MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance waterx

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
916.00401880 p1 ( gdx sol )
(infeas: 4e-15)
910.47114520 p2 ( gdx sol )
(infeas: 3e-15)
909.02786260 p3 ( gdx sol )
(infeas: 2e-15)
Other points (infeas > 1e-08)  
Dual Bounds
806.00216700 (BARON)
612.91897410 (COUENNE)
909.02786260 (LINDO)
867.99224360 (SCIP)
0.00000000 (SHOT)
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 waterx
Application Water Network Design
Added to library 01 May 2001
Problem type MBNLP
#Variables 70
#Binary Variables 14
#Integer Variables 0
#Nonlinear Variables 46
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 0
#Constraints 54
#Linear Constraints 38
#Quadratic Constraints 1
#Polynomial Constraints 0
#Signomial Constraints 15
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 236
#Nonlinear Nonzeros in Jacobian 60
#Nonzeros in (Upper-Left) Hessian of Lagrangian 130
#Nonzeros in Diagonal of Hessian of Lagrangian 42
#Blocks in Hessian of Lagrangian 16
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 2.875
#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
*         55       27        0       28        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         71       57       14        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        241      181       60        0
*
*  Solve m using MINLP 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,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,objvar,x57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69
          ,b70,b71;

Positive 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,x51,x52;

Binary Variables  b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71;

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,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55;


e1..  - x1 - x2 - x3 + x15 + x16 + x17 + x51 =E= 0;

e2..  - x4 - x5 - x6 - x7 + x18 + x19 + x20 + x21 + x52 =E= 0;

e3..    x1 + x4 - x8 - x9 - x10 - x11 - x15 - x18 + x22 + x23 + x24 + x25
      =E= 1.212;

e4..    x2 + x8 + x12 - x16 - x22 - x26 =E= 0.452;

e5..    x9 - x12 + x13 - x23 + x26 - x27 =E= 0.245;

e6..    x5 + x10 - x13 - x14 - x19 - x24 + x27 + x28 =E= 0.652;

e7..    x6 + x14 - x20 - x28 =E= 0.252;

e8..    x3 + x7 + x11 - x17 - x21 - x25 =E= 0.456;

e9.. -(1.5722267648148*x1 + 1.5722267648148*x15)*(x1 - x15)/x29**5.33 + x43
      - x45 =E= 0;

e10.. -(1.32004857865156*x2 + 1.32004857865156*x16)*(x2 - x16)/x30**5.33 + x43
       - x46 =E= 0;

e11.. -(2.57705917665854*x3 + 2.57705917665854*x17)*(x3 - x17)/x31**5.33 + x43
       - x50 =E= 0;

e12.. -(2.06257339263358*x4 + 2.06257339263358*x18)*(x4 - x18)/x32**5.33 + x44
       - x45 =E= 0;

e13.. -(2.40235218067626*x5 + 2.40235218067626*x19)*(x5 - x19)/x33**5.33 + x44
       - x48 =E= 0;

e14.. -(1.339*x6 + 1.339*x20)*(x6 - x20)/x34**5.33 + x44 - x49 =E= 0;

e15.. -(1.37419139860501*x7 + 1.37419139860501*x21)*(x7 - x21)/x35**5.33 + x44
       - x50 =E= 0;

e16.. -(1.2916134290104*x8 + 1.2916134290104*x22)*(x8 - x22)/x36**5.33 + x45
       - x46 =E= 0;

e17.. -(1.60230396616872*x9 + 1.60230396616872*x23)*(x9 - x23)/x37**5.33 + x45
       - x47 =E= 0;

e18.. -(1.339*x10 + 1.339*x24)*(x10 - x24)/x38**5.33 + x45 - x48 =E= 0;

e19.. -(2.14329116080854*x11 + 2.14329116080854*x25)*(x11 - x25)/x39**5.33
       + x45 - x50 =E= 0;

e20.. -(1.24561882211213*x12 + 1.24561882211213*x26)*(x12 - x26)/x40**5.33
       - x46 + x47 =E= 0;

e21.. -(1.15157500841239*x13 + 1.15157500841239*x27)*(x13 - x27)/x41**5.33
       - x47 + x48 =E= 0;

e22.. -(2.06257339263358*x14 + 2.06257339263358*x28)*(x14 - x28)/x42**5.33
       + x48 - x49 =E= 0;

e23.. -(1.02*x51*(-6.5 + x43) + 1.02*x52*(-3.25 + x44)) + x53 =E= 0;

e24.. -0.069*(1526.43375224737*x29**1.29 + 1281.60056179763*x30**1.29 + 
      2501.99920063936*x31**1.29 + 2002.49843945008*x32**1.29 + 
      2332.38075793812*x33**1.29 + 1300*x34**1.29 + 1334.16640641263*x35**1.29
       + 1253.99362039845*x36**1.29 + 1555.6349186104*x37**1.29 + 1300*x38**
      1.29 + 2080.86520466848*x39**1.29 + 1209.33866224478*x40**1.29 + 
      1118.03398874989*x41**1.29 + 2002.49843945008*x42**1.29) + x54 =E= 0;

e25..  - 0.2*x51 - 0.17*x52 + x55 =E= 0;

e26..  - 10*x53 - x54 - 10*x55 + objvar - x57 =E= 0;

e27..  - 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 + x57 =E= 0;

e28..    x1 - 2*b58 =L= 0;

e29..    x2 - 2*b59 =L= 0;

e30..    x3 - 2*b60 =L= 0;

e31..    x4 - 2*b61 =L= 0;

e32..    x5 - 2*b62 =L= 0;

e33..    x6 - 2*b63 =L= 0;

e34..    x7 - 2*b64 =L= 0;

e35..    x8 - 2*b65 =L= 0;

e36..    x9 - 2*b66 =L= 0;

e37..    x10 - 2*b67 =L= 0;

e38..    x11 - 2*b68 =L= 0;

e39..    x12 - 2*b69 =L= 0;

e40..    x13 - 2*b70 =L= 0;

e41..    x14 - 2*b71 =L= 0;

e42..    x15 + 2*b58 =L= 2;

e43..    x16 + 2*b59 =L= 2;

e44..    x17 + 2*b60 =L= 2;

e45..    x18 + 2*b61 =L= 2;

e46..    x19 + 2*b62 =L= 2;

e47..    x20 + 2*b63 =L= 2;

e48..    x21 + 2*b64 =L= 2;

e49..    x22 + 2*b65 =L= 2;

e50..    x23 + 2*b66 =L= 2;

e51..    x24 + 2*b67 =L= 2;

e52..    x25 + 2*b68 =L= 2;

e53..    x26 + 2*b69 =L= 2;

e54..    x27 + 2*b70 =L= 2;

e55..    x28 + 2*b71 =L= 2;

* set non-default bounds
x29.lo = 0.15; x29.up = 2;
x30.lo = 0.15; x30.up = 2;
x31.lo = 0.15; x31.up = 2;
x32.lo = 0.15; x32.up = 2;
x33.lo = 0.15; x33.up = 2;
x34.lo = 0.15; x34.up = 2;
x35.lo = 0.15; x35.up = 2;
x36.lo = 0.15; x36.up = 2;
x37.lo = 0.15; x37.up = 2;
x38.lo = 0.15; x38.up = 2;
x39.lo = 0.15; x39.up = 2;
x40.lo = 0.15; x40.up = 2;
x41.lo = 0.15; x41.up = 2;
x42.lo = 0.15; x42.up = 2;
x43.lo = 6.5;
x44.lo = 3.25;
x45.lo = 16.58;
x46.lo = 14.92;
x47.lo = 12.925;
x48.lo = 12.26;
x49.lo = 8.76;
x50.lo = 16.08;
x51.up = 2.5;
x52.up = 6;

* set non-default levels
x29.l = 0.547722557505166;
x30.l = 0.547722557505166;
x31.l = 0.547722557505166;
x32.l = 0.547722557505166;
x33.l = 0.547722557505166;
x34.l = 0.547722557505166;
x35.l = 0.547722557505166;
x36.l = 0.547722557505166;
x37.l = 0.547722557505166;
x38.l = 0.547722557505166;
x39.l = 0.547722557505166;
x40.l = 0.547722557505166;
x41.l = 0.547722557505166;
x42.l = 0.547722557505166;
x43.l = 11.5;
x44.l = 8.25;
x45.l = 21.58;
x46.l = 19.92;
x47.l = 17.925;
x48.l = 17.26;
x49.l = 13.76;
x50.l = 21.08;
x51.l = 0.961470588235294;
x52.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 MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2024-12-17 Git hash: 8eaceb91
Imprint / Privacy Policy / License: CC-BY 4.0