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Instance syn05m04m
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ⓘ | 5510.55800000 (ALPHAECP) 5510.38780000 (ANTIGONE) 5510.38735200 (BARON) 5510.38734500 (BONMIN) 5510.38744600 (COUENNE) 5510.38734500 (LINDO) 5510.38768300 (SCIP) 5510.38764800 (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ⓘ | Syn05M04M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 120 |
| #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ⓘ | 44 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 262 |
| #Linear Constraintsⓘ | 250 |
| #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ⓘ | 622 |
| #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
* 263 21 44 198 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 121 81 40 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 667 655 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,x52
,x53,x54,x55,x56,x57,x58,x59,x60,x61,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,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,x102
,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
,x116,x117,x118,x119,x120,x121;
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
,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61;
Binary Variables 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,b92,b93
,b94,b95,b96,b97,b98,b99,b100,b101;
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,e200,e201,e202,e203,e204,e205,e206,e207
,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
,e260,e261,e262,e263;
e1.. objvar + x2 + x3 + x4 + x5 - 5*x26 - 10*x27 - 5*x28 - 10*x29 + 2*x46
+ x47 + 2*x48 + x49 - 80*x50 - 90*x51 - 120*x52 - 100*x53 - 285*x54
- 390*x55 - 350*x56 - 300*x57 - 290*x58 - 405*x59 - 190*x60 - 340*x61
+ 5*b82 + 4*b83 + 6*b84 + 3*b85 + 8*b86 + 7*b87 + 6*b88 + 5*b89 + 6*b90
+ 9*b91 + 4*b92 + 3*b93 + 10*b94 + 9*b95 + 5*b96 + 6*b97 + 6*b98 + 10*b99
+ 6*b100 + 9*b101 =E= 0;
e2.. x2 - x6 - x10 =E= 0;
e3.. x3 - x7 - x11 =E= 0;
e4.. x4 - x8 - x12 =E= 0;
e5.. x5 - x9 - x13 =E= 0;
e6.. - x14 - x18 + x22 =E= 0;
e7.. - x15 - x19 + x23 =E= 0;
e8.. - x16 - x20 + x24 =E= 0;
e9.. - x17 - x21 + x25 =E= 0;
e10.. x22 - x26 - x30 =E= 0;
e11.. x23 - x27 - x31 =E= 0;
e12.. x24 - x28 - x32 =E= 0;
e13.. x25 - x29 - x33 =E= 0;
e14.. x30 - x34 - x38 - x42 =E= 0;
e15.. x31 - x35 - x39 - x43 =E= 0;
e16.. x32 - x36 - x40 - x44 =E= 0;
e17.. x33 - x37 - x41 - x45 =E= 0;
e18.. -log(1 + x6) + x14 + b62 =L= 1;
e19.. -log(1 + x7) + x15 + b63 =L= 1;
e20.. -log(1 + x8) + x16 + b64 =L= 1;
e21.. -log(1 + x9) + x17 + b65 =L= 1;
e22.. x6 - 40*b62 =L= 0;
e23.. x7 - 40*b63 =L= 0;
e24.. x8 - 40*b64 =L= 0;
e25.. x9 - 40*b65 =L= 0;
e26.. x14 - 3.71357206670431*b62 =L= 0;
e27.. x15 - 3.71357206670431*b63 =L= 0;
e28.. x16 - 3.71357206670431*b64 =L= 0;
e29.. x17 - 3.71357206670431*b65 =L= 0;
e30.. -1.2*log(1 + x10) + x18 + b66 =L= 1;
e31.. -1.2*log(1 + x11) + x19 + b67 =L= 1;
e32.. -1.2*log(1 + x12) + x20 + b68 =L= 1;
e33.. -1.2*log(1 + x13) + x21 + b69 =L= 1;
e34.. x10 - 40*b66 =L= 0;
e35.. x11 - 40*b67 =L= 0;
e36.. x12 - 40*b68 =L= 0;
e37.. x13 - 40*b69 =L= 0;
e38.. x18 - 4.45628648004517*b66 =L= 0;
e39.. x19 - 4.45628648004517*b67 =L= 0;
e40.. x20 - 4.45628648004517*b68 =L= 0;
e41.. x21 - 4.45628648004517*b69 =L= 0;
e42.. - 0.75*x34 + x50 + b70 =L= 1;
e43.. - 0.75*x35 + x51 + b71 =L= 1;
e44.. - 0.75*x36 + x52 + b72 =L= 1;
e45.. - 0.75*x37 + x53 + b73 =L= 1;
e46.. - 0.75*x34 + x50 - b70 =G= -1;
e47.. - 0.75*x35 + x51 - b71 =G= -1;
e48.. - 0.75*x36 + x52 - b72 =G= -1;
e49.. - 0.75*x37 + x53 - b73 =G= -1;
e50.. x34 - 4.45628648004517*b70 =L= 0;
e51.. x35 - 4.45628648004517*b71 =L= 0;
e52.. x36 - 4.45628648004517*b72 =L= 0;
e53.. x37 - 4.45628648004517*b73 =L= 0;
e54.. x50 - 3.34221486003388*b70 =L= 0;
e55.. x51 - 3.34221486003388*b71 =L= 0;
e56.. x52 - 3.34221486003388*b72 =L= 0;
e57.. x53 - 3.34221486003388*b73 =L= 0;
e58.. -1.5*log(1 + x38) + x54 + b74 =L= 1;
e59.. -1.5*log(1 + x39) + x55 + b75 =L= 1;
e60.. -1.5*log(1 + x40) + x56 + b76 =L= 1;
e61.. -1.5*log(1 + x41) + x57 + b77 =L= 1;
e62.. x38 - 4.45628648004517*b74 =L= 0;
e63.. x39 - 4.45628648004517*b75 =L= 0;
e64.. x40 - 4.45628648004517*b76 =L= 0;
e65.. x41 - 4.45628648004517*b77 =L= 0;
e66.. x54 - 2.54515263975353*b74 =L= 0;
e67.. x55 - 2.54515263975353*b75 =L= 0;
e68.. x56 - 2.54515263975353*b76 =L= 0;
e69.. x57 - 2.54515263975353*b77 =L= 0;
e70.. - x42 + x58 + b78 =L= 1;
e71.. - x43 + x59 + b79 =L= 1;
e72.. - x44 + x60 + b80 =L= 1;
e73.. - x45 + x61 + b81 =L= 1;
e74.. - x42 + x58 - b78 =G= -1;
e75.. - x43 + x59 - b79 =G= -1;
e76.. - x44 + x60 - b80 =G= -1;
e77.. - x45 + x61 - b81 =G= -1;
e78.. - 0.5*x46 + x58 + b78 =L= 1;
e79.. - 0.5*x47 + x59 + b79 =L= 1;
e80.. - 0.5*x48 + x60 + b80 =L= 1;
e81.. - 0.5*x49 + x61 + b81 =L= 1;
e82.. - 0.5*x46 + x58 - b78 =G= -1;
e83.. - 0.5*x47 + x59 - b79 =G= -1;
e84.. - 0.5*x48 + x60 - b80 =G= -1;
e85.. - 0.5*x49 + x61 - b81 =G= -1;
e86.. x42 - 4.45628648004517*b78 =L= 0;
e87.. x43 - 4.45628648004517*b79 =L= 0;
e88.. x44 - 4.45628648004517*b80 =L= 0;
e89.. x45 - 4.45628648004517*b81 =L= 0;
e90.. x46 - 30*b78 =L= 0;
e91.. x47 - 30*b79 =L= 0;
e92.. x48 - 30*b80 =L= 0;
e93.. x49 - 30*b81 =L= 0;
e94.. x58 - 15*b78 =L= 0;
e95.. x59 - 15*b79 =L= 0;
e96.. x60 - 15*b80 =L= 0;
e97.. x61 - 15*b81 =L= 0;
e98.. 5*b82 + x102 =L= 0;
e99.. 4*b83 + x103 =L= 0;
e100.. 6*b84 + x104 =L= 0;
e101.. 3*b85 + x105 =L= 0;
e102.. 8*b86 + x106 =L= 0;
e103.. 7*b87 + x107 =L= 0;
e104.. 6*b88 + x108 =L= 0;
e105.. 5*b89 + x109 =L= 0;
e106.. 6*b90 + x110 =L= 0;
e107.. 9*b91 + x111 =L= 0;
e108.. 4*b92 + x112 =L= 0;
e109.. 3*b93 + x113 =L= 0;
e110.. 10*b94 + x114 =L= 0;
e111.. 9*b95 + x115 =L= 0;
e112.. 5*b96 + x116 =L= 0;
e113.. 6*b97 + x117 =L= 0;
e114.. 6*b98 + x118 =L= 0;
e115.. 10*b99 + x119 =L= 0;
e116.. 6*b100 + x120 =L= 0;
e117.. 9*b101 + x121 =L= 0;
e118.. 5*b82 + x102 =G= 0;
e119.. 4*b83 + x103 =G= 0;
e120.. 6*b84 + x104 =G= 0;
e121.. 3*b85 + x105 =G= 0;
e122.. 8*b86 + x106 =G= 0;
e123.. 7*b87 + x107 =G= 0;
e124.. 6*b88 + x108 =G= 0;
e125.. 5*b89 + x109 =G= 0;
e126.. 6*b90 + x110 =G= 0;
e127.. 9*b91 + x111 =G= 0;
e128.. 4*b92 + x112 =G= 0;
e129.. 3*b93 + x113 =G= 0;
e130.. 10*b94 + x114 =G= 0;
e131.. 9*b95 + x115 =G= 0;
e132.. 5*b96 + x116 =G= 0;
e133.. 6*b97 + x117 =G= 0;
e134.. 6*b98 + x118 =G= 0;
e135.. 10*b99 + x119 =G= 0;
e136.. 6*b100 + x120 =G= 0;
e137.. 9*b101 + x121 =G= 0;
e138.. b62 - b63 =L= 0;
e139.. b62 - b64 =L= 0;
e140.. b62 - b65 =L= 0;
e141.. b63 - b64 =L= 0;
e142.. b63 - b65 =L= 0;
e143.. b64 - b65 =L= 0;
e144.. b66 - b67 =L= 0;
e145.. b66 - b68 =L= 0;
e146.. b66 - b69 =L= 0;
e147.. b67 - b68 =L= 0;
e148.. b67 - b69 =L= 0;
e149.. b68 - b69 =L= 0;
e150.. b70 - b71 =L= 0;
e151.. b70 - b72 =L= 0;
e152.. b70 - b73 =L= 0;
e153.. b71 - b72 =L= 0;
e154.. b71 - b73 =L= 0;
e155.. b72 - b73 =L= 0;
e156.. b74 - b75 =L= 0;
e157.. b74 - b76 =L= 0;
e158.. b74 - b77 =L= 0;
e159.. b75 - b76 =L= 0;
e160.. b75 - b77 =L= 0;
e161.. b76 - b77 =L= 0;
e162.. b78 - b79 =L= 0;
e163.. b78 - b80 =L= 0;
e164.. b78 - b81 =L= 0;
e165.. b79 - b80 =L= 0;
e166.. b79 - b81 =L= 0;
e167.. b80 - b81 =L= 0;
e168.. b82 + b83 =L= 1;
e169.. b82 + b84 =L= 1;
e170.. b82 + b85 =L= 1;
e171.. b82 + b83 =L= 1;
e172.. b83 + b84 =L= 1;
e173.. b83 + b85 =L= 1;
e174.. b82 + b84 =L= 1;
e175.. b83 + b84 =L= 1;
e176.. b84 + b85 =L= 1;
e177.. b82 + b85 =L= 1;
e178.. b83 + b85 =L= 1;
e179.. b84 + b85 =L= 1;
e180.. b86 + b87 =L= 1;
e181.. b86 + b88 =L= 1;
e182.. b86 + b89 =L= 1;
e183.. b86 + b87 =L= 1;
e184.. b87 + b88 =L= 1;
e185.. b87 + b89 =L= 1;
e186.. b86 + b88 =L= 1;
e187.. b87 + b88 =L= 1;
e188.. b88 + b89 =L= 1;
e189.. b86 + b89 =L= 1;
e190.. b87 + b89 =L= 1;
e191.. b88 + b89 =L= 1;
e192.. b90 + b91 =L= 1;
e193.. b90 + b92 =L= 1;
e194.. b90 + b93 =L= 1;
e195.. b90 + b91 =L= 1;
e196.. b91 + b92 =L= 1;
e197.. b91 + b93 =L= 1;
e198.. b90 + b92 =L= 1;
e199.. b91 + b92 =L= 1;
e200.. b92 + b93 =L= 1;
e201.. b90 + b93 =L= 1;
e202.. b91 + b93 =L= 1;
e203.. b92 + b93 =L= 1;
e204.. b94 + b95 =L= 1;
e205.. b94 + b96 =L= 1;
e206.. b94 + b97 =L= 1;
e207.. b94 + b95 =L= 1;
e208.. b95 + b96 =L= 1;
e209.. b95 + b97 =L= 1;
e210.. b94 + b96 =L= 1;
e211.. b95 + b96 =L= 1;
e212.. b96 + b97 =L= 1;
e213.. b94 + b97 =L= 1;
e214.. b95 + b97 =L= 1;
e215.. b96 + b97 =L= 1;
e216.. b98 + b99 =L= 1;
e217.. b98 + b100 =L= 1;
e218.. b98 + b101 =L= 1;
e219.. b98 + b99 =L= 1;
e220.. b99 + b100 =L= 1;
e221.. b99 + b101 =L= 1;
e222.. b98 + b100 =L= 1;
e223.. b99 + b100 =L= 1;
e224.. b100 + b101 =L= 1;
e225.. b98 + b101 =L= 1;
e226.. b99 + b101 =L= 1;
e227.. b100 + b101 =L= 1;
e228.. b62 - b82 =L= 0;
e229.. - b62 + b63 - b83 =L= 0;
e230.. - b62 - b63 + b64 - b84 =L= 0;
e231.. - b62 - b63 - b64 + b65 - b85 =L= 0;
e232.. b66 - b86 =L= 0;
e233.. - b66 + b67 - b87 =L= 0;
e234.. - b66 - b67 + b68 - b88 =L= 0;
e235.. - b66 - b67 - b68 + b69 - b89 =L= 0;
e236.. b70 - b90 =L= 0;
e237.. - b70 + b71 - b91 =L= 0;
e238.. - b70 - b71 + b72 - b92 =L= 0;
e239.. - b70 - b71 - b72 + b73 - b93 =L= 0;
e240.. b74 - b94 =L= 0;
e241.. - b74 + b75 - b95 =L= 0;
e242.. - b74 - b75 + b76 - b96 =L= 0;
e243.. - b74 - b75 - b76 + b77 - b97 =L= 0;
e244.. b78 - b98 =L= 0;
e245.. - b78 + b79 - b99 =L= 0;
e246.. - b78 - b79 + b80 - b100 =L= 0;
e247.. - b78 - b79 - b80 + b81 - b101 =L= 0;
e248.. b62 + b66 =E= 1;
e249.. b63 + b67 =E= 1;
e250.. b64 + b68 =E= 1;
e251.. b65 + b69 =E= 1;
e252.. b62 + b66 - b70 =G= 0;
e253.. b63 + b67 - b71 =G= 0;
e254.. b64 + b68 - b72 =G= 0;
e255.. b65 + b69 - b73 =G= 0;
e256.. b62 + b66 - b74 =G= 0;
e257.. b63 + b67 - b75 =G= 0;
e258.. b64 + b68 - b76 =G= 0;
e259.. b65 + b69 - b77 =G= 0;
e260.. b62 + b66 - b78 =G= 0;
e261.. b63 + b67 - b79 =G= 0;
e262.. b64 + b68 - b80 =G= 0;
e263.. b65 + b69 - b81 =G= 0;
* set non-default bounds
x2.up = 40;
x3.up = 40;
x4.up = 40;
x5.up = 40;
x46.up = 30;
x47.up = 30;
x48.up = 30;
x49.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