MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance: genpooling_lee2

Formats ams gms lp mod nl osil pip
Primal Bounds
-3849.26542400 p1 ( gdx sol )
(infeas: 3e-14)
Dual Bounds
-3849.26542400 (ANTIGONE)
-3849.26543300 (BARON)
-3849.26683100 (COUENNE)
-3849.26542400 (LINDO)
-3849.26546800 (SCIP)
References Misener, Ruth and Floudas, C A, Generalized Pooling Problem, 2011.
Source generalizedpooling_lee2.gms from minlp.org model 123
Application Pooling Problem
Added to library 25 Sep 2013
Problem type MBQCP
#Variables 53
#Binary Variables 9
#Integer Variables 0
#Nonlinear Variables 24
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 41
#Nonlinear Nonzeros in Objective 0
#Constraints 92
#Linear Constraints 62
#Quadratic Constraints 30
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 412
#Nonlinear Nonzeros in Jacobian 192
#Nonzeros in (Upper-Left) Hessian of Lagrangian 72
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 4
Minimal blocksize in Hessian of Lagrangian 6
Maximal blocksize in Hessian of Lagrangian 6
Average blocksize in Hessian of Lagrangian 6.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 284
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
*         93       17        0       76        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         54       45        9        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        454      262      192        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,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,objvar;

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,x29,x30,x31,x32;

Binary Variables  b45,b46,b47,b48,b49,b50,b51,b52,b53;

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,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91,e92,e93;


e1..  - 6.2*x1 - 9.4*x2 - 7.6*x3 - 10.2*x4 - 1.67*x5 - 2.53*x6 - 2.05*x7
      - 2.75*x8 - 3.58*x9 - 5.42*x10 - 4.39*x11 - 5.89*x12 - 4.53*x13
      - 6.87*x14 - 5.55*x15 - 7.45*x16 - 2.62*x17 - 3.98*x18 - 3.22*x19
      - 4.32*x20 + 10.5*x21 + 11.2*x22 + 12.5*x23 + 10.5*x24 + 11.2*x25
      + 12.5*x26 + 10.5*x27 + 11.2*x28 + 12.5*x29 + 10.5*x30 + 11.2*x31
      + 12.5*x32 - 260*b45 - 70*b46 - 150*b47 - 190*b48 - 110*b49 - 310*b50
      - 470*b51 - 380*b52 - 510*b53 + objvar =E= 0;

e2..  - x21 - x24 - x27 - x30 =L= -229;

e3..  - x22 - x25 - x28 - x31 =L= -173;

e4..  - x23 - x26 - x29 - x32 =L= -284;

e5..    x21 + x24 + x27 + x30 =L= 229;

e6..    x22 + x25 + x28 + x31 =L= 173;

e7..    x23 + x26 + x29 + x32 =L= 284;

e8..    x1 + x5 + x9 + x13 + x17 - x21 - x22 - x23 =E= 0;

e9..    x2 + x6 + x10 + x14 + x18 - x24 - x25 - x26 =E= 0;

e10..    x3 + x7 + x11 + x15 + x19 - x27 - x28 - x29 =E= 0;

e11..    x4 + x8 + x12 + x16 + x20 - x30 - x31 - x32 =E= 0;

e12.. -(x33*x21 + x33*x22 + x33*x23) + 0.0909*x1 + 0.5*x5 + 0.32*x9
       + 0.4286*x13 + 0.1299*x17 =E= 0;

e13.. -(x34*x21 + x34*x22 + x34*x23) + 0.5455*x1 + 0.125*x5 + 0.44*x9
       + 0.4286*x13 + 0.3506*x17 =E= 0;

e14.. -(x35*x21 + x35*x22 + x35*x23) + 0.3636*x1 + 0.375*x5 + 0.24*x9
       + 0.1428*x13 + 0.5195*x17 =E= 0;

e15.. -(x36*x24 + x36*x25 + x36*x26) + 0.0909*x2 + 0.5*x6 + 0.32*x10
       + 0.4286*x14 + 0.1299*x18 =E= 0;

e16.. -(x37*x24 + x37*x25 + x37*x26) + 0.5455*x2 + 0.125*x6 + 0.44*x10
       + 0.4286*x14 + 0.3506*x18 =E= 0;

e17.. -(x38*x24 + x38*x25 + x38*x26) + 0.3636*x2 + 0.375*x6 + 0.24*x10
       + 0.1428*x14 + 0.5195*x18 =E= 0;

e18.. -(x39*x27 + x39*x28 + x39*x29) + 0.0909*x3 + 0.5*x7 + 0.32*x11
       + 0.4286*x15 + 0.1299*x19 =E= 0;

e19.. -(x40*x27 + x40*x28 + x40*x29) + 0.5455*x3 + 0.125*x7 + 0.44*x11
       + 0.4286*x15 + 0.3506*x19 =E= 0;

e20.. -(x41*x27 + x41*x28 + x41*x29) + 0.3636*x3 + 0.375*x7 + 0.24*x11
       + 0.1428*x15 + 0.5195*x19 =E= 0;

e21.. -(x42*x30 + x42*x31 + x42*x32) + 0.0909*x4 + 0.5*x8 + 0.32*x12
       + 0.4286*x16 + 0.1299*x20 =E= 0;

e22.. -(x43*x30 + x43*x31 + x43*x32) + 0.5455*x4 + 0.125*x8 + 0.44*x12
       + 0.4286*x16 + 0.3506*x20 =E= 0;

e23.. -(x44*x30 + x44*x31 + x44*x32) + 0.3636*x4 + 0.375*x8 + 0.24*x12
       + 0.1428*x16 + 0.5195*x20 =E= 0;

e24.. 0.13*x21 - (x33*x21 + x36*x24 + x39*x27 + x42*x30) + 0.13*x24 + 0.13*x27
       + 0.13*x30 =L= 0;

e25.. 0.38*x21 - (x34*x21 + x37*x24 + x40*x27 + x43*x30) + 0.38*x24 + 0.38*x27
       + 0.38*x30 =L= 0;

e26.. 0.49*x21 - (x35*x21 + x38*x24 + x41*x27 + x44*x30) + 0.49*x24 + 0.49*x27
       + 0.49*x30 =L= 0;

e27.. 0.27*x22 - (x33*x22 + x36*x25 + x39*x28 + x42*x31) + 0.27*x25 + 0.27*x28
       + 0.27*x31 =L= 0;

e28.. 0.43*x22 - (x34*x22 + x37*x25 + x40*x28 + x43*x31) + 0.43*x25 + 0.43*x28
       + 0.43*x31 =L= 0;

e29.. 0.3*x22 - (x35*x22 + x38*x25 + x41*x28 + x44*x31) + 0.3*x25 + 0.3*x28 + 
      0.3*x31 =L= 0;

e30.. 0.45*x23 - (x33*x23 + x36*x26 + x39*x29 + x42*x32) + 0.45*x26 + 0.45*x29
       + 0.45*x32 =L= 0;

e31.. 0.2*x23 - (x34*x23 + x37*x26 + x40*x29 + x43*x32) + 0.2*x26 + 0.2*x29 + 
      0.2*x32 =L= 0;

e32.. 0.35*x23 - (x35*x23 + x38*x26 + x41*x29 + x44*x32) + 0.35*x26 + 0.35*x29
       + 0.35*x32 =L= 0;

e33.. x33*x21 + x36*x24 + x39*x27 + x42*x30 - 0.13*x21 - 0.13*x24 - 0.13*x27 - 
      0.13*x30 =L= 0;

e34.. x34*x21 + x37*x24 + x40*x27 + x43*x30 - 0.38*x21 - 0.38*x24 - 0.38*x27 - 
      0.38*x30 =L= 0;

e35.. x35*x21 + x38*x24 + x41*x27 + x44*x30 - 0.49*x21 - 0.49*x24 - 0.49*x27 - 
      0.49*x30 =L= 0;

e36.. x33*x22 + x36*x25 + x39*x28 + x42*x31 - 0.27*x22 - 0.27*x25 - 0.27*x28 - 
      0.27*x31 =L= 0;

e37.. x34*x22 + x37*x25 + x40*x28 + x43*x31 - 0.43*x22 - 0.43*x25 - 0.43*x28 - 
      0.43*x31 =L= 0;

e38.. x35*x22 + x38*x25 + x41*x28 + x44*x31 - 0.3*x22 - 0.3*x25 - 0.3*x28 - 0.3
      *x31 =L= 0;

e39.. x33*x23 + x36*x26 + x39*x29 + x42*x32 - 0.45*x23 - 0.45*x26 - 0.45*x29 - 
      0.45*x32 =L= 0;

e40.. x34*x23 + x37*x26 + x40*x29 + x43*x32 - 0.2*x23 - 0.2*x26 - 0.2*x29 - 0.2
      *x32 =L= 0;

e41.. x35*x23 + x38*x26 + x41*x29 + x44*x32 - 0.35*x23 - 0.35*x26 - 0.35*x29 - 
      0.35*x32 =L= 0;

e42..    x1 - 686*b50 =L= 0;

e43..    x2 - 686*b51 =L= 0;

e44..    x3 - 686*b52 =L= 0;

e45..    x4 - 686*b53 =L= 0;

e46..    x5 - 686*b50 =L= 0;

e47..    x6 - 686*b51 =L= 0;

e48..    x7 - 686*b52 =L= 0;

e49..    x8 - 686*b53 =L= 0;

e50..    x9 - 686*b50 =L= 0;

e51..    x10 - 686*b51 =L= 0;

e52..    x11 - 686*b52 =L= 0;

e53..    x12 - 686*b53 =L= 0;

e54..    x13 - 686*b50 =L= 0;

e55..    x14 - 686*b51 =L= 0;

e56..    x15 - 686*b52 =L= 0;

e57..    x16 - 686*b53 =L= 0;

e58..    x17 - 686*b50 =L= 0;

e59..    x18 - 686*b51 =L= 0;

e60..    x19 - 686*b52 =L= 0;

e61..    x20 - 686*b53 =L= 0;

e62..    x1 - 686*b45 =L= 0;

e63..    x2 - 686*b45 =L= 0;

e64..    x3 - 686*b45 =L= 0;

e65..    x4 - 686*b45 =L= 0;

e66..    x5 - 686*b46 =L= 0;

e67..    x6 - 686*b46 =L= 0;

e68..    x7 - 686*b46 =L= 0;

e69..    x8 - 686*b46 =L= 0;

e70..    x9 - 686*b47 =L= 0;

e71..    x10 - 686*b47 =L= 0;

e72..    x11 - 686*b47 =L= 0;

e73..    x12 - 686*b47 =L= 0;

e74..    x13 - 686*b48 =L= 0;

e75..    x14 - 686*b48 =L= 0;

e76..    x15 - 686*b48 =L= 0;

e77..    x16 - 686*b48 =L= 0;

e78..    x17 - 686*b49 =L= 0;

e79..    x18 - 686*b49 =L= 0;

e80..    x19 - 686*b49 =L= 0;

e81..    x20 - 686*b49 =L= 0;

e82..    x21 - 229*b50 =L= 0;

e83..    x22 - 173*b50 =L= 0;

e84..    x23 - 284*b50 =L= 0;

e85..    x24 - 229*b51 =L= 0;

e86..    x25 - 173*b51 =L= 0;

e87..    x26 - 284*b51 =L= 0;

e88..    x27 - 229*b52 =L= 0;

e89..    x28 - 173*b52 =L= 0;

e90..    x29 - 284*b52 =L= 0;

e91..    x30 - 229*b53 =L= 0;

e92..    x31 - 173*b53 =L= 0;

e93..    x32 - 284*b53 =L= 0;

* set non-default bounds
x1.up = 686;
x2.up = 686;
x3.up = 686;
x4.up = 686;
x5.up = 686;
x6.up = 686;
x7.up = 686;
x8.up = 686;
x9.up = 686;
x10.up = 686;
x11.up = 686;
x12.up = 686;
x13.up = 686;
x14.up = 686;
x15.up = 686;
x16.up = 686;
x17.up = 686;
x18.up = 686;
x19.up = 686;
x20.up = 686;
x21.up = 229;
x22.up = 173;
x23.up = 284;
x24.up = 229;
x25.up = 173;
x26.up = 284;
x27.up = 229;
x28.up = 173;
x29.up = 284;
x30.up = 229;
x31.up = 173;
x32.up = 284;
x33.lo = 0.0909; x33.up = 0.5;
x34.lo = 0.125; x34.up = 0.5455;
x35.lo = 0.1428; x35.up = 0.5195;
x36.lo = 0.0909; x36.up = 0.5;
x37.lo = 0.125; x37.up = 0.5455;
x38.lo = 0.1428; x38.up = 0.5195;
x39.lo = 0.0909; x39.up = 0.5;
x40.lo = 0.125; x40.up = 0.5455;
x41.lo = 0.1428; x41.up = 0.5195;
x42.lo = 0.0909; x42.up = 0.5;
x43.lo = 0.125; x43.up = 0.5455;
x44.lo = 0.1428; x44.up = 0.5195;

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: 2018-09-14 Git hash: ac5a5314
Imprint / Privacy Policy