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DNIEPER.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DNIEPER
* Problem :
* *********
* This problem models the planning of systematic use of water resources
* in the basin of the river Dnieper.
* Source: p. 139sq in
* B.N. Pshenichnyj
* "The Linearization Method for Constrained Optimization",
* Springer Verlag, SCM Series 22, Heidelberg, 1994
* SIF input: Ph. Toint, December 1994.
* classification QOR2-MN-61-24
* Problem data
RE C1 5.61
RE C2 4.68
RE C3 1.62
RE C4 1.8
RE C5 2.13
RE C6 2.1
RE C7 1.99
RE C8 2.02
RE C9 2.14
RE C10 2.15
RE C11 2.36
RE C12 2.63
RE C13 -0.02
RE C14 -0.01
RE C15 -0.16
RE C16 -0.47
RE C17 -0.75
RE C18 -0.94
RE C19 -0.93
RE C20 -0.99
RE C21 -0.42
RE C22 -0.07
RE C23 0.04
RE C24 -0.06
* Constants
IE 1 1
IE 2 2
IE 4 4
IE 5 5
IE 8 8
IE 9 9
IE 12 12
IE 13 13
IE 14 14
IE 16 16
IE 17 17
IE 20 20
IE 21 21
IE 24 24
IE 25 25
IE 36 36
IE 37 37
IE 48 48
IE 49 49
IE 52 52
IE 53 53
IE 56 56
VARIABLES
DO I 1 56
X X(I)
OD I
X0F
X24F
X12F
X36F
AC
GROUPS
* Objective function
DO I 1 12
IA I0 I 12
IA I1 I 24
IA I2 I 36
XN OBJ X(I1) 19.95 X(I) 0.07656
XN OBJ X(I2) -24.89 X(I0) -0.7135
OD I
* Ensure maximization
XN OBJ 'SCALE' -1.0
* Equality constraints
DO I 1 4
IA I0 I 24
XE CC(I) X(I0) -2.68
OD I
DO I 5 8
IA I0 I 24
IA I1 I 44
XE CC(I) X(I0) -2.68 X(I1) -2.68
OD I
DO I 9 12
IA I0 I 24
XE CC(I) X(I0) -2.68
OD I
DO I 13 16
IA I0 I 12
IA I1 I 24
XE CC(I) X(I0) -2.68 X(I1) -2.68
XE CC(I) AC -1.0
OD I
DO I 17 20
IA I0 I 12
IA I1 I 24
IA I2 I 36
XE CC(I) X(I0) -2.68 X(I1) -2.68
XE CC(I) X(I2) -2.68
XE CC(I) AC -1.0
OD I
DO I 21 24
IA I0 I 12
IA I1 I 24
XE CC(I) X(I0) -2.68 X(I1) -2.68
XE CC(I) AC -1.0
OD I
CONSTANTS
X DNIEPER OBJ -112.464
DO I 1 24
AM CST C(I) -1.0
Z DNIEPER CC(I) CST
OD I
BOUNDS
DO I 1 12
XL DNIEPER X(I) 51.2
XU DNIEPER X(I) 51.4
OD I
DO I 13 24
XL DNIEPER X(I) 15.0
XU DNIEPER X(I) 16.1
OD I
DO I 25 36
XL DNIEPER X(I) 0.4
XU DNIEPER X(I) 4.6
OD I
DO I 37 48
XL DNIEPER X(I) 0.5
XU DNIEPER X(I) 4.8
OD I
DO I 49 56
XL DNIEPER X(I) 0.0
XU DNIEPER X(I) 0.7
OD I
FX DNIEPER X0F 50.82
FX DNIEPER X24F 2.0
FX DNIEPER X12F 15.5
FX DNIEPER X36F 2.3
FR DNIEPER AC
START POINT
DO I 1 12
XV DNIEPER X(I) 51.35
OD I
DO I 13 24
XV DNIEPER X(I) 15.5
OD I
DO I 25 36
XV DNIEPER X(I) 2.5
OD I
DO I 37 48
XV DNIEPER X(I) 2.6
OD I
DO I 49 56
XV DNIEPER X(I) 0.3
OD I
XV DNIEPER X0F 50.82
XV DNIEPER X24F 2.0
XV DNIEPER X12F 15.5
XV DNIEPER X36F 2.3
* Solution
*XV SOLUTION X1 5.14000D+01
*XV SOLUTION X2 5.12000D+01
*XV SOLUTION X3 5.14000D+01
*XV SOLUTION X4 5.12000D+01
*XV SOLUTION X5 5.14000D+01
*XV SOLUTION X6 5.14000D+01
*XV SOLUTION X7 5.14000D+01
*XV SOLUTION X8 5.14000D+01
*XV SOLUTION X9 5.14000D+01
*XV SOLUTION X10 5.12000D+01
*XV SOLUTION X11 5.14000D+01
*XV SOLUTION X12 5.12000D+01
*XV SOLUTION X13 1.53142D+01
*XV SOLUTION X14 1.51879D+01
*XV SOLUTION X15 1.51846D+01
*XV SOLUTION X16 1.51650D+01
*XV SOLUTION X17 1.51615D+01
*XV SOLUTION X18 1.51495D+01
*XV SOLUTION X19 1.51380D+01
*XV SOLUTION X20 1.51238D+01
*XV SOLUTION X21 1.50864D+01
*XV SOLUTION X22 1.50690D+01
*XV SOLUTION X23 1.50389D+01
*XV SOLUTION X24 1.50000D+01
*XV SOLUTION X25 2.18087D+00
*XV SOLUTION X26 1.70780D+00
*XV SOLUTION X27 6.18689D-01
*XV SOLUTION X28 6.39532D-01
*XV SOLUTION X29 4.00000D-01
*XV SOLUTION X30 4.00000D-01
*XV SOLUTION X31 4.00000D-01
*XV SOLUTION X32 4.00000D-01
*XV SOLUTION X33 8.04561D-01
*XV SOLUTION X34 7.69470D-01
*XV SOLUTION X35 9.15035D-01
*XV SOLUTION X36 9.49886D-01
*XV SOLUTION X37 5.00000D-01
*XV SOLUTION X38 5.00000D-01
*XV SOLUTION X39 5.00000D-01
*XV SOLUTION X40 5.00000D-01
*XV SOLUTION X41 5.00000D-01
*XV SOLUTION X42 5.00000D-01
*XV SOLUTION X43 5.00000D-01
*XV SOLUTION X44 5.00000D-01
*XV SOLUTION X45 5.00000D-01
*XV SOLUTION X46 5.00000D-01
*XV SOLUTION X47 5.00000D-01
*XV SOLUTION X48 5.00000D-01
*XV SOLUTION X49 4.23624D-01
*XV SOLUTION X50 3.83582D-01
*XV SOLUTION X51 3.42537D-01
*XV SOLUTION X52 3.53731D-01
*XV SOLUTION X53 0.00000D+00
*XV SOLUTION X54 0.00000D+00
*XV SOLUTION X55 0.00000D+00
*XV SOLUTION X56 0.00000D+00
*XV SOLUTION X0F 5.08200D+01
*XV SOLUTION X24F 2.00000D+00
*XV SOLUTION X12F 1.55000D+01
*XV SOLUTION X36F 2.30000D+00
*XV SOLUTION AC -3.08411D+00
ELEMENT TYPE
EV WJ X Y
EV WK X Y
EV 2PR X Y
EV SQ X
ELEMENT USES
* Objective function
DO I 1 12
IA I1 I 12
IA I2 I 36
XT E(I) 2PR
ZV E(I) X X(I1)
ZV E(I) Y X(I2)
OD I
XT ACSQ SQ
ZV ACSQ X AC
* Constraints
DO I 1 12
IA I0 I 24
XT W1(I) WJ
ZV W1(I) X X(I)
ZV W1(I) Y X(I0)
OD I
XT W2(1) WJ
ZV W2(1) X X0F
ZV W2(1) Y X24F
DO I 2 12
IA I0 I 23
IA I1 I -1
XT W2(I) WJ
ZV W2(I) X X(I1)
ZV W2(I) Y X(I0)
OD I
DO I 13 24
IA I1 I 24
XT W1(I) WK
ZV W1(I) X X(I)
ZV W1(I) Y X(I1)
OD I
XT W2(13) WK
ZV W2(13) X X12F
ZV W2(13) Y X36F
DO I 14 24
IA I0 I 23
IA I1 I -1
XT W2(I) WK
ZV W2(I) X X(I1)
ZV W2(I) Y X(I0)
OD I
GROUP USES
* Objective groups
DO I 1 12
XE OBJ E(I) 2.155
OD I
XE OBJ ACSQ -2000.0
* Constraint groups
DO I 1 24
XE CC(I) W1(I) W2(I) -1.0
OD I
OBJECT BOUND
* Solution
*LO SOLUTION 1.87439D+04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DNIEPER
TEMPORARIES
R A1
R A2
R A3
R A4
R A5
R A6
R A7
R A8
R A9
R A10
INDIVIDUALS
T WJ
A A1 34.547
A A2 -0.55878
A A3 8.05339
A A4 -0.02252
A A5 -0.29316
A A6 -0.013521
A A7 0.00042
A A8 0.00267
A A9 0.000281
A A10 0.0000032
F A1 + A2*X + A3*Y + A4*X**2 + A5*X*Y
F+ + A6*Y**2 + A7*X**3 + A8*X**2*Y
F+ + A9*X*Y**2 + A10*Y**3
G X A2 + 2.0*A4*X + A5*Y +3.0*A7*X**2
G+ + 2.0*A8*X*Y + A9*Y**2
G Y A3 + A5*X + 2.0*A6*Y + A8*X**2
G+ + 2.0*A9*X*Y + 3.0*A10*Y**2
H X X 2.0*A4 + 6.0*A7*X + 2.0*A8*Y
H X Y A5 + 2.0*A8*X + 2.0*A9*Y
H Y Y 2.0*A6 + 2.0*A9*X +6.0*A10*Y
T WK
A A1 20.923
A A2 -4.22088
A A3 1.42061
A A4 -0.41040
A A5 -0.15082
A A7 -0.00826
A A8 0.00404
A A9 0.000168
A A10 -0.000038
F A1 + A2*X + A3*Y + A4*X**2 + A5*X*Y
F+ + A7*X**3 + A8*X**2*Y
F+ + A9*X*Y**2 + A10*Y**3
G X A2 + 2.0*A4*X + A5*Y +3.0*A7*X**2
G+ + 2.0*A8*X*Y + A9*Y**2
G Y A3 + A5*X + A8*X**2
G+ + 2.0*A9*X*Y + 3.0*A10*Y**2
H X X 2.0*A4 + 6.0*A7*X + 2.0*A8*Y
H X Y A5 + 2.0*A8*X + 2.0*A9*Y
H Y Y 2.0*A9*X +6.0*A10*Y
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
T SQ
F X * X
G X X + X
H X X 2.0
ENDATA