MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance batch
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 285506.50820000 (ALPHAECP) 285506.50820000 (ANTIGONE) 285506.50820000 (BARON) 285506.50820000 (BONMIN) 285506.00000000 (COUENNE) 285506.50820000 (LINDO) 285506.50820000 (SCIP) 285506.47800000 (SHOT) |
| Referencesⓘ | Kocis, Gary R and Grossmann, I E, Global Optimization of Nonconvex MINLP Problems in Process Synthesis, Industrial and Engineering Chemistry Research, 27:8, 1988, 1407-1421. |
| Sourceⓘ | modified MINOPT Model Library model kocis88-4a.dat, MacMINLP model batch.mod |
| Applicationⓘ | Batch processing |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 46 |
| #Binary Variablesⓘ | 24 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 22 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 12 |
| #Nonlinear Nonzeros in Objectiveⓘ | 12 |
| #Constraintsⓘ | 73 |
| #Linear Constraintsⓘ | 72 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 1 |
| Operands in Gen. Nonlin. Functionsⓘ | exp |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 178 |
| #Nonlinear Nonzeros in Jacobianⓘ | 10 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 44 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 22 |
| #Blocks in Hessian of Lagrangianⓘ | 11 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 2 |
| Average blocksize in Hessian of Lagrangianⓘ | 2.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 6.0000e-01 |
| Maximal coefficientⓘ | 2.5000e+05 |
| Infeasibility of initial pointⓘ | 2.486e+04 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 74 13 60 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 47 23 24 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 191 169 22 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,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,objvar;
Positive Variables x1,x2,x3,x4,x5,x6;
Binary Variables b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36,b37
,b38,b39,b40,b41,b42,b43,b44,b45,b46;
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;
e1.. -(250*exp(x1 + 0.6*x7) + 250*exp(x2 + 0.6*x8) + 250*exp(x3 + 0.6*x9) + 250
*exp(x4 + 0.6*x10) + 250*exp(x5 + 0.6*x11) + 250*exp(x6 + 0.6*x12))
+ objvar =E= 0;
e2.. x7 - x13 =G= 2.06686275947298;
e3.. x8 - x13 =G= 0.693147180559945;
e4.. x9 - x13 =G= 1.64865862558738;
e5.. x10 - x13 =G= 1.58923520511658;
e6.. x11 - x13 =G= 1.80828877117927;
e7.. x12 - x13 =G= 1.43508452528932;
e8.. x7 - x14 =G= -0.356674943938732;
e9.. x8 - x14 =G= -0.22314355131421;
e10.. x9 - x14 =G= -0.105360515657826;
e11.. x10 - x14 =G= 1.22377543162212;
e12.. x11 - x14 =G= 0.741937344729377;
e13.. x12 - x14 =G= 0.916290731874155;
e14.. x7 - x15 =G= -0.356674943938732;
e15.. x8 - x15 =G= 0.955511445027436;
e16.. x9 - x15 =G= 0.470003629245736;
e17.. x10 - x15 =G= 1.28093384546206;
e18.. x11 - x15 =G= 1.16315080980568;
e19.. x12 - x15 =G= 1.06471073699243;
e20.. x7 - x16 =G= 1.54756250871601;
e21.. x8 - x16 =G= 0.832909122935104;
e22.. x9 - x16 =G= 0.470003629245736;
e23.. x10 - x16 =G= 0.993251773010283;
e24.. x11 - x16 =G= 0.182321556793955;
e25.. x12 - x16 =G= 0.916290731874155;
e26.. x7 - x17 =G= 0.182321556793955;
e27.. x8 - x17 =G= 1.28093384546206;
e28.. x9 - x17 =G= 0.8754687373539;
e29.. x10 - x17 =G= 1.50407739677627;
e30.. x11 - x17 =G= 0.470003629245736;
e31.. x12 - x17 =G= 0.741937344729377;
e32.. x1 + x18 =G= 1.85629799036563;
e33.. x2 + x18 =G= 1.54756250871601;
e34.. x3 + x18 =G= 2.11625551480255;
e35.. x4 + x18 =G= 1.3609765531356;
e36.. x5 + x18 =G= 0.741937344729377;
e37.. x6 + x18 =G= 0.182321556793955;
e38.. x1 + x19 =G= 1.91692261218206;
e39.. x2 + x19 =G= 1.85629799036563;
e40.. x3 + x19 =G= 1.87180217690159;
e41.. x4 + x19 =G= 1.48160454092422;
e42.. x5 + x19 =G= 0.832909122935104;
e43.. x6 + x19 =G= 1.16315080980568;
e44.. x1 + x20 =G= 0;
e45.. x2 + x20 =G= 1.84054963339749;
e46.. x3 + x20 =G= 1.68639895357023;
e47.. x4 + x20 =G= 2.47653840011748;
e48.. x5 + x20 =G= 1.7404661748405;
e49.. x6 + x20 =G= 1.82454929205105;
e50.. x1 + x21 =G= 1.16315080980568;
e51.. x2 + x21 =G= 1.09861228866811;
e52.. x3 + x21 =G= 1.25276296849537;
e53.. x4 + x21 =G= 1.19392246847243;
e54.. x5 + x21 =G= 1.02961941718116;
e55.. x6 + x21 =G= 1.22377543162212;
e56.. x1 + x22 =G= 0.741937344729377;
e57.. x2 + x22 =G= 0.916290731874155;
e58.. x3 + x22 =G= 1.43508452528932;
e59.. x4 + x22 =G= 1.28093384546206;
e60.. x5 + x22 =G= 1.30833281965018;
e61.. x6 + x22 =G= 0.78845736036427;
e62.. 250000*exp(x18 - x13) + 150000*exp(x19 - x14) + 180000*exp(x20 - x15) +
160000*exp(x21 - x16) + 120000*exp(x22 - x17) =L= 6000;
e63.. x1 - 0.693147180559945*b29 - 1.09861228866811*b35
- 1.38629436111989*b41 =E= 0;
e64.. x2 - 0.693147180559945*b30 - 1.09861228866811*b36
- 1.38629436111989*b42 =E= 0;
e65.. x3 - 0.693147180559945*b31 - 1.09861228866811*b37
- 1.38629436111989*b43 =E= 0;
e66.. x4 - 0.693147180559945*b32 - 1.09861228866811*b38
- 1.38629436111989*b44 =E= 0;
e67.. x5 - 0.693147180559945*b33 - 1.09861228866811*b39
- 1.38629436111989*b45 =E= 0;
e68.. x6 - 0.693147180559945*b34 - 1.09861228866811*b40
- 1.38629436111989*b46 =E= 0;
e69.. b23 + b29 + b35 + b41 =E= 1;
e70.. b24 + b30 + b36 + b42 =E= 1;
e71.. b25 + b31 + b37 + b43 =E= 1;
e72.. b26 + b32 + b38 + b44 =E= 1;
e73.. b27 + b33 + b39 + b45 =E= 1;
e74.. b28 + b34 + b40 + b46 =E= 1;
* set non-default bounds
x1.up = 1.38629436111989;
x2.up = 1.38629436111989;
x3.up = 1.38629436111989;
x4.up = 1.38629436111989;
x5.up = 1.38629436111989;
x6.up = 1.38629436111989;
x7.lo = 5.7037824746562; x7.up = 8.00636756765025;
x8.lo = 5.7037824746562; x8.up = 8.00636756765025;
x9.lo = 5.7037824746562; x9.up = 8.00636756765025;
x10.lo = 5.7037824746562; x10.up = 8.00636756765025;
x11.lo = 5.7037824746562; x11.up = 8.00636756765025;
x12.lo = 5.7037824746562; x12.up = 8.00636756765025;
x13.lo = 4.45966; x13.up = 397.747;
x14.lo = 3.7495; x14.up = 882.353;
x15.lo = 4.49144; x15.up = 833.333;
x16.lo = 3.14988; x16.up = 638.298;
x17.lo = 3.04452; x17.up = 666.667;
x18.lo = 0.729961; x18.up = 2.11626;
x19.lo = 0.530628; x19.up = 1.91626;
x20.lo = 1.09024; x20.up = 2.47654;
x21.lo = -0.133531; x21.up = 1.25276;
x22.lo = 0.0487901; x22.up = 1.43508;
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