MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Removed Instance minlphix

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
316.69269540 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)
-7062.66462800 p2 ( gdx sol )
(infeas: 6e-07)
-12295.92839000 p3 ( gdx sol )
(infeas: 1e-06)
Dual Bounds
316.69269540 (ANTIGONE)
316.69269540 (COUENNE)
316.69269520 (LINDO)
-35061589860.00000000 (SCIP)
0.00000000 (SHOT)
References Floudas, C A and Paules IV, Granville E, A Mixed-Integer Nonlinear Programming Formulation for the Synthesis of Heat Integrated Distillation Sequence, Computers and Chemical Engineering, 12:6, 1988, 531-546.
Source GAMS Model Library model minlphi
Application Heat Integrated Distillation Sequences
Added to library 01 May 2001
Removed from library 16 Feb 2022
Removed because Difficult numerical behavior. Optimal value changes sign and by several orders of magnitude when increasing feasibility tolerance.
Problem type MBNLP
#Variables 84
#Binary Variables 20
#Integer Variables 0
#Nonlinear Variables 36
#Nonlinear Binary Variables 4
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature indefinite
#Nonzeros in Objective 52
#Nonlinear Nonzeros in Objective 36
#Constraints 92
#Linear Constraints 88
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 4
Operands in Gen. Nonlin. Functions div mul sqrt
Constraints curvature indefinite
#Nonzeros in Jacobian 264
#Nonlinear Nonzeros in Jacobian 4
#Nonzeros in (Upper-Left) Hessian of Lagrangian 112
#Nonzeros in Diagonal of Hessian of Lagrangian 16
#Blocks in Hessian of Lagrangian 4
Minimal blocksize in Hessian of Lagrangian 9
Maximal blocksize in Hessian of Lagrangian 9
Average blocksize in Hessian of Lagrangian 9.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 8.9300e-04
Maximal coefficient 1.5000e+03
Infeasibility of initial point 396
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       31        0       62        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         85       65       20        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        317      277       40        0
*
*  Solve m using MINLP minimizing objvar;


Variables  objvar,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,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,b66,b67,b68,b69
          ,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85;

Positive Variables  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,x31,x33,x34,x35,x36
          ,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65;

Binary Variables  b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80
          ,b81,b82,b83,b84,b85;

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.. -(0.4*((-1.15398 + 0.003375*x30)*x2 + (-0.30630793 + 0.000893*x31)*x3 + (-
     1.57608132 + 0.004458*x32)*x4 + (-1.08593792 + 0.003176*x33)*x5 + 
     31.8928571428571*x14/(1 + x30 - x36 - b82) + 31.8928571428571*x15/(1 + x31
      - x37 - b83) + 31.8928571428571*x16/(1 + x32 - x34 - b84) + 
     31.8928571428571*x17/(1 + x33 - x35 - b85) + 151.125*b82 + 180.003*b83 + 
     4.2286*b84 + 213.42*b85 + 31.8928571428571*x26/(1 + x38 - b82) + 
     31.8928571428571*x27/(1 + x39 - b83) + 31.8928571428571*x28/(1 + x40 - b84
     ) + 31.8928571428571*x29/(1 + x41 - b85) + 31.8928571428571*x18/(421 - x34
     ) + 31.8928571428571*x19/(421 - x35) + 31.8928571428571*x20/(421 - x36) + 
     31.8928571428571*x21/(421 - x37) + 31.8928571428571*x22/(373 - x34) + 
     31.8928571428571*x23/(373 - x35) + 31.8928571428571*x24/(373 - x36) + 
     31.8928571428571*x25/(373 - x37)) + 12.95216*x18 + 12.95216*x19 + 12.95216
     *x20 + 12.95216*x21 + 4.75228*x22 + 4.75228*x23 + 4.75228*x24 + 4.75228*
     x25 + 2.418*x26 + 2.418*x27 + 2.418*x28 + 2.418*x29) + objvar - 1.3568*b66
      - 1.3568*b67 - 1.3568*b68 - 1.3568*b69 - 1.3568*b70 - 1.3568*b71
      - 1.3568*b72 - 1.3568*b73 - 1.3568*b74 - 1.3568*b75 - 1.3568*b76
      - 1.3568*b77 - 1.3568*b78 - 1.3568*b79 - 1.3568*b80 - 1.3568*b81 =E= 0;

e2.. -(0.666666666666667*sqrt((-305 + x30)*(-325 + x30)) + 0.333333333333333*
     x30) + x38 - x42 + x46 =E= -105;

e3.. -(0.666666666666667*sqrt((-305 + x31)*(-325 + x31)) + 0.333333333333333*
     x31) + x39 - x43 + x47 =E= -105;

e4.. -(0.666666666666667*sqrt((-305 + x32)*(-325 + x32)) + 0.333333333333333*
     x32) + x40 - x44 + x48 =E= -105;

e5.. -(0.666666666666667*sqrt((-305 + x33)*(-325 + x33)) + 0.333333333333333*
     x33) + x41 - x45 + x49 =E= -105;

e6..    x30 + x34 + x38 - 1500*b82 =L= 0;

e7..    x31 + x35 + x39 - 1500*b83 =L= 0;

e8..    x32 + x36 + x40 - 1500*b84 =L= 0;

e9..    x33 + x37 + x41 - 1500*b85 =L= 0;

e10..    x42 + x50 + x54 + 1500*b82 =L= 1500;

e11..    x43 + x51 + x55 + 1500*b83 =L= 1500;

e12..    x44 + x52 + x56 + 1500*b84 =L= 1500;

e13..    x45 + x53 + x57 + 1500*b85 =L= 1500;

e14..    x46 + x58 + x62 + 1500*b82 =L= 1500;

e15..    x47 + x59 + x63 + 1500*b83 =L= 1500;

e16..    x48 + x60 + x64 + 1500*b84 =L= 1500;

e17..    x49 + x61 + x65 + 1500*b85 =L= 1500;

e18..    0.9*x3 - x5 =E= 0;

e19..    0.2*x2 - x4 =E= 0;

e20..    x2 + x3 =E= 396;

e21..    x2 - 1500*b82 =L= 0;

e22..    x3 - 1500*b83 =L= 0;

e23..    x4 - 1500*b84 =L= 0;

e24..    x5 - 1500*b85 =L= 0;

e25..    x10 - 0.0225*x30 - x58 + x62 =E= 24.7068;

e26..    x11 - 0.013*x31 - x59 + x63 =E= 20.54087;

e27..    x12 - 0.0043*x32 - x60 + x64 =E= 2.239778;

e28..    x13 - 0.0156*x33 - x61 + x65 =E= 29.766048;

e29..    x6 - x10 =E= 0;

e30..    x7 - x11 =E= 0;

e31..    x8 - x12 =E= 0;

e32..    x9 - x13 =E= 0;

e33..    x10 - x14 - x26 =E= 0;

e34..    x11 - x15 - x27 =E= 0;

e35..    x12 - x16 - x28 =E= 0;

e36..    x13 - x17 - x29 =E= 0;

e37..    x6 - x16 - x18 - x22 =E= 0;

e38..    x7 - x17 - x19 - x23 =E= 0;

e39..    x8 - x14 - x20 - x24 =E= 0;

e40..    x9 - x15 - x21 - x25 =E= 0;

e41..    x34 =L= 411;

e42..    x35 =L= 411;

e43..    x36 =L= 411;

e44..    x37 =L= 411;

e45..  - x30 + 1500*b82 =L= 1158.08;

e46..  - x31 + 1500*b83 =L= 1156.99;

e47..  - x32 + 1500*b84 =L= 1146.46;

e48..  - x33 + 1500*b85 =L= 1158.08;

e49..  - 1.028*x30 + x34 - x50 + x54 =E= -341.95276;

e50..  - 1.05*x31 + x35 - x51 + x55 =E= -347.9205;

e51..  - 1.029*x32 + x36 - x52 + x56 =E= -355.03666;

e52..  - 1.005*x33 + x37 - x53 + x57 =E= -334.4486;

e53..  - x30 + x36 + 1500*b66 =L= 1490;

e54..  - x31 + x37 + 1500*b67 =L= 1490;

e55..  - x32 + x34 + 1500*b68 =L= 1490;

e56..  - x33 + x35 + 1500*b69 =L= 1490;

e57..    x34 + 1500*b74 =L= 1863;

e58..    x35 + 1500*b75 =L= 1863;

e59..    x36 + 1500*b76 =L= 1863;

e60..    x37 + 1500*b77 =L= 1863;

e61..    x14 - 1500*b66 =L= 0;

e62..    x15 - 1500*b67 =L= 0;

e63..    x16 - 1500*b68 =L= 0;

e64..    x17 - 1500*b69 =L= 0;

e65..    x18 - 1500*b70 =L= 0;

e66..    x19 - 1500*b71 =L= 0;

e67..    x20 - 1500*b72 =L= 0;

e68..    x21 - 1500*b73 =L= 0;

e69..    x22 - 1500*b74 =L= 0;

e70..    x23 - 1500*b75 =L= 0;

e71..    x24 - 1500*b76 =L= 0;

e72..    x25 - 1500*b77 =L= 0;

e73..    x26 - 1500*b78 =L= 0;

e74..    x27 - 1500*b79 =L= 0;

e75..    x28 - 1500*b80 =L= 0;

e76..    x29 - 1500*b81 =L= 0;

e77..    x6 + x10 - 1500*b82 =L= 0;

e78..    x7 + x11 - 1500*b83 =L= 0;

e79..    x8 + x12 - 1500*b84 =L= 0;

e80..    x9 + x13 - 1500*b85 =L= 0;

e81..    b83 - b85 =E= 0;

e82..    b82 - b84 =E= 0;

e83..    b82 + b83 =E= 1;

e84..    b70 + b74 =L= 1;

e85..    b71 + b75 =L= 1;

e86..    b72 + b76 =L= 1;

e87..    b73 + b77 =L= 1;

e88..    b66 + b68 =L= 1;

e89..    b67 + b69 =L= 1;

e90..    b66 + b68 + b70 + b74 + b78 - 20*b82 =L= 0;

e91..    b67 + b69 + b71 + b75 + b79 - 20*b83 =L= 0;

e92..    b66 + b68 + b72 + b76 + b80 - 20*b84 =L= 0;

e93..    b67 + b69 + b73 + b77 + b81 - 20*b85 =L= 0;

* set non-default bounds
x30.lo = 326;
x31.up = 304;
x32.lo = 326;
x33.up = 304;
x34.up = 1000;
x35.up = 1000;
x36.up = 1000;
x37.up = 1000;

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: 2022-05-24 Git hash: 1198c186
Imprint / Privacy Policy / License: CC-BY 4.0