MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Removed Instance ethanolh
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ⓘ | -157.58653850 (ANTIGONE) -157.58653210 (BARON) -157.58654000 (COUENNE) -157.58653210 (LINDO) -157.58654790 (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 |
| Removed from libraryⓘ | 28 Feb 2022 |
| Removed becauseⓘ | Use of eps in original GAMS model probably a bug. |
| 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 |
| Minimal coefficientⓘ | 0.0000e+00 |
| Maximal coefficientⓘ | 3.2508e+02 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity 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: 2025-08-07 Git hash: e62cedfc