MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance ethanolm
Note, that in the GAMS models the constant eps has the numerical value of 0.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -157.58654000 (ANTIGONE) -157.58653210 (BARON) -157.59507490 (COUENNE) -157.58653210 (LINDO) -157.58654520 (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 |
| Removed from libraryⓘ | 28 Feb 2022 |
| Removed becauseⓘ | Use of eps in original GAMS model probably a bug. |
| 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 |
| Minimal coefficientⓘ | 0.0000e+00 |
| Maximal coefficientⓘ | 1.0000e+05 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity 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: 2025-08-07 Git hash: e62cedfc