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Instance water

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
923.71089140 p1 ( gdx sol )
(infeas: 3e-15)
906.35191110 p2 ( gdx sol )
(infeas: 3e-15)
904.90215930 p3 ( gdx sol )
(infeas: 3e-15)
Other points (infeas > 1e-08)  
Dual Bounds
676.74287480 (BARON)
324.68461220 (COUENNE)
670.36320240 (LINDO)
826.50997960 (SCIP)
References Brooke, Anthony, Drud, Arne S, and Meeraus, Alexander, Modeling Systems and Nonlinear Programming in a Research Environment. In Ragavan, R and Rohde, S M, Eds, Computers in Engineering, Vol. III, ACME, 1985.
Drud, Arne S and Rosenborg, A, Dimensioning Water Distribution Networks, Masters thesis, Institute of Mathematical Statistics and Operations Research, Technical University of Denmark, 1973. In Danish.
Source GAMS Model Library model water
Application Water Network Design
Added to library 31 Jul 2001
Problem type NLP
#Variables 41
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 32
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 0
#Constraints 25
#Linear Constraints 9
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 1
#General Nonlinear Constraints 14
Operands in Gen. Nonlin. Functions abs div mul vcpower
Constraints curvature indefinite
#Nonzeros in Jacobian 109
#Nonlinear Nonzeros in Jacobian 46
#Nonzeros in (Upper-Left) Hessian of Lagrangian 60
#Nonzeros in Diagonal of Hessian of Lagrangian 28
#Blocks in Hessian of Lagrangian 16
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 2.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 6.9000e-02
Maximal coefficient 2.5020e+03
Infeasibility of initial point 723.6
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         26       26        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         42       42        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        113       67       46        0
*
*  Solve m using DNLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,x41,objvar;

Positive Variables  x37,x38;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26;


e1..  - x1 - x2 - x3 + x37 =E= 0;

e2..  - x4 - x5 - x6 - x7 + x38 =E= 0;

e3..    x1 + x4 - x8 - x9 - x10 - x11 =E= 1.212;

e4..    x2 + x8 + x12 =E= 0.452;

e5..    x9 - x12 + x13 =E= 0.245;

e6..    x5 + x10 - x13 - x14 =E= 0.652;

e7..    x6 + x14 =E= 0.252;

e8..    x3 + x7 + x11 =E= 0.456;

e9.. -1.5722267648148*abs(x1)*x1/x15**5.33 + x29 - x31 =E= 0;

e10.. -1.32004857865156*abs(x2)*x2/x16**5.33 + x29 - x32 =E= 0;

e11.. -2.57705917665854*abs(x3)*x3/x17**5.33 + x29 - x36 =E= 0;

e12.. -2.06257339263358*abs(x4)*x4/x18**5.33 + x30 - x31 =E= 0;

e13.. -2.40235218067626*abs(x5)*x5/x19**5.33 + x30 - x34 =E= 0;

e14.. -1.339*abs(x6)*x6/x20**5.33 + x30 - x35 =E= 0;

e15.. -1.37419139860501*abs(x7)*x7/x21**5.33 + x30 - x36 =E= 0;

e16.. -1.2916134290104*abs(x8)*x8/x22**5.33 + x31 - x32 =E= 0;

e17.. -1.60230396616872*abs(x9)*x9/x23**5.33 + x31 - x33 =E= 0;

e18.. -1.339*abs(x10)*x10/x24**5.33 + x31 - x34 =E= 0;

e19.. -2.14329116080854*abs(x11)*x11/x25**5.33 + x31 - x36 =E= 0;

e20.. -1.24561882211213*abs(x12)*x12/x26**5.33 - x32 + x33 =E= 0;

e21.. -1.15157500841239*abs(x13)*x13/x27**5.33 - x33 + x34 =E= 0;

e22.. -2.06257339263358*abs(x14)*x14/x28**5.33 + x34 - x35 =E= 0;

e23.. -(1.02*x37*(-6.5 + x29) + 1.02*x38*(-3.25 + x30)) + x39 =E= 0;

e24.. -0.069*(1526.43375224737*x15**1.29 + 1281.60056179763*x16**1.29 + 
      2501.99920063936*x17**1.29 + 2002.49843945008*x18**1.29 + 
      2332.38075793812*x19**1.29 + 1300*x20**1.29 + 1334.16640641263*x21**1.29
       + 1253.99362039845*x22**1.29 + 1555.6349186104*x23**1.29 + 1300*x24**
      1.29 + 2080.86520466848*x25**1.29 + 1209.33866224478*x26**1.29 + 
      1118.03398874989*x27**1.29 + 2002.49843945008*x28**1.29) + x40 =E= 0;

e25..  - 0.2*x37 - 0.17*x38 + x41 =E= 0;

e26..  - 10*x39 - x40 - 10*x41 + objvar =E= 0;

* set non-default bounds
x15.lo = 0.15; x15.up = 2;
x16.lo = 0.15; x16.up = 2;
x17.lo = 0.15; x17.up = 2;
x18.lo = 0.15; x18.up = 2;
x19.lo = 0.15; x19.up = 2;
x20.lo = 0.15; x20.up = 2;
x21.lo = 0.15; x21.up = 2;
x22.lo = 0.15; x22.up = 2;
x23.lo = 0.15; x23.up = 2;
x24.lo = 0.15; x24.up = 2;
x25.lo = 0.15; x25.up = 2;
x26.lo = 0.15; x26.up = 2;
x27.lo = 0.15; x27.up = 2;
x28.lo = 0.15; x28.up = 2;
x29.lo = 6.5;
x30.lo = 3.25;
x31.lo = 16.58;
x32.lo = 14.92;
x33.lo = 12.925;
x34.lo = 12.26;
x35.lo = 8.76;
x36.lo = 16.08;
x37.up = 2.5;
x38.up = 6;

* set non-default levels
x15.l = 0.547722557505166;
x16.l = 0.547722557505166;
x17.l = 0.547722557505166;
x18.l = 0.547722557505166;
x19.l = 0.547722557505166;
x20.l = 0.547722557505166;
x21.l = 0.547722557505166;
x22.l = 0.547722557505166;
x23.l = 0.547722557505166;
x24.l = 0.547722557505166;
x25.l = 0.547722557505166;
x26.l = 0.547722557505166;
x27.l = 0.547722557505166;
x28.l = 0.547722557505166;
x29.l = 7.5;
x30.l = 4.25;
x31.l = 17.58;
x32.l = 15.92;
x33.l = 13.925;
x34.l = 13.26;
x35.l = 9.76;
x36.l = 17.08;
x37.l = 0.961470588235294;
x38.l = 2.30752941176471;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set DNLP $set DNLP DNLP
Solve m using %DNLP% minimizing objvar;


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