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DALLASS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME DALLASS
* Problem :
* *********
* The small Dallas water distribution problem
* The problem is also named "W30" in some references.
* This is a nonlinear network problem with conditioning of
* the order of 10**4.
* Source:
* R. Dembo,
* private communication, 1986.
* SIF input: Ph. Toint, June 1990.
* classification ONR2-MN-46-31
* Number of arcs
IE N 46
* Number of nodes
IE NODES 31
* Constants
IE 1 1
VARIABLES
DO I 1 N
X X(I)
ND
GROUPS
* Linear elements
N OBJ X42 -6.38400D+02 X43 -6.33000D+02
N OBJ X44 -5.54500D+02 X45 -5.05000D+02
N OBJ X46 -4.36900D+02
* Network flow constraints
E N1 X46 1.0 X41 1.0
E N1 X1 -1.0
E N2 X45 1.0 X2 -1.0
E N3 X44 1.0 X3 -1.0
E N4 X4 -1.0
E N5 X16 1.0 X7 -1.0
E N5 X6 -1.0 X5 -1.0
E N6 X7 1.0
E N6 X9 -1.0 X8 -1.0
E N7 X9 1.0 X10 -1.0
E N8 X10 1.0 X2 1.0
E N8 X12 -1.0 X11 -1.0
E N9 X12 1.0 X3 1.0
E N9 X13 -1.0
E N10 X4 1.0 X16 -1.0
E N10 X15 -1.0 X14 -1.0
E N11 X15 1.0 X13 1.0
E N11 X5 1.0 X17 -1.0
E N12 X20 1.0 X19 1.0
E N12 X8 1.0 X6 1.0
E N12 X18 -1.0
E N13 X42 1.0 X18 1.0
E N13 X19 -1.0
E N14 X21 1.0 X20 -1.0
E N15 X43 1.0 X21 -1.0
E N16 X14 1.0 X11 1.0
E N16 X23 -1.0 X22 -1.0
E N17 X23 1.0
E N17 X25 -1.0 X24 -1.0
E N18 X31 1.0 X25 1.0
E N18 X22 1.0 X26 -1.0
E N19 X26 1.0 X17 1.0
E N19 X28 -1.0 X27 -1.0
E N20 X28 1.0
E N21 X31 -1.0 X30 -1.0
E N21 X29 -1.0
E N22 X30 1.0 X27 1.0
E N23 X24 1.0 X32 -1.0
E N24 X38 1.0 X29 1.0
E N24 X34 -1.0 X33 -1.0
E N25 X32 1.0 X35 -1.0
E N26 X35 1.0
E N26 X37 -1.0 X36 -1.0
E N27 X37 1.0 X34 1.0
E N28 X36 1.0 X40 -1.0
E N28 X39 -1.0 X38 -1.0
E N29 X39 1.0 X33 1.0
E N29 X1 1.0
E N30 X40 1.0 X41 -1.0
E N31 X46 -1.0 X45 -1.0
E N31 X44 -1.0 X43 -1.0
E N31 X42 -1.0
CONSTANTS
DALLASS N5 2.80000D+00 N7 4.03000D-01
DALLASS N8 5.92000D-01 N9 1.15600D+00
DALLASS N10 2.00000D-01 N11 4.95000D-01
DALLASS N16 3.13000D-01 N17 8.44000D-01
DALLASS N18 3.31000D-01 N19 5.30000D-02
DALLASS N21 2.72000D-01 N22 8.83000D-01
DALLASS N23 5.71000D-01 N24 7.55000D-01
DALLASS N26 5.27000D-01 N29 1.00000D-03
DALLASS N31 -1.01960D+01
BOUNDS
XL DALLASS 'DEFAULT' -2.00000D+02
XU DALLASS 'DEFAULT' 2.00000D+02
LO DALLASS X1 0.00000D+00
UP DALLASS X1 2.11673D+01
LO DALLASS X2 0.00000D+00
UP DALLASS X2 4.37635D+01
LO DALLASS X3 0.00000D+00
UP DALLASS X3 3.28255D+01
LO DALLASS X19 0.00000D+00
UP DALLASS X19 2.20120D+01
LO DALLASS X21 0.00000D+00
UP DALLASS X21 1.36703D+01
START POINT
XV DALLASS 'DEFAULT' -2.00000D+02
DALLASS X1 2.11673D+01 X2 4.37635D+01
DALLASS X3 3.28255D+01 X4 1.42109D-14
DALLASS X5 1.68826D+02 X7 2.81745D+01
DALLASS X8 8.75603D+01 X9 -5.93858D+01
DALLASS X10 -5.97888D+01 X11 1.83383D+02
DALLASS X13 -1.68331D+02 X15 2.00000D+02
DALLASS X16 2.00000D-01 X17 2.00000D+02
DALLASS X18 -7.67574D+01 X19 2.20120D+01
DALLASS X20 1.36703D+01 X21 1.36703D+01
DALLASS X22 -1.98461D+02 X23 1.81531D+02
DALLASS X24 -1.93133D+01 X25 2.00000D+02
DALLASS X26 -1.98792D+02 X27 1.15500D+00
DALLASS X28 0.00000D+00 X29 2.00000D+02
DALLASS X30 2.72000D-01 X32 -1.98843D+01
DALLASS X33 1.78834D+02 X34 -1.79589D+02
DALLASS X35 -1.98843D+01 X37 1.79589D+02
DALLASS X40 2.00000D+02 X41 2.00000D+02
DALLASS X42 9.87694D+01 X43 1.36703D+01
DALLASS X44 3.28255D+01 X45 4.37635D+01
DALLASS X46 -1.78833D+02
ELEMENT TYPE
EV T1 ARC
EP T1 C1
EP T1 C2
EP T1 C3
EV T4 ARC
EP T4 C1
EP T4 C2
ELEMENT USES
XT 'DEFAULT' T1
T E1 T4
V E1 ARC X1
P E1 C1 4.48060D+02
P E1 C2 2.51200D+02
T E2 T4
V E2 ARC X2
P E2 C1 1.91526D+03
P E2 C2 6.46300D+01
T E3 T4
V E3 ARC X3
P E3 C1 1.07752D+03
P E3 C2 4.81400D+01
V E4 ARC X4
P E4 C1 6.90000D+03
P E4 C2 6.60000D+01
P E4 C3 1.22000D+02
V E5 ARC X5
P E5 C1 1.00000D+02
P E5 C2 1.00000D+01
P E5 C3 1.00000D+02
V E6 ARC X6
P E6 C1 6.63000D+02
P E6 C2 3.60000D+01
P E6 C3 1.20000D+02
V E7 ARC X7
P E7 C1 5.10000D+03
P E7 C2 6.60000D+01
P E7 C3 1.22000D+02
V E8 ARC X8
P E8 C1 6.45000D+02
P E8 C2 3.00000D+01
P E8 C3 1.20000D+02
V E9 ARC X9
P E9 C1 7.40000D+03
P E9 C2 6.60000D+01
P E9 C3 1.22000D+02
V E10 ARC X10
P E10 C1 5.00000D+03
P E10 C2 6.60000D+01
P E10 C3 9.50000D+01
V E11 ARC X11
P E11 C1 8.00000D+02
P E11 C2 5.40000D+01
P E11 C3 1.07000D+02
V E12 ARC X12
P E12 C1 5.20000D+03
P E12 C2 4.80000D+01
P E12 C3 1.10000D+02
V E13 ARC X13
P E13 C1 6.00000D+03
P E13 C2 4.80000D+01
P E13 C3 1.10000D+02
V E14 ARC X14
P E14 C1 4.00000D+02
P E14 C2 5.40000D+01
P E14 C3 1.00000D+02
V E15 ARC X15
P E15 C1 4.00000D+01
P E15 C2 3.12200D+01
P E15 C3 1.30000D+02
V E16 ARC X16
P E16 C1 4.50000D+03
P E16 C2 6.60000D+01
P E16 C3 1.22000D+02
V E17 ARC X17
P E17 C1 5.10000D+03
P E17 C2 2.40000D+01
P E17 C3 1.10000D+02
V E18 ARC X18
P E18 C1 3.00000D+01
P E18 C2 4.80000D+01
P E18 C3 1.18000D+02
T E19 T4
V E19 ARC X19
P E19 C1 4.84530D+02
P E19 C2 1.12970D+02
V E20 ARC X20
P E20 C1 2.60000D+04
P E20 C2 4.80000D+01
P E20 C3 1.10000D+02
T E21 T4
V E21 ARC X21
P E21 C1 1.86880D+02
P E21 C2 1.60610D+02
V E22 ARC X22
P E22 C1 5.20000D+02
P E22 C2 3.36100D+01
P E22 C3 1.30000D+02
V E23 ARC X23
P E23 C1 4.60000D+03
P E23 C2 5.40000D+01
P E23 C3 9.50000D+01
V E24 ARC X24
P E24 C1 5.40000D+03
P E24 C2 5.40000D+01
P E24 C3 9.50000D+01
V E25 ARC X25
P E25 C1 5.60000D+03
P E25 C2 1.20000D+01
P E25 C3 1.10000D+02
V E26 ARC X26
P E26 C1 3.30000D+03
P E26 C2 1.20000D+01
P E26 C3 1.10000D+02
V E27 ARC X27
P E27 C1 2.20000D+03
P E27 C2 2.40000D+01
P E27 C3 1.24000D+02
V E28 ARC X28
P E28 C1 1.00000D+03
P E28 C2 2.40000D+01
P E28 C3 1.10000D+02
V E29 ARC X29
P E29 C1 5.90000D+03
P E29 C2 2.40000D+01
P E29 C3 1.13000D+02
V E30 ARC X30
P E30 C1 2.80000D+03
P E30 C2 2.40000D+01
P E30 C3 1.13000D+02
V E31 ARC X31
P E31 C1 2.70000D+03
P E31 C2 1.20000D+01
P E31 C3 1.10000D+02
V E32 ARC X32
P E32 C1 3.10000D+03
P E32 C2 5.40000D+01
P E32 C3 9.50000D+01
V E33 ARC X33
P E33 C1 1.00000D+02
P E33 C2 1.00000D+01
P E33 C3 1.00000D+02
V E34 ARC X34
P E34 C1 4.30000D+03
P E34 C2 2.40000D+01
P E34 C3 1.13000D+02
V E35 ARC X35
P E35 C1 2.20000D+03
P E35 C2 5.40000D+01
P E35 C3 9.50000D+01
V E36 ARC X36
P E36 C1 1.80000D+03
P E36 C2 5.40000D+01
P E36 C3 1.10000D+02
V E37 ARC X37
P E37 C1 1.00000D+02
P E37 C2 2.40000D+01
P E37 C3 1.10000D+02
V E38 ARC X38
P E38 C1 1.31000D+03
P E38 C2 3.00000D+01
P E38 C3 1.00000D+02
V E39 ARC X39
P E39 C1 6.65000D+02
P E39 C2 3.60000D+01
P E39 C3 1.20000D+02
V E40 ARC X40
P E40 C1 1.10000D+03
P E40 C2 3.60000D+01
P E40 C3 1.20000D+02
V E41 ARC X41
P E41 C1 3.23000D+01
P E41 C2 1.00000D+01
P E41 C3 1.00000D+02
GROUP USES
E OBJ E1 E2
E OBJ E3 E4
E OBJ E5 E6
E OBJ E7 E8
E OBJ E9 E10
E OBJ E11 E12
E OBJ E13 E14
E OBJ E15 E16
E OBJ E17 E18
E OBJ E19 E20
E OBJ E21 E22
E OBJ E23 E24
E OBJ E25 E26
E OBJ E27 E28
E OBJ E29 E30
E OBJ E31 E32
E OBJ E33 E34
E OBJ E35 E36
E OBJ E37 E38
E OBJ E39 E40
E OBJ E41
OBJECT BOUND
* Solution
*LO SOLTN -3.2393D+04
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS DALLASS
TEMPORARIES
R TMP
R TMP2
R X
R XEXP
R SQC1
R EPS2
M ABS
M SQRT
M MAX
M MIN
M ASIN
INDIVIDUALS
* Pipe function
T T1
A TMP 850559.0D0 / 2.85 * C1
A TMP TMP / ( C3**1.85 )
A TMP TMP / ( C2**4.87 )
A X ABS( ARC )
A XEXP X**0.85
F TMP * X**2 * XEXP
G ARC 2.85 * TMP * ARC * XEXP
H ARC ARC 5.2725 * TMP * XEXP
* Elliptic pump
T T4
A EPS2 1.0D-14
A SQC1 SQRT( C1 )
A X MIN( ARC, SQC1 )
A TMP C2 * ( C1 - X * X )
A TMP SQRT( MAX( TMP, EPS2 ) )
A TMP2 SQRT( C2 ) * ASIN( X / SQC1 )
F 0.5 * ( - X * TMP - C1 * TMP2 )
G ARC - TMP
H ARC ARC C2 * X / TMP
ENDATA