495 Y U4
V b495 Z ALPHA4
T c495 LINE
V c495 X V5
V c495 Y V4
V c495 Z ALPHA4
T b5101 LINE
V b5101 X U1
V b5101 Y U5
V b5101 Z ALPHA5
T c5101 LINE
V c5101 X V1
V c5101 Y V5
V c5101 Z ALPHA5
T b5111 LINE
V b5111 X U1
V b5111 Y U5
V b5111 Z ALPHA5
T c5111 LINE
V c5111 X V1
V c5111 Y V5
V c5111 Z ALPHA5
DO I 1 NNODES
XT b(I) CIRCLE
ZV b(I) X U(I)
ZV b(I) Y V(I)
ZV b(I) Z EPSILON
ZP b(I) P1 X(I)
ZP b(I) P2 Y(I)
ND
GROUP USES
DO I 1 NNODES
XE B(I) b(I)
ND
E B162 b162
E C162 c162
E B273 b273
E C273 c273
E B384 b384
E C384 c384
E B495 b495
E C495 c495
E B5101 b5101
E C5101 c5101
E B5111 b5111
E C5111 c5111
OBJECT BOUND
*ZL DISC2 RNODES
* Solution
*LO SOLTN(12) 20.46122911
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DISC2
TEMPORARIES
R ARG1
R ARG2
INDIVIDUALS
T CIRCLE
A ARG1 X - P1
A ARG2 Y - P2
F ARG1**2 + ARG2**2 - Z**2
G X 2.0*ARG1
G Y 2.0*ARG2
G Z -2.0*Z
H X X 2.0
H Y Y 2.0
H Z Z -2.0
T LINE
R U X 1.0 Y -1.0
R V Z -1.0
F U * V
G U V
G V U
H U V 1.0
ENDATA