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HIMMELBI.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HIMMELBI
* Problem :
* *********
* An unpleasant weapon assignment problem by Bracken and McCormick.
* The real problem has integer variables.
* Also, the sign of ci have been reversed in order to have a
* meaningful constraints on the total number of weapons (a fully
* desirable situation).
* Source: problem 23 in
* D.H. Himmelblau,
* "Applied nonlinear programming",
* McGraw-Hill, New-York, 1972.
* SIF input: Ph. Toint, March 1991.
* minor correction by Ph. Shott, Jan 1995.
* classification OLR2-MN-100-12
* Number of variables
IE N 100
* Number of targets
IE NT 20
* Probability that weapon i will damage target j
RE A1,1 1.0
RE A2,1 0.84
RE A3,1 0.96
RE A4,1 1.0
RE A5,1 0.92
RE A1,2 0.95
RE A2,2 0.83
RE A3,2 0.95
RE A4,2 1.0
RE A5,2 0.94
RE A1,3 1.0
RE A2,3 0.85
RE A3,3 0.95
RE A4,3 1.0
RE A5,3 0.92
RE A1,4 1.0
RE A2,4 0.84
RE A3,4 0.96
RE A4,4 1.0
RE A5,4 0.95
RE A1,5 1.0
RE A2,5 0.85
RE A3,5 0.96
RE A4,5 1.0
RE A5,5 0.95
RE A1,6 0.85
RE A2,6 0.81
RE A3,6 0.90
RE A4,6 1.0
RE A5,6 0.98
RE A1,7 0.90
RE A2,7 0.81
RE A3,7 0.92
RE A4,7 1.0
RE A5,7 0.98
RE A1,8 0.85
RE A2,8 0.82
RE A3,8 0.91
RE A4,8 1.0
RE A5,8 1.0
RE A1,9 0.80
RE A2,9 0.80
RE A3,9 0.92
RE A4,9 1.0
RE A5,9 1.0
RE A1,10 1.0
RE A2,10 0.86
RE A3,10 0.95
RE A4,10 0.96
RE A5,10 0.90
RE A1,11 1.0
RE A2,11 1.0
RE A3,11 0.99
RE A4,11 0.91
RE A5,11 0.95
RE A1,12 1.0
RE A2,12 0.98
RE A3,12 0.98
RE A4,12 0.92
RE A5,12 0.96
RE A1,13 1.0
RE A2,13 1.0
RE A3,13 0.99
RE A4,13 0.91
RE A5,13 0.91
RE A1,14 1.0
RE A2,14 0.88
RE A3,14 0.98
RE A4,14 0.92
RE A5,14 0.98
RE A1,15 1.0
RE A2,15 0.87
RE A3,15 0.97
RE A4,15 0.98
RE A5,15 0.99
RE A1,16 1.0
RE A2,16 0.88
RE A3,16 0.98
RE A4,16 0.93
RE A5,16 0.99
RE A1,17 1.0
RE A2,17 0.85
RE A3,17 0.95
RE A4,17 1.0
RE A5,17 1.0
RE A1,18 0.95
RE A2,18 0.84
RE A3,18 0.92
RE A4,18 1.0
RE A5,18 1.0
RE A1,19 1.0
RE A2,19 0.85
RE A3,19 0.93
RE A4,19 1.0
RE A5,19 1.0
RE A1,20 1.0
RE A2,20 0.85
RE A3,20 0.92
RE A4,20 1.0
RE A5,20 1.0
* Minimum number of weapons assigned to target j
RE B1 30.0
RE B6 100.0
RE B10 40.0
RE B14 50.0
RE B15 70.0
RE B16 35.0
RE B20 10.0
* Military value (???) of target j
RE U1 60.
RE U2 50.
RE U3 50.
RE U4 75.
RE U5 40.
RE U6 60.
RE U7 35.
RE U8 30.
RE U9 25.
RE U10 150.
RE U11 30.
RE U12 45.
RE U13 125.
RE U14 200.
RE U15 200.
RE U16 130.
RE U17 100.
RE U18 100.
RE U19 100.
RE U20 150.
* Number of available weapons of type i
RE C1 200.0
RE C2 100.0
RE C3 300.0
RE C4 150.0
RE C5 250.0
* Constants
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
* Total number of weapons
RE NW 0.0
DO I 1 5
A+ NW NW C(I)
ND
VARIABLES
DO J 1 NT
DO I 1 5
X X(I,J)
ND
GROUPS
DO J 1 NT
XN P(J)
AD 1/UJ U(J) 1.0
ZN P(J) 'SCALE' 1/UJ
OD J
IE J 1
DO I 1 5
XG CB(J) X(I,J) 1.0
ND
IE J 6
DO I 1 5
XG CB(J) X(I,J) 1.0
ND
IE J 10
DO I 1 5
XG CB(J) X(I,J) 1.0
ND
IE J 14
DO I 1 5
XG CB(J) X(I,J) 1.0
ND
IE J 15
DO I 1 5
XG CB(J) X(I,J) 1.0
ND
IE J 16
DO I 1 5
XG CB(J) X(I,J) 1.0
ND
IE J 20
DO I 1 5
XG CB(J) X(I,J) 1.0
ND
DO I 1 5
DO J 1 NT
XL CC(I) X(I,J) 1.0
ND
CONSTANTS
DO J 1 NT
X HIMMELBI P(J) 1.0
ND
IE J 1
Z HIMMELBI CB(J) B(J)
IE J 6
Z HIMMELBI CB(J) B(J)
IE J 10
Z HIMMELBI CB(J) B(J)
IE J 14
Z HIMMELBI CB(J) B(J)
IE J 15
Z HIMMELBI CB(J) B(J)
IE J 16
Z HIMMELBI CB(J) B(J)
IE J 20
Z HIMMELBI CB(J) B(J)
DO I 1 5
Z HIMMELBI CC(I) C(I)
ND
BOUNDS
ZU HIMMELBI 'DEFAULT' NW
ELEMENT TYPE
EV 5PEXP Y1 Y2
EV 5PEXP Y3 Y4
EV 5PEXP Y5
EP 5PEXP A1 A2
EP 5PEXP A3 A4
EP 5PEXP A5
ELEMENT USES
DO J 1 NT
XT PP(J) 5PEXP
ZV PP(J) Y1 X(1,J)
ZV PP(J) Y2 X(2,J)
ZV PP(J) Y3 X(3,J)
ZV PP(J) Y4 X(4,J)
ZV PP(J) Y5 X(5,J)
ZP PP(J) A1 A(1,J)
ZP PP(J) A2 A(2,J)
ZP PP(J) A3 A(3,J)
ZP PP(J) A4 A(4,J)
ZP PP(J) A5 A(5,J)
ND
GROUP USES
DO J 1 NT
XE P(J) PP(J)
ND
OBJECT BOUND
* Solution
*LO SOLTN -1735.56958
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HIMMELBI
TEMPORARIES
R LA1
R LA2
R LA3
R LA4
R LA5
R FF
M LOG
INDIVIDUALS
T 5PEXP
A LA1 LOG( A1 )
A LA2 LOG( A2 )
A LA3 LOG( A3 )
A LA4 LOG( A4 )
A LA5 LOG( A5 )
A FF A1**Y1 * A2**Y2 * A3**Y3 * A4**Y4 *A5**Y5
F FF
G Y1 LA1 * FF
G Y2 LA2 * FF
G Y3 LA3 * FF
G Y4 LA4 * FF
G Y5 LA5 * FF
H Y1 Y1 LA1 * LA1 * FF
H Y1 Y2 LA1 * LA2 * FF
H Y1 Y3 LA1 * LA3 * FF
H Y1 Y4 LA1 * LA4 * FF
H Y1 Y5 LA1 * LA5 * FF
H Y2 Y2 LA2 * LA2 * FF
H Y2 Y3 LA2 * LA3 * FF
H Y2 Y4 LA2 * LA4 * FF
H Y2 Y5 LA2 * LA5 * FF
H Y3 Y3 LA3 * LA3 * FF
H Y3 Y4 LA3 * LA4 * FF
H Y3 Y5 LA3 * LA5 * FF
H Y4 Y4 LA4 * LA4 * FF
H Y4 Y5 LA4 * LA5 * FF
H Y5 Y5 LA5 * LA5 * FF
ENDATA