MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Removed Instance minlphix
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 316.6926954 (ANTIGONE) 316.6926954 (COUENNE) 316.6926952 (LINDO) -35061589860. (SCIP) 0. (SHOT) |
| Referencesⓘ | Floudas, C A and Paules IV, Granville E, A Mixed-Integer Nonlinear Programming Formulation for the Synthesis of Heat Integrated Distillation Sequence, Computers and Chemical Engineering, 12:6, 1988, 531-546. |
| Sourceⓘ | GAMS Model Library model minlphi |
| Applicationⓘ | Heat Integrated Distillation Sequences |
| Added to libraryⓘ | 01 May 2001 |
| Removed from libraryⓘ | 16 Feb 2022 |
| Removed becauseⓘ | Difficult numerical behavior. Optimal value changes sign and by several orders of magnitude when increasing feasibility tolerance. |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 84 |
| #Binary Variablesⓘ | 20 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 36 |
| #Nonlinear Binary Variablesⓘ | 4 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | nonlinear |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 52 |
| #Nonlinear Nonzeros in Objectiveⓘ | 36 |
| #Constraintsⓘ | 92 |
| #Linear Constraintsⓘ | 88 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 4 |
| Operands in Gen. Nonlin. Functionsⓘ | div mul sqrt |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 264 |
| #Nonlinear Nonzeros in Jacobianⓘ | 4 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 112 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 16 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 9 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 9 |
| Average blocksize in Hessian of Lagrangianⓘ | 9.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 8.9300e-04 |
| Maximal coefficientⓘ | 1.5000e+03 |
| Infeasibility of initial pointⓘ | 396 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 93 31 0 62 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 85 65 20 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 317 277 40 0
*
* Solve m using MINLP minimizing objvar;
Variables objvar,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,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,b66,b67,b68,b69
,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85;
Positive Variables 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,x31,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65;
Binary Variables b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80
,b81,b82,b83,b84,b85;
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,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93;
e1.. -(0.4*((-1.15398 + 0.003375*x30)*x2 + (-0.30630793 + 0.000893*x31)*x3 + (-
1.57608132 + 0.004458*x32)*x4 + (-1.08593792 + 0.003176*x33)*x5 +
31.8928571428571*x14/(1 + x30 - x36 - b82) + 31.8928571428571*x15/(1 + x31
- x37 - b83) + 31.8928571428571*x16/(1 + x32 - x34 - b84) +
31.8928571428571*x17/(1 + x33 - x35 - b85) + 151.125*b82 + 180.003*b83 +
4.2286*b84 + 213.42*b85 + 31.8928571428571*x26/(1 + x38 - b82) +
31.8928571428571*x27/(1 + x39 - b83) + 31.8928571428571*x28/(1 + x40 - b84
) + 31.8928571428571*x29/(1 + x41 - b85) + 31.8928571428571*x18/(421 - x34
) + 31.8928571428571*x19/(421 - x35) + 31.8928571428571*x20/(421 - x36) +
31.8928571428571*x21/(421 - x37) + 31.8928571428571*x22/(373 - x34) +
31.8928571428571*x23/(373 - x35) + 31.8928571428571*x24/(373 - x36) +
31.8928571428571*x25/(373 - x37)) + 12.95216*x18 + 12.95216*x19 + 12.95216
*x20 + 12.95216*x21 + 4.75228*x22 + 4.75228*x23 + 4.75228*x24 + 4.75228*
x25 + 2.418*x26 + 2.418*x27 + 2.418*x28 + 2.418*x29) + objvar - 1.3568*b66
- 1.3568*b67 - 1.3568*b68 - 1.3568*b69 - 1.3568*b70 - 1.3568*b71
- 1.3568*b72 - 1.3568*b73 - 1.3568*b74 - 1.3568*b75 - 1.3568*b76
- 1.3568*b77 - 1.3568*b78 - 1.3568*b79 - 1.3568*b80 - 1.3568*b81 =E= 0;
e2.. -(0.666666666666667*sqrt((-305 + x30)*(-325 + x30)) + 0.333333333333333*
x30) + x38 - x42 + x46 =E= -105;
e3.. -(0.666666666666667*sqrt((-305 + x31)*(-325 + x31)) + 0.333333333333333*
x31) + x39 - x43 + x47 =E= -105;
e4.. -(0.666666666666667*sqrt((-305 + x32)*(-325 + x32)) + 0.333333333333333*
x32) + x40 - x44 + x48 =E= -105;
e5.. -(0.666666666666667*sqrt((-305 + x33)*(-325 + x33)) + 0.333333333333333*
x33) + x41 - x45 + x49 =E= -105;
e6.. x30 + x34 + x38 - 1500*b82 =L= 0;
e7.. x31 + x35 + x39 - 1500*b83 =L= 0;
e8.. x32 + x36 + x40 - 1500*b84 =L= 0;
e9.. x33 + x37 + x41 - 1500*b85 =L= 0;
e10.. x42 + x50 + x54 + 1500*b82 =L= 1500;
e11.. x43 + x51 + x55 + 1500*b83 =L= 1500;
e12.. x44 + x52 + x56 + 1500*b84 =L= 1500;
e13.. x45 + x53 + x57 + 1500*b85 =L= 1500;
e14.. x46 + x58 + x62 + 1500*b82 =L= 1500;
e15.. x47 + x59 + x63 + 1500*b83 =L= 1500;
e16.. x48 + x60 + x64 + 1500*b84 =L= 1500;
e17.. x49 + x61 + x65 + 1500*b85 =L= 1500;
e18.. 0.9*x3 - x5 =E= 0;
e19.. 0.2*x2 - x4 =E= 0;
e20.. x2 + x3 =E= 396;
e21.. x2 - 1500*b82 =L= 0;
e22.. x3 - 1500*b83 =L= 0;
e23.. x4 - 1500*b84 =L= 0;
e24.. x5 - 1500*b85 =L= 0;
e25.. x10 - 0.0225*x30 - x58 + x62 =E= 24.7068;
e26.. x11 - 0.013*x31 - x59 + x63 =E= 20.54087;
e27.. x12 - 0.0043*x32 - x60 + x64 =E= 2.239778;
e28.. x13 - 0.0156*x33 - x61 + x65 =E= 29.766048;
e29.. x6 - x10 =E= 0;
e30.. x7 - x11 =E= 0;
e31.. x8 - x12 =E= 0;
e32.. x9 - x13 =E= 0;
e33.. x10 - x14 - x26 =E= 0;
e34.. x11 - x15 - x27 =E= 0;
e35.. x12 - x16 - x28 =E= 0;
e36.. x13 - x17 - x29 =E= 0;
e37.. x6 - x16 - x18 - x22 =E= 0;
e38.. x7 - x17 - x19 - x23 =E= 0;
e39.. x8 - x14 - x20 - x24 =E= 0;
e40.. x9 - x15 - x21 - x25 =E= 0;
e41.. x34 =L= 411;
e42.. x35 =L= 411;
e43.. x36 =L= 411;
e44.. x37 =L= 411;
e45.. - x30 + 1500*b82 =L= 1158.08;
e46.. - x31 + 1500*b83 =L= 1156.99;
e47.. - x32 + 1500*b84 =L= 1146.46;
e48.. - x33 + 1500*b85 =L= 1158.08;
e49.. - 1.028*x30 + x34 - x50 + x54 =E= -341.95276;
e50.. - 1.05*x31 + x35 - x51 + x55 =E= -347.9205;
e51.. - 1.029*x32 + x36 - x52 + x56 =E= -355.03666;
e52.. - 1.005*x33 + x37 - x53 + x57 =E= -334.4486;
e53.. - x30 + x36 + 1500*b66 =L= 1490;
e54.. - x31 + x37 + 1500*b67 =L= 1490;
e55.. - x32 + x34 + 1500*b68 =L= 1490;
e56.. - x33 + x35 + 1500*b69 =L= 1490;
e57.. x34 + 1500*b74 =L= 1863;
e58.. x35 + 1500*b75 =L= 1863;
e59.. x36 + 1500*b76 =L= 1863;
e60.. x37 + 1500*b77 =L= 1863;
e61.. x14 - 1500*b66 =L= 0;
e62.. x15 - 1500*b67 =L= 0;
e63.. x16 - 1500*b68 =L= 0;
e64.. x17 - 1500*b69 =L= 0;
e65.. x18 - 1500*b70 =L= 0;
e66.. x19 - 1500*b71 =L= 0;
e67.. x20 - 1500*b72 =L= 0;
e68.. x21 - 1500*b73 =L= 0;
e69.. x22 - 1500*b74 =L= 0;
e70.. x23 - 1500*b75 =L= 0;
e71.. x24 - 1500*b76 =L= 0;
e72.. x25 - 1500*b77 =L= 0;
e73.. x26 - 1500*b78 =L= 0;
e74.. x27 - 1500*b79 =L= 0;
e75.. x28 - 1500*b80 =L= 0;
e76.. x29 - 1500*b81 =L= 0;
e77.. x6 + x10 - 1500*b82 =L= 0;
e78.. x7 + x11 - 1500*b83 =L= 0;
e79.. x8 + x12 - 1500*b84 =L= 0;
e80.. x9 + x13 - 1500*b85 =L= 0;
e81.. b83 - b85 =E= 0;
e82.. b82 - b84 =E= 0;
e83.. b82 + b83 =E= 1;
e84.. b70 + b74 =L= 1;
e85.. b71 + b75 =L= 1;
e86.. b72 + b76 =L= 1;
e87.. b73 + b77 =L= 1;
e88.. b66 + b68 =L= 1;
e89.. b67 + b69 =L= 1;
e90.. b66 + b68 + b70 + b74 + b78 - 20*b82 =L= 0;
e91.. b67 + b69 + b71 + b75 + b79 - 20*b83 =L= 0;
e92.. b66 + b68 + b72 + b76 + b80 - 20*b84 =L= 0;
e93.. b67 + b69 + b73 + b77 + b81 - 20*b85 =L= 0;
* set non-default bounds
x30.lo = 326;
x31.up = 304;
x32.lo = 326;
x33.up = 304;
x34.up = 1000;
x35.up = 1000;
x36.up = 1000;
x37.up = 1000;
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: 2026-09-14 Git hash: 9472b011