MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance syn05m02m
Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 3032.87700000 (ALPHAECP) 3032.73579200 (ANTIGONE) 3032.73542300 (BARON) 3032.73540000 (BONMIN) 3032.73538600 (COUENNE) 3032.73538600 (LINDO) 3032.73546900 (SCIP) 3032.73590200 (SHOT) |
| Referencesⓘ | Duran, Marco A and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-integer Nonlinear Programs, Mathematical Programming, 36:3, 1986, 307-339. Türkay, Metin and Grossmann, I E, Logic-based MINLP Algorithms for optimal synthesis of process networks, Computers and Chemical Engineering, 20:8, 1996, 959-978. |
| Sourceⓘ | Syn05M02M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 60 |
| #Binary Variablesⓘ | 20 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 6 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 22 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 101 |
| #Linear Constraintsⓘ | 95 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 6 |
| Operands in Gen. Nonlin. Functionsⓘ | log |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 241 |
| #Nonlinear Nonzeros in Jacobianⓘ | 6 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 6 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 6 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 5.0000e-01 |
| Maximal coefficientⓘ | 4.0500e+02 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 102 11 22 69 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 61 41 20 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 264 258 6 0
*
* Solve m using MINLP maximizing 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,b32,b33,b34,b35
,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,x52
,x53,x54,x55,x56,x57,x58,x59,x60,x61;
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,x30,x31;
Binary Variables b32,b33,b34,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46
,b47,b48,b49,b50,b51;
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,e94,e95,e96,e97,e98,e99,e100,e101,e102;
e1.. objvar + x2 + x3 - 5*x14 - 10*x15 + 2*x24 + x25 - 80*x26 - 90*x27
- 285*x28 - 390*x29 - 290*x30 - 405*x31 + 5*b42 + 4*b43 + 8*b44 + 7*b45
+ 6*b46 + 9*b47 + 10*b48 + 9*b49 + 6*b50 + 10*b51 =E= 0;
e2.. x2 - x4 - x6 =E= 0;
e3.. x3 - x5 - x7 =E= 0;
e4.. - x8 - x10 + x12 =E= 0;
e5.. - x9 - x11 + x13 =E= 0;
e6.. x12 - x14 - x16 =E= 0;
e7.. x13 - x15 - x17 =E= 0;
e8.. x16 - x18 - x20 - x22 =E= 0;
e9.. x17 - x19 - x21 - x23 =E= 0;
e10.. -log(1 + x4) + x8 + b32 =L= 1;
e11.. -log(1 + x5) + x9 + b33 =L= 1;
e12.. x4 - 40*b32 =L= 0;
e13.. x5 - 40*b33 =L= 0;
e14.. x8 - 3.71357206670431*b32 =L= 0;
e15.. x9 - 3.71357206670431*b33 =L= 0;
e16.. -1.2*log(1 + x6) + x10 + b34 =L= 1;
e17.. -1.2*log(1 + x7) + x11 + b35 =L= 1;
e18.. x6 - 40*b34 =L= 0;
e19.. x7 - 40*b35 =L= 0;
e20.. x10 - 4.45628648004517*b34 =L= 0;
e21.. x11 - 4.45628648004517*b35 =L= 0;
e22.. - 0.75*x18 + x26 + b36 =L= 1;
e23.. - 0.75*x19 + x27 + b37 =L= 1;
e24.. - 0.75*x18 + x26 - b36 =G= -1;
e25.. - 0.75*x19 + x27 - b37 =G= -1;
e26.. x18 - 4.45628648004517*b36 =L= 0;
e27.. x19 - 4.45628648004517*b37 =L= 0;
e28.. x26 - 3.34221486003388*b36 =L= 0;
e29.. x27 - 3.34221486003388*b37 =L= 0;
e30.. -1.5*log(1 + x20) + x28 + b38 =L= 1;
e31.. -1.5*log(1 + x21) + x29 + b39 =L= 1;
e32.. x20 - 4.45628648004517*b38 =L= 0;
e33.. x21 - 4.45628648004517*b39 =L= 0;
e34.. x28 - 2.54515263975353*b38 =L= 0;
e35.. x29 - 2.54515263975353*b39 =L= 0;
e36.. - x22 + x30 + b40 =L= 1;
e37.. - x23 + x31 + b41 =L= 1;
e38.. - x22 + x30 - b40 =G= -1;
e39.. - x23 + x31 - b41 =G= -1;
e40.. - 0.5*x24 + x30 + b40 =L= 1;
e41.. - 0.5*x25 + x31 + b41 =L= 1;
e42.. - 0.5*x24 + x30 - b40 =G= -1;
e43.. - 0.5*x25 + x31 - b41 =G= -1;
e44.. x22 - 4.45628648004517*b40 =L= 0;
e45.. x23 - 4.45628648004517*b41 =L= 0;
e46.. x24 - 30*b40 =L= 0;
e47.. x25 - 30*b41 =L= 0;
e48.. x30 - 15*b40 =L= 0;
e49.. x31 - 15*b41 =L= 0;
e50.. 5*b42 + x52 =L= 0;
e51.. 4*b43 + x53 =L= 0;
e52.. 8*b44 + x54 =L= 0;
e53.. 7*b45 + x55 =L= 0;
e54.. 6*b46 + x56 =L= 0;
e55.. 9*b47 + x57 =L= 0;
e56.. 10*b48 + x58 =L= 0;
e57.. 9*b49 + x59 =L= 0;
e58.. 6*b50 + x60 =L= 0;
e59.. 10*b51 + x61 =L= 0;
e60.. 5*b42 + x52 =G= 0;
e61.. 4*b43 + x53 =G= 0;
e62.. 8*b44 + x54 =G= 0;
e63.. 7*b45 + x55 =G= 0;
e64.. 6*b46 + x56 =G= 0;
e65.. 9*b47 + x57 =G= 0;
e66.. 10*b48 + x58 =G= 0;
e67.. 9*b49 + x59 =G= 0;
e68.. 6*b50 + x60 =G= 0;
e69.. 10*b51 + x61 =G= 0;
e70.. b32 - b33 =L= 0;
e71.. b34 - b35 =L= 0;
e72.. b36 - b37 =L= 0;
e73.. b38 - b39 =L= 0;
e74.. b40 - b41 =L= 0;
e75.. b42 + b43 =L= 1;
e76.. b42 + b43 =L= 1;
e77.. b44 + b45 =L= 1;
e78.. b44 + b45 =L= 1;
e79.. b46 + b47 =L= 1;
e80.. b46 + b47 =L= 1;
e81.. b48 + b49 =L= 1;
e82.. b48 + b49 =L= 1;
e83.. b50 + b51 =L= 1;
e84.. b50 + b51 =L= 1;
e85.. b32 - b42 =L= 0;
e86.. - b32 + b33 - b43 =L= 0;
e87.. b34 - b44 =L= 0;
e88.. - b34 + b35 - b45 =L= 0;
e89.. b36 - b46 =L= 0;
e90.. - b36 + b37 - b47 =L= 0;
e91.. b38 - b48 =L= 0;
e92.. - b38 + b39 - b49 =L= 0;
e93.. b40 - b50 =L= 0;
e94.. - b40 + b41 - b51 =L= 0;
e95.. b32 + b34 =E= 1;
e96.. b33 + b35 =E= 1;
e97.. b32 + b34 - b36 =G= 0;
e98.. b33 + b35 - b37 =G= 0;
e99.. b32 + b34 - b38 =G= 0;
e100.. b33 + b35 - b39 =G= 0;
e101.. b32 + b34 - b40 =G= 0;
e102.. b33 + b35 - b41 =G= 0;
* set non-default bounds
x2.up = 40;
x3.up = 40;
x24.up = 30;
x25.up = 30;
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% maximizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc