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Instance: ethanolm

Formats ams gms mod nl osil
Primal Bounds
-157.58653210 p1 ( gdx sol )
(infeas: 3e-14)
Dual Bounds
-157.58654000 (ANTIGONE)
-157.58653210 (BARON)
-157.59507490 (COUENNE)
-157.58653210 (LINDO)
-249.78775370 (SCIP)
References Guillen, Gonzalo and Pozo, Carlos, Optimization of metabolic networks in biotechnology, 2010.
Source GMA_ethanol_model_BigM.gms from minlp.org model 81
Application Metabolic Networks
Added to library 25 Sep 2013
Problem type MBNLP
#Variables 37
#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 72
#Linear Constraints 67
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 5
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 171
#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
*         73       14       13       46        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         38       14       24        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        178      131       47        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,objvar,b15,b16,b17,b18
          ,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35
          ,b36,b37,b38;

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

Binary Variables  b15,b16,b17,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29
          ,b30,b31,b32,b33,b34,b35,b36,b37,b38;

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;


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 + 100000*b15 =L= 100000.999999995;

e18..    x7 + 100000*b16 =L= 100000.999999995;

e19..    x8 + 100000*b17 =L= 100000.999999995;

e20..    x9 + 100000*b18 =L= 100000.999999995;

e21..    x10 + 100000*b19 =L= 100000.999999995;

e22..    x11 + 100000*b20 =L= 100000.999999995;

e23..    x12 + 100000*b21 =L= 100000.999999995;

e24..    x13 + 100000*b22 =L= 100000.999999995;

e25..  - x6 + 100000*b23 =L= 99999.000000005;

e26..  - x7 + 100000*b24 =L= 99999.000000005;

e27..  - x8 + 100000*b25 =L= 99999.000000005;

e28..  - x9 + 100000*b26 =L= 99999.000000005;

e29..  - x10 + 100000*b27 =L= 99999.000000005;

e30..  - x11 + 100000*b28 =L= 99999.000000005;

e31..  - x12 + 100000*b29 =L= 99999.000000005;

e32..  - x13 + 100000*b30 =L= 99999.000000005;

e33..    x6 + 100000*b23 =L= 100001.000000005;

e34..    x7 + 100000*b24 =L= 100001.000000005;

e35..    x8 + 100000*b25 =L= 100001.000000005;

e36..    x9 + 100000*b26 =L= 100001.000000005;

e37..    x10 + 100000*b27 =L= 100001.000000005;

e38..    x11 + 100000*b28 =L= 100001.000000005;

e39..    x12 + 100000*b29 =L= 100001.000000005;

e40..    x13 + 100000*b30 =L= 100001.000000005;

e41..  - x6 + 100000*b31 =L= 99998.999999995;

e42..  - x7 + 100000*b32 =L= 99998.999999995;

e43..  - x8 + 100000*b33 =L= 99998.999999995;

e44..  - x9 + 100000*b34 =L= 99998.999999995;

e45..  - x10 + 100000*b35 =L= 99998.999999995;

e46..  - x11 + 100000*b36 =L= 99998.999999995;

e47..  - x12 + 100000*b37 =L= 99998.999999995;

e48..  - x13 + 100000*b38 =L= 99998.999999995;

e49..    x6 =G= 0.2;

e50..    x7 =G= 0.2;

e51..    x8 =G= 0.2;

e52..    x9 =G= 0.2;

e53..    x10 =G= 0.2;

e54..    x11 =G= 0.2;

e55..    x12 =G= 0.2;

e56..    x13 =G= 0.2;

e57..    x6 =L= 5;

e58..    x7 =L= 5;

e59..    x8 =L= 5;

e60..    x9 =L= 5;

e61..    x10 =L= 5;

e62..    x11 =L= 5;

e63..    x12 =L= 5;

e64..    x13 =L= 5;

e65..    b15 + b23 + b31 =E= 1;

e66..    b16 + b24 + b32 =E= 1;

e67..    b17 + b25 + b33 =E= 1;

e68..    b18 + b26 + b34 =E= 1;

e69..    b19 + b27 + b35 =E= 1;

e70..    b20 + b28 + b36 =E= 1;

e71..    b21 + b29 + b37 =E= 1;

e72..    b22 + b30 + b38 =E= 1;

e73..    b15 + b16 + b17 + b18 + b19 + b20 + b21 + b22 + b31 + b32 + b33 + b34
       + b35 + b36 + b37 + b38 =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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