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Instance: ethanolh

Formats ams gms mod nl osil
Primal Bounds
-133.37441080 p1 ( gdx sol )
(infeas: 1e-13)
-157.58653210 p2 ( gdx sol )
(infeas: 3e-14)
Dual Bounds
-157.58653900 (ANTIGONE)
-157.58653210 (BARON)
-157.58654000 (COUENNE)
-157.58653210 (LINDO)
-374.49416930 (SCIP)
References Guillen, Gonzalo and Pozo, Carlos, Optimization of metabolic networks in biotechnology, 2010.
Source GMA_ethanol_model_CH.gms from minlp.org model 81
Application Metabolic Networks
Added to library 25 Sep 2013
Problem type MBNLP
#Variables 61
#Binary Variables 24
#Integer Variables 0
#Nonlinear Variables 13
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type signomial
Objective curvature indefinite
#Nonzeros in Objective 6
#Nonlinear Nonzeros in Objective 6
#Constraints 80
#Linear Constraints 75
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 5
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 219
#Nonlinear Nonzeros in Jacobian 41
#Nonzeros in (Upper-Left) Hessian of Lagrangian 105
#Nonzeros in Diagonal of Hessian of Lagrangian 5
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 13
Maximal blocksize in Hessian of Lagrangian 13
Average blocksize in Hessian of Lagrangian 13.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1
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
*         81       22       29       30        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         62       38       24        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        226      179       47        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,objvar,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52
          ,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13;

Binary Variables  b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62;

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;


e1.. 325.08*x1**eps*x2**eps*x3**0.05*x4**0.533*x5**(-0.0822)*x12 + objvar =E= 0
     ;

e2.. -(16.00034*x1**eps*x2**(-0.2344)*x3**eps*x4**eps*x5**eps*x6 - 196.1292*x1
     **0.7464*x2**eps*x3**eps*x4**eps*x5**0.0243*x7) =E= 0;

e3.. -(196.1292*x1**0.7464*x2**eps*x3**eps*x4**eps*x5**0.0243*x7 - 16.58544*x1
     **eps*x2**0.7318*x3**eps*x4**eps*x5**(-0.3941)*x8 - 0.012879*x1**eps*x2**
     8.6107*x3**eps*x4**eps*x5**eps*x9) =E= 0;

e4.. -(16.58544*x1**eps*x2**0.7318*x3**eps*x4**eps*x5**(-0.3941)*x8 - 
     3.78145609890476*x1**eps*x2**eps*x3**0.6159*x4**eps*x5**0.1308*x10 - 
     9.59175*x1**eps*x2**eps*x3**0.05*x4**0.533*x5**(-0.0822)*x11) =E= 0;

e5.. -(7.56291219780952*x1**eps*x2**eps*x3**0.6159*x4**eps*x5**0.1308*x10 - 
     325.08*x1**eps*x2**eps*x3**0.05*x4**0.533*x5**(-0.0822)*x12) =E= 0;

e6.. -(-196.1292*x1**0.7464*x2**eps*x3**eps*x4**eps*x5**0.0243*x7 - 16.58544*x1
     **eps*x2**0.7318*x3**eps*x4**eps*x5**(-0.3941)*x8 - 0.012879*x1**eps*x2**
     8.6107*x3**eps*x4**eps*x5**eps*x9 + 7.56291219780952*x1**eps*x2**eps*x3**
     0.6159*x4**eps*x5**0.1308*x10 + 325.08*x1**eps*x2**eps*x3**0.05*x4**0.533*
     x5**(-0.0822)*x12 - 25.1*x1**eps*x2**eps*x3**eps*x4**eps*x5**1*x13) =E= 0;

e7..    x1 =G= 0.00345;

e8..    x2 =G= 0.1011;

e9..    x3 =G= 0.9144;

e10..    x4 =G= 0.00095;

e11..    x5 =G= 0.11278;

e12..    x1 =L= 0.345;

e13..    x2 =L= 10.11;

e14..    x3 =L= 91.44;

e15..    x4 =L= 0.095;

e16..    x5 =L= 11.278;

e17..    x6 - x14 - x22 - x30 =E= 0;

e18..    x7 - x15 - x23 - x31 =E= 0;

e19..    x8 - x16 - x24 - x32 =E= 0;

e20..    x9 - x17 - x25 - x33 =E= 0;

e21..    x10 - x18 - x26 - x34 =E= 0;

e22..    x11 - x19 - x27 - x35 =E= 0;

e23..    x12 - x20 - x28 - x36 =E= 0;

e24..    x13 - x21 - x29 - x37 =E= 0;

e25..    x14 - 0.2*b39 =G= 0;

e26..    x15 - 0.2*b40 =G= 0;

e27..    x16 - 0.2*b41 =G= 0;

e28..    x17 - 0.2*b42 =G= 0;

e29..    x18 - 0.2*b43 =G= 0;

e30..    x19 - 0.2*b44 =G= 0;

e31..    x20 - 0.2*b45 =G= 0;

e32..    x21 - 0.2*b46 =G= 0;

e33..    x14 - 0.999999995*b39 =L= 0;

e34..    x15 - 0.999999995*b40 =L= 0;

e35..    x16 - 0.999999995*b41 =L= 0;

e36..    x17 - 0.999999995*b42 =L= 0;

e37..    x18 - 0.999999995*b43 =L= 0;

e38..    x19 - 0.999999995*b44 =L= 0;

e39..    x20 - 0.999999995*b45 =L= 0;

e40..    x21 - 0.999999995*b46 =L= 0;

e41..    x22 - 0.999999995*b47 =G= 0;

e42..    x23 - 0.999999995*b48 =G= 0;

e43..    x24 - 0.999999995*b49 =G= 0;

e44..    x25 - 0.999999995*b50 =G= 0;

e45..    x26 - 0.999999995*b51 =G= 0;

e46..    x27 - 0.999999995*b52 =G= 0;

e47..    x28 - 0.999999995*b53 =G= 0;

e48..    x29 - 0.999999995*b54 =G= 0;

e49..    x22 - 1.000000005*b47 =L= 0;

e50..    x23 - 1.000000005*b48 =L= 0;

e51..    x24 - 1.000000005*b49 =L= 0;

e52..    x25 - 1.000000005*b50 =L= 0;

e53..    x26 - 1.000000005*b51 =L= 0;

e54..    x27 - 1.000000005*b52 =L= 0;

e55..    x28 - 1.000000005*b53 =L= 0;

e56..    x29 - 1.000000005*b54 =L= 0;

e57..    x30 - 1.000000005*b55 =G= 0;

e58..    x31 - 1.000000005*b56 =G= 0;

e59..    x32 - 1.000000005*b57 =G= 0;

e60..    x33 - 1.000000005*b58 =G= 0;

e61..    x34 - 1.000000005*b59 =G= 0;

e62..    x35 - 1.000000005*b60 =G= 0;

e63..    x36 - 1.000000005*b61 =G= 0;

e64..    x37 - 1.000000005*b62 =G= 0;

e65..    x30 - 5*b55 =L= 0;

e66..    x31 - 5*b56 =L= 0;

e67..    x32 - 5*b57 =L= 0;

e68..    x33 - 5*b58 =L= 0;

e69..    x34 - 5*b59 =L= 0;

e70..    x35 - 5*b60 =L= 0;

e71..    x36 - 5*b61 =L= 0;

e72..    x37 - 5*b62 =L= 0;

e73..    b39 + b47 + b55 =E= 1;

e74..    b40 + b48 + b56 =E= 1;

e75..    b41 + b49 + b57 =E= 1;

e76..    b42 + b50 + b58 =E= 1;

e77..    b43 + b51 + b59 =E= 1;

e78..    b44 + b52 + b60 =E= 1;

e79..    b45 + b53 + b61 =E= 1;

e80..    b46 + b54 + b62 =E= 1;

e81..    b39 + b40 + b41 + b42 + b43 + b44 + b45 + b46 + b55 + b56 + b57 + b58
       + b59 + b60 + b61 + b62 =L= 8;

* set non-default levels
x1.l = 0.0345;
x2.l = 1.011;
x3.l = 9.144;
x4.l = 0.0095;
x5.l = 1.1278;

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
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