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Instance syn10m02m
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ⓘ | 2310.39180000 (ALPHAECP) 2310.30116200 (ANTIGONE) 2310.30069300 (BARON) 2310.30070000 (BONMIN) 2310.30076900 (COUENNE) 2310.30069300 (LINDO) 2310.30086300 (SCIP) 2310.30133000 (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ⓘ | Syn10M02M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 110 |
| #Binary Variablesⓘ | 40 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 12 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 38 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 198 |
| #Linear Constraintsⓘ | 186 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 12 |
| Operands in Gen. Nonlin. Functionsⓘ | log |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 462 |
| #Nonlinear Nonzeros in Jacobianⓘ | 12 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 12 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 12 |
| #Blocks in Hessian of Lagrangianⓘ | 12 |
| 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
* 199 15 50 134 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 111 71 40 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 501 489 12 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,x47,x48,x49,x50,x51,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,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86
,b87,b88,b89,b90,b91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
,x103,x104,x105,x106,x107,x108,x109,x110,x111;
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,x47,x48,x49,x50,x51;
Binary Variables 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,b77,b78,b79,b80,b81,b82,b83
,b84,b85,b86,b87,b88,b89,b90,b91;
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,e176,e177,e178,e179,e180,e181
,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
,e195,e196,e197,e198,e199;
e1.. objvar + x2 + x3 - 5*x14 - 10*x15 + 2*x24 + x25 - 80*x40 - 90*x41
- 285*x42 - 390*x43 - 290*x44 - 405*x45 - 280*x46 - 400*x47 - 290*x48
- 300*x49 - 350*x50 - 250*x51 + 5*b72 + 4*b73 + 8*b74 + 7*b75 + 6*b76
+ 9*b77 + 10*b78 + 9*b79 + 6*b80 + 10*b81 + 7*b82 + 7*b83 + 4*b84 + 3*b85
+ 5*b86 + 6*b87 + 2*b88 + 5*b89 + 4*b90 + 7*b91 =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.. x26 - x32 - x34 =E= 0;
e11.. x27 - x33 - x35 =E= 0;
e12.. x30 - x36 - x38 - x40 =E= 0;
e13.. x31 - x37 - x39 - x41 =E= 0;
e14.. -log(1 + x4) + x8 + b52 =L= 1;
e15.. -log(1 + x5) + x9 + b53 =L= 1;
e16.. x4 - 40*b52 =L= 0;
e17.. x5 - 40*b53 =L= 0;
e18.. x8 - 3.71357206670431*b52 =L= 0;
e19.. x9 - 3.71357206670431*b53 =L= 0;
e20.. -1.2*log(1 + x6) + x10 + b54 =L= 1;
e21.. -1.2*log(1 + x7) + x11 + b55 =L= 1;
e22.. x6 - 40*b54 =L= 0;
e23.. x7 - 40*b55 =L= 0;
e24.. x10 - 4.45628648004517*b54 =L= 0;
e25.. x11 - 4.45628648004517*b55 =L= 0;
e26.. - 0.75*x18 + x26 + b56 =L= 1;
e27.. - 0.75*x19 + x27 + b57 =L= 1;
e28.. - 0.75*x18 + x26 - b56 =G= -1;
e29.. - 0.75*x19 + x27 - b57 =G= -1;
e30.. x18 - 4.45628648004517*b56 =L= 0;
e31.. x19 - 4.45628648004517*b57 =L= 0;
e32.. x26 - 3.34221486003388*b56 =L= 0;
e33.. x27 - 3.34221486003388*b57 =L= 0;
e34.. -1.5*log(1 + x20) + x28 + b58 =L= 1;
e35.. -1.5*log(1 + x21) + x29 + b59 =L= 1;
e36.. x20 - 4.45628648004517*b58 =L= 0;
e37.. x21 - 4.45628648004517*b59 =L= 0;
e38.. x28 - 2.54515263975353*b58 =L= 0;
e39.. x29 - 2.54515263975353*b59 =L= 0;
e40.. - x22 + x30 + b60 =L= 1;
e41.. - x23 + x31 + b61 =L= 1;
e42.. - x22 + x30 - b60 =G= -1;
e43.. - x23 + x31 - b61 =G= -1;
e44.. - 0.5*x24 + x30 + b60 =L= 1;
e45.. - 0.5*x25 + x31 + b61 =L= 1;
e46.. - 0.5*x24 + x30 - b60 =G= -1;
e47.. - 0.5*x25 + x31 - b61 =G= -1;
e48.. x22 - 4.45628648004517*b60 =L= 0;
e49.. x23 - 4.45628648004517*b61 =L= 0;
e50.. x24 - 30*b60 =L= 0;
e51.. x25 - 30*b61 =L= 0;
e52.. x30 - 15*b60 =L= 0;
e53.. x31 - 15*b61 =L= 0;
e54.. -1.25*log(1 + x32) + x42 + b62 =L= 1;
e55.. -1.25*log(1 + x33) + x43 + b63 =L= 1;
e56.. x32 - 3.34221486003388*b62 =L= 0;
e57.. x33 - 3.34221486003388*b63 =L= 0;
e58.. x42 - 1.83548069293539*b62 =L= 0;
e59.. x43 - 1.83548069293539*b63 =L= 0;
e60.. -0.9*log(1 + x34) + x44 + b64 =L= 1;
e61.. -0.9*log(1 + x35) + x45 + b65 =L= 1;
e62.. x34 - 3.34221486003388*b64 =L= 0;
e63.. x35 - 3.34221486003388*b65 =L= 0;
e64.. x44 - 1.32154609891348*b64 =L= 0;
e65.. x45 - 1.32154609891348*b65 =L= 0;
e66.. -log(1 + x28) + x46 + b66 =L= 1;
e67.. -log(1 + x29) + x47 + b67 =L= 1;
e68.. x28 - 2.54515263975353*b66 =L= 0;
e69.. x29 - 2.54515263975353*b67 =L= 0;
e70.. x46 - 1.26558121681553*b66 =L= 0;
e71.. x47 - 1.26558121681553*b67 =L= 0;
e72.. - 0.9*x36 + x48 + b68 =L= 1;
e73.. - 0.9*x37 + x49 + b69 =L= 1;
e74.. - 0.9*x36 + x48 - b68 =G= -1;
e75.. - 0.9*x37 + x49 - b69 =G= -1;
e76.. x36 - 15*b68 =L= 0;
e77.. x37 - 15*b69 =L= 0;
e78.. x48 - 13.5*b68 =L= 0;
e79.. x49 - 13.5*b69 =L= 0;
e80.. - 0.6*x38 + x50 + b70 =L= 1;
e81.. - 0.6*x39 + x51 + b71 =L= 1;
e82.. - 0.6*x38 + x50 - b70 =G= -1;
e83.. - 0.6*x39 + x51 - b71 =G= -1;
e84.. x38 - 15*b70 =L= 0;
e85.. x39 - 15*b71 =L= 0;
e86.. x50 - 9*b70 =L= 0;
e87.. x51 - 9*b71 =L= 0;
e88.. 5*b72 + x92 =L= 0;
e89.. 4*b73 + x93 =L= 0;
e90.. 8*b74 + x94 =L= 0;
e91.. 7*b75 + x95 =L= 0;
e92.. 6*b76 + x96 =L= 0;
e93.. 9*b77 + x97 =L= 0;
e94.. 10*b78 + x98 =L= 0;
e95.. 9*b79 + x99 =L= 0;
e96.. 6*b80 + x100 =L= 0;
e97.. 10*b81 + x101 =L= 0;
e98.. 7*b82 + x102 =L= 0;
e99.. 7*b83 + x103 =L= 0;
e100.. 4*b84 + x104 =L= 0;
e101.. 3*b85 + x105 =L= 0;
e102.. 5*b86 + x106 =L= 0;
e103.. 6*b87 + x107 =L= 0;
e104.. 2*b88 + x108 =L= 0;
e105.. 5*b89 + x109 =L= 0;
e106.. 4*b90 + x110 =L= 0;
e107.. 7*b91 + x111 =L= 0;
e108.. 5*b72 + x92 =G= 0;
e109.. 4*b73 + x93 =G= 0;
e110.. 8*b74 + x94 =G= 0;
e111.. 7*b75 + x95 =G= 0;
e112.. 6*b76 + x96 =G= 0;
e113.. 9*b77 + x97 =G= 0;
e114.. 10*b78 + x98 =G= 0;
e115.. 9*b79 + x99 =G= 0;
e116.. 6*b80 + x100 =G= 0;
e117.. 10*b81 + x101 =G= 0;
e118.. 7*b82 + x102 =G= 0;
e119.. 7*b83 + x103 =G= 0;
e120.. 4*b84 + x104 =G= 0;
e121.. 3*b85 + x105 =G= 0;
e122.. 5*b86 + x106 =G= 0;
e123.. 6*b87 + x107 =G= 0;
e124.. 2*b88 + x108 =G= 0;
e125.. 5*b89 + x109 =G= 0;
e126.. 4*b90 + x110 =G= 0;
e127.. 7*b91 + x111 =G= 0;
e128.. b52 - b53 =L= 0;
e129.. b54 - b55 =L= 0;
e130.. b56 - b57 =L= 0;
e131.. b58 - b59 =L= 0;
e132.. b60 - b61 =L= 0;
e133.. b62 - b63 =L= 0;
e134.. b64 - b65 =L= 0;
e135.. b66 - b67 =L= 0;
e136.. b68 - b69 =L= 0;
e137.. b70 - b71 =L= 0;
e138.. b72 + b73 =L= 1;
e139.. b72 + b73 =L= 1;
e140.. b74 + b75 =L= 1;
e141.. b74 + b75 =L= 1;
e142.. b76 + b77 =L= 1;
e143.. b76 + b77 =L= 1;
e144.. b78 + b79 =L= 1;
e145.. b78 + b79 =L= 1;
e146.. b80 + b81 =L= 1;
e147.. b80 + b81 =L= 1;
e148.. b82 + b83 =L= 1;
e149.. b82 + b83 =L= 1;
e150.. b84 + b85 =L= 1;
e151.. b84 + b85 =L= 1;
e152.. b86 + b87 =L= 1;
e153.. b86 + b87 =L= 1;
e154.. b88 + b89 =L= 1;
e155.. b88 + b89 =L= 1;
e156.. b90 + b91 =L= 1;
e157.. b90 + b91 =L= 1;
e158.. b52 - b72 =L= 0;
e159.. - b52 + b53 - b73 =L= 0;
e160.. b54 - b74 =L= 0;
e161.. - b54 + b55 - b75 =L= 0;
e162.. b56 - b76 =L= 0;
e163.. - b56 + b57 - b77 =L= 0;
e164.. b58 - b78 =L= 0;
e165.. - b58 + b59 - b79 =L= 0;
e166.. b60 - b80 =L= 0;
e167.. - b60 + b61 - b81 =L= 0;
e168.. b62 - b82 =L= 0;
e169.. - b62 + b63 - b83 =L= 0;
e170.. b64 - b84 =L= 0;
e171.. - b64 + b65 - b85 =L= 0;
e172.. b66 - b86 =L= 0;
e173.. - b66 + b67 - b87 =L= 0;
e174.. b68 - b88 =L= 0;
e175.. - b68 + b69 - b89 =L= 0;
e176.. b70 - b90 =L= 0;
e177.. - b70 + b71 - b91 =L= 0;
e178.. b52 + b54 =E= 1;
e179.. b53 + b55 =E= 1;
e180.. - b56 + b62 + b64 =G= 0;
e181.. - b57 + b63 + b65 =G= 0;
e182.. - b58 + b66 =G= 0;
e183.. - b59 + b67 =G= 0;
e184.. b52 + b54 - b56 =G= 0;
e185.. b53 + b55 - b57 =G= 0;
e186.. b52 + b54 - b58 =G= 0;
e187.. b53 + b55 - b59 =G= 0;
e188.. b52 + b54 - b60 =G= 0;
e189.. b53 + b55 - b61 =G= 0;
e190.. b56 - b62 =G= 0;
e191.. b57 - b63 =G= 0;
e192.. b56 - b64 =G= 0;
e193.. b57 - b65 =G= 0;
e194.. b58 - b66 =G= 0;
e195.. b59 - b67 =G= 0;
e196.. b60 - b68 =G= 0;
e197.. b61 - b69 =G= 0;
e198.. b60 - b70 =G= 0;
e199.. b61 - b71 =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