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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance syn05m03m
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ⓘ | 4027.37300000 (ALPHAECP) 4027.37220000 (ANTIGONE) 4027.37176000 (BARON) 4027.37180000 (BONMIN) 4027.37178500 (COUENNE) 4027.37175500 (LINDO) 4027.37201700 (SCIP) 4027.37198300 (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ⓘ | Syn05M03M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 90 |
| #Binary Variablesⓘ | 30 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 9 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 33 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 174 |
| #Linear Constraintsⓘ | 165 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 9 |
| Operands in Gen. Nonlin. Functionsⓘ | log |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 414 |
| #Nonlinear Nonzeros in Jacobianⓘ | 9 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 9 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 9 |
| #Blocks in Hessian of Lagrangianⓘ | 9 |
| 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
* 175 16 33 126 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 91 61 30 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 448 439 9 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,x32,x33,x34,x35
,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,b47,b48,b49,b50,b51,b52
,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69
,b70,b71,b72,b73,b74,b75,b76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
,x87,x88,x89,x90,x91;
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,x32,x33,x34
,x35,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46;
Binary Variables b47,b48,b49,b50,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61
,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72,b73,b74,b75,b76;
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,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
,e169,e170,e171,e172,e173,e174,e175;
e1.. objvar + x2 + x3 + x4 - 5*x20 - 10*x21 - 5*x22 + 2*x35 + x36 + 2*x37
- 80*x38 - 90*x39 - 120*x40 - 285*x41 - 390*x42 - 350*x43 - 290*x44
- 405*x45 - 190*x46 + 5*b62 + 4*b63 + 6*b64 + 8*b65 + 7*b66 + 6*b67
+ 6*b68 + 9*b69 + 4*b70 + 10*b71 + 9*b72 + 5*b73 + 6*b74 + 10*b75 + 6*b76
=E= 0;
e2.. x2 - x5 - x8 =E= 0;
e3.. x3 - x6 - x9 =E= 0;
e4.. x4 - x7 - x10 =E= 0;
e5.. - x11 - x14 + x17 =E= 0;
e6.. - x12 - x15 + x18 =E= 0;
e7.. - x13 - x16 + x19 =E= 0;
e8.. x17 - x20 - x23 =E= 0;
e9.. x18 - x21 - x24 =E= 0;
e10.. x19 - x22 - x25 =E= 0;
e11.. x23 - x26 - x29 - x32 =E= 0;
e12.. x24 - x27 - x30 - x33 =E= 0;
e13.. x25 - x28 - x31 - x34 =E= 0;
e14.. -log(1 + x5) + x11 + b47 =L= 1;
e15.. -log(1 + x6) + x12 + b48 =L= 1;
e16.. -log(1 + x7) + x13 + b49 =L= 1;
e17.. x5 - 40*b47 =L= 0;
e18.. x6 - 40*b48 =L= 0;
e19.. x7 - 40*b49 =L= 0;
e20.. x11 - 3.71357206670431*b47 =L= 0;
e21.. x12 - 3.71357206670431*b48 =L= 0;
e22.. x13 - 3.71357206670431*b49 =L= 0;
e23.. -1.2*log(1 + x8) + x14 + b50 =L= 1;
e24.. -1.2*log(1 + x9) + x15 + b51 =L= 1;
e25.. -1.2*log(1 + x10) + x16 + b52 =L= 1;
e26.. x8 - 40*b50 =L= 0;
e27.. x9 - 40*b51 =L= 0;
e28.. x10 - 40*b52 =L= 0;
e29.. x14 - 4.45628648004517*b50 =L= 0;
e30.. x15 - 4.45628648004517*b51 =L= 0;
e31.. x16 - 4.45628648004517*b52 =L= 0;
e32.. - 0.75*x26 + x38 + b53 =L= 1;
e33.. - 0.75*x27 + x39 + b54 =L= 1;
e34.. - 0.75*x28 + x40 + b55 =L= 1;
e35.. - 0.75*x26 + x38 - b53 =G= -1;
e36.. - 0.75*x27 + x39 - b54 =G= -1;
e37.. - 0.75*x28 + x40 - b55 =G= -1;
e38.. x26 - 4.45628648004517*b53 =L= 0;
e39.. x27 - 4.45628648004517*b54 =L= 0;
e40.. x28 - 4.45628648004517*b55 =L= 0;
e41.. x38 - 3.34221486003388*b53 =L= 0;
e42.. x39 - 3.34221486003388*b54 =L= 0;
e43.. x40 - 3.34221486003388*b55 =L= 0;
e44.. -1.5*log(1 + x29) + x41 + b56 =L= 1;
e45.. -1.5*log(1 + x30) + x42 + b57 =L= 1;
e46.. -1.5*log(1 + x31) + x43 + b58 =L= 1;
e47.. x29 - 4.45628648004517*b56 =L= 0;
e48.. x30 - 4.45628648004517*b57 =L= 0;
e49.. x31 - 4.45628648004517*b58 =L= 0;
e50.. x41 - 2.54515263975353*b56 =L= 0;
e51.. x42 - 2.54515263975353*b57 =L= 0;
e52.. x43 - 2.54515263975353*b58 =L= 0;
e53.. - x32 + x44 + b59 =L= 1;
e54.. - x33 + x45 + b60 =L= 1;
e55.. - x34 + x46 + b61 =L= 1;
e56.. - x32 + x44 - b59 =G= -1;
e57.. - x33 + x45 - b60 =G= -1;
e58.. - x34 + x46 - b61 =G= -1;
e59.. - 0.5*x35 + x44 + b59 =L= 1;
e60.. - 0.5*x36 + x45 + b60 =L= 1;
e61.. - 0.5*x37 + x46 + b61 =L= 1;
e62.. - 0.5*x35 + x44 - b59 =G= -1;
e63.. - 0.5*x36 + x45 - b60 =G= -1;
e64.. - 0.5*x37 + x46 - b61 =G= -1;
e65.. x32 - 4.45628648004517*b59 =L= 0;
e66.. x33 - 4.45628648004517*b60 =L= 0;
e67.. x34 - 4.45628648004517*b61 =L= 0;
e68.. x35 - 30*b59 =L= 0;
e69.. x36 - 30*b60 =L= 0;
e70.. x37 - 30*b61 =L= 0;
e71.. x44 - 15*b59 =L= 0;
e72.. x45 - 15*b60 =L= 0;
e73.. x46 - 15*b61 =L= 0;
e74.. 5*b62 + x77 =L= 0;
e75.. 4*b63 + x78 =L= 0;
e76.. 6*b64 + x79 =L= 0;
e77.. 8*b65 + x80 =L= 0;
e78.. 7*b66 + x81 =L= 0;
e79.. 6*b67 + x82 =L= 0;
e80.. 6*b68 + x83 =L= 0;
e81.. 9*b69 + x84 =L= 0;
e82.. 4*b70 + x85 =L= 0;
e83.. 10*b71 + x86 =L= 0;
e84.. 9*b72 + x87 =L= 0;
e85.. 5*b73 + x88 =L= 0;
e86.. 6*b74 + x89 =L= 0;
e87.. 10*b75 + x90 =L= 0;
e88.. 6*b76 + x91 =L= 0;
e89.. 5*b62 + x77 =G= 0;
e90.. 4*b63 + x78 =G= 0;
e91.. 6*b64 + x79 =G= 0;
e92.. 8*b65 + x80 =G= 0;
e93.. 7*b66 + x81 =G= 0;
e94.. 6*b67 + x82 =G= 0;
e95.. 6*b68 + x83 =G= 0;
e96.. 9*b69 + x84 =G= 0;
e97.. 4*b70 + x85 =G= 0;
e98.. 10*b71 + x86 =G= 0;
e99.. 9*b72 + x87 =G= 0;
e100.. 5*b73 + x88 =G= 0;
e101.. 6*b74 + x89 =G= 0;
e102.. 10*b75 + x90 =G= 0;
e103.. 6*b76 + x91 =G= 0;
e104.. b47 - b48 =L= 0;
e105.. b47 - b49 =L= 0;
e106.. b48 - b49 =L= 0;
e107.. b50 - b51 =L= 0;
e108.. b50 - b52 =L= 0;
e109.. b51 - b52 =L= 0;
e110.. b53 - b54 =L= 0;
e111.. b53 - b55 =L= 0;
e112.. b54 - b55 =L= 0;
e113.. b56 - b57 =L= 0;
e114.. b56 - b58 =L= 0;
e115.. b57 - b58 =L= 0;
e116.. b59 - b60 =L= 0;
e117.. b59 - b61 =L= 0;
e118.. b60 - b61 =L= 0;
e119.. b62 + b63 =L= 1;
e120.. b62 + b64 =L= 1;
e121.. b62 + b63 =L= 1;
e122.. b63 + b64 =L= 1;
e123.. b62 + b64 =L= 1;
e124.. b63 + b64 =L= 1;
e125.. b65 + b66 =L= 1;
e126.. b65 + b67 =L= 1;
e127.. b65 + b66 =L= 1;
e128.. b66 + b67 =L= 1;
e129.. b65 + b67 =L= 1;
e130.. b66 + b67 =L= 1;
e131.. b68 + b69 =L= 1;
e132.. b68 + b70 =L= 1;
e133.. b68 + b69 =L= 1;
e134.. b69 + b70 =L= 1;
e135.. b68 + b70 =L= 1;
e136.. b69 + b70 =L= 1;
e137.. b71 + b72 =L= 1;
e138.. b71 + b73 =L= 1;
e139.. b71 + b72 =L= 1;
e140.. b72 + b73 =L= 1;
e141.. b71 + b73 =L= 1;
e142.. b72 + b73 =L= 1;
e143.. b74 + b75 =L= 1;
e144.. b74 + b76 =L= 1;
e145.. b74 + b75 =L= 1;
e146.. b75 + b76 =L= 1;
e147.. b74 + b76 =L= 1;
e148.. b75 + b76 =L= 1;
e149.. b47 - b62 =L= 0;
e150.. - b47 + b48 - b63 =L= 0;
e151.. - b47 - b48 + b49 - b64 =L= 0;
e152.. b50 - b65 =L= 0;
e153.. - b50 + b51 - b66 =L= 0;
e154.. - b50 - b51 + b52 - b67 =L= 0;
e155.. b53 - b68 =L= 0;
e156.. - b53 + b54 - b69 =L= 0;
e157.. - b53 - b54 + b55 - b70 =L= 0;
e158.. b56 - b71 =L= 0;
e159.. - b56 + b57 - b72 =L= 0;
e160.. - b56 - b57 + b58 - b73 =L= 0;
e161.. b59 - b74 =L= 0;
e162.. - b59 + b60 - b75 =L= 0;
e163.. - b59 - b60 + b61 - b76 =L= 0;
e164.. b47 + b50 =E= 1;
e165.. b48 + b51 =E= 1;
e166.. b49 + b52 =E= 1;
e167.. b47 + b50 - b53 =G= 0;
e168.. b48 + b51 - b54 =G= 0;
e169.. b49 + b52 - b55 =G= 0;
e170.. b47 + b50 - b56 =G= 0;
e171.. b48 + b51 - b57 =G= 0;
e172.. b49 + b52 - b58 =G= 0;
e173.. b47 + b50 - b59 =G= 0;
e174.. b48 + b51 - b60 =G= 0;
e175.. b49 + b52 - b61 =G= 0;
* set non-default bounds
x2.up = 40;
x3.up = 40;
x4.up = 40;
x35.up = 30;
x36.up = 30;
x37.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