MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: minlphix

Formats ams gms mod nl osil
Primal Bounds (infeas ≤ 1e-08)
316.69269540 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
316.69269540 (ANTIGONE)
316.69269540 (COUENNE)
316.69269520 (LINDO)
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
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 mul div 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
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: 2019-07-12 Git hash: 46a7b4f1
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