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Instance syn05m03hfsg
Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections. Equivalent perspective reformulation of syn05m03.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 4027.89698100 (ALPHAECP) 4027.37224100 (ANTIGONE) 4027.37321900 (BARON) 4027.37175600 (BONMIN) 4027.37328500 (COUENNE) 4027.37175600 (LINDO) 4027.37214700 (SCIP) 6484.03212600 (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. Kevin C. Furman, Nicolas W. Sawaya, Ignacio E. Grossmann, A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function, Tech. Rep., 2019. |
| Applicationⓘ | Synthesis of processing system |
| Added to libraryⓘ | 25 Sep 2019 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 156 |
| #Binary Variablesⓘ | 30 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 27 |
| #Nonlinear Binary Variablesⓘ | 9 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 33 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 249 |
| #Linear Constraintsⓘ | 240 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 9 |
| Operands in Gen. Nonlin. Functionsⓘ | div log mul |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 546 |
| #Nonlinear Nonzeros in Jacobianⓘ | 27 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 54 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 18 |
| #Blocks in Hessian of Lagrangianⓘ | 9 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-03 |
| 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
* 250 106 9 135 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 157 127 30 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 580 553 27 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,x62,x63,x64,x65,x66,x67,x68,x69
,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,b128
,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141
,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154
,b155,b156,b157;
Positive Variables 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,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81
,x82,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98
,x99,x100,x101,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111
,x112,x113,x114,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124
,x125,x126,x127;
Binary Variables b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139
,b140,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152
,b153,b154,b155,b156,b157;
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;
e1.. objvar + x17 + x18 + x19 - 5*x35 - 10*x36 - 5*x37 + 2*x50 + x51 + 2*x52
- 80*x53 - 90*x54 - 120*x55 - 285*x56 - 390*x57 - 350*x58 - 290*x59
- 405*x60 - 190*x61 + 5*b143 + 4*b144 + 6*b145 + 8*b146 + 7*b147 + 6*b148
+ 6*b149 + 9*b150 + 4*b151 + 10*b152 + 9*b153 + 5*b154 + 6*b155 + 10*b156
+ 6*b157 =E= 0;
e2.. x17 - x20 - x23 =E= 0;
e3.. x18 - x21 - x24 =E= 0;
e4.. x19 - x22 - x25 =E= 0;
e5.. - x26 - x29 + x32 =E= 0;
e6.. - x27 - x30 + x33 =E= 0;
e7.. - x28 - x31 + x34 =E= 0;
e8.. x32 - x35 - x38 =E= 0;
e9.. x33 - x36 - x39 =E= 0;
e10.. x34 - x37 - x40 =E= 0;
e11.. x38 - x41 - x44 - x47 =E= 0;
e12.. x39 - x42 - x45 - x48 =E= 0;
e13.. x40 - x43 - x46 - x49 =E= 0;
e14.. (x74/(0.001 + 0.999*b128) - log(1 + x62/(0.001 + 0.999*b128)))*(0.001 +
0.999*b128) =L= 0;
e15.. (x75/(0.001 + 0.999*b129) - log(1 + x63/(0.001 + 0.999*b129)))*(0.001 +
0.999*b129) =L= 0;
e16.. (x76/(0.001 + 0.999*b130) - log(1 + x64/(0.001 + 0.999*b130)))*(0.001 +
0.999*b130) =L= 0;
e17.. x65 =E= 0;
e18.. x66 =E= 0;
e19.. x67 =E= 0;
e20.. x77 =E= 0;
e21.. x78 =E= 0;
e22.. x79 =E= 0;
e23.. x20 - x62 - x65 =E= 0;
e24.. x21 - x63 - x66 =E= 0;
e25.. x22 - x64 - x67 =E= 0;
e26.. x26 - x74 - x77 =E= 0;
e27.. x27 - x75 - x78 =E= 0;
e28.. x28 - x76 - x79 =E= 0;
e29.. x62 - 40*b128 =L= 0;
e30.. x63 - 40*b129 =L= 0;
e31.. x64 - 40*b130 =L= 0;
e32.. x65 + 40*b128 =L= 40;
e33.. x66 + 40*b129 =L= 40;
e34.. x67 + 40*b130 =L= 40;
e35.. x74 - 3.71357206670431*b128 =L= 0;
e36.. x75 - 3.71357206670431*b129 =L= 0;
e37.. x76 - 3.71357206670431*b130 =L= 0;
e38.. x77 + 3.71357206670431*b128 =L= 3.71357206670431;
e39.. x78 + 3.71357206670431*b129 =L= 3.71357206670431;
e40.. x79 + 3.71357206670431*b130 =L= 3.71357206670431;
e41.. (x80/(0.001 + 0.999*b131) - 1.2*log(1 + x68/(0.001 + 0.999*b131)))*(0.001
+ 0.999*b131) =L= 0;
e42.. (x81/(0.001 + 0.999*b132) - 1.2*log(1 + x69/(0.001 + 0.999*b132)))*(0.001
+ 0.999*b132) =L= 0;
e43.. (x82/(0.001 + 0.999*b133) - 1.2*log(1 + x70/(0.001 + 0.999*b133)))*(0.001
+ 0.999*b133) =L= 0;
e44.. x71 =E= 0;
e45.. x72 =E= 0;
e46.. x73 =E= 0;
e47.. x83 =E= 0;
e48.. x84 =E= 0;
e49.. x85 =E= 0;
e50.. x23 - x68 - x71 =E= 0;
e51.. x24 - x69 - x72 =E= 0;
e52.. x25 - x70 - x73 =E= 0;
e53.. x29 - x80 - x83 =E= 0;
e54.. x30 - x81 - x84 =E= 0;
e55.. x31 - x82 - x85 =E= 0;
e56.. x68 - 40*b131 =L= 0;
e57.. x69 - 40*b132 =L= 0;
e58.. x70 - 40*b133 =L= 0;
e59.. x71 + 40*b131 =L= 40;
e60.. x72 + 40*b132 =L= 40;
e61.. x73 + 40*b133 =L= 40;
e62.. x80 - 4.45628648004517*b131 =L= 0;
e63.. x81 - 4.45628648004517*b132 =L= 0;
e64.. x82 - 4.45628648004517*b133 =L= 0;
e65.. x83 + 4.45628648004517*b131 =L= 4.45628648004517;
e66.. x84 + 4.45628648004517*b132 =L= 4.45628648004517;
e67.. x85 + 4.45628648004517*b133 =L= 4.45628648004517;
e68.. - 0.75*x86 + x110 =E= 0;
e69.. - 0.75*x87 + x111 =E= 0;
e70.. - 0.75*x88 + x112 =E= 0;
e71.. x89 =E= 0;
e72.. x90 =E= 0;
e73.. x91 =E= 0;
e74.. x113 =E= 0;
e75.. x114 =E= 0;
e76.. x115 =E= 0;
e77.. x41 - x86 - x89 =E= 0;
e78.. x42 - x87 - x90 =E= 0;
e79.. x43 - x88 - x91 =E= 0;
e80.. x53 - x110 - x113 =E= 0;
e81.. x54 - x111 - x114 =E= 0;
e82.. x55 - x112 - x115 =E= 0;
e83.. x86 - 4.45628648004517*b134 =L= 0;
e84.. x87 - 4.45628648004517*b135 =L= 0;
e85.. x88 - 4.45628648004517*b136 =L= 0;
e86.. x89 + 4.45628648004517*b134 =L= 4.45628648004517;
e87.. x90 + 4.45628648004517*b135 =L= 4.45628648004517;
e88.. x91 + 4.45628648004517*b136 =L= 4.45628648004517;
e89.. x110 - 3.34221486003388*b134 =L= 0;
e90.. x111 - 3.34221486003388*b135 =L= 0;
e91.. x112 - 3.34221486003388*b136 =L= 0;
e92.. x113 + 3.34221486003388*b134 =L= 3.34221486003388;
e93.. x114 + 3.34221486003388*b135 =L= 3.34221486003388;
e94.. x115 + 3.34221486003388*b136 =L= 3.34221486003388;
e95.. (x116/(0.001 + 0.999*b137) - 1.5*log(1 + x92/(0.001 + 0.999*b137)))*(
0.001 + 0.999*b137) =L= 0;
e96.. (x117/(0.001 + 0.999*b138) - 1.5*log(1 + x93/(0.001 + 0.999*b138)))*(
0.001 + 0.999*b138) =L= 0;
e97.. (x118/(0.001 + 0.999*b139) - 1.5*log(1 + x94/(0.001 + 0.999*b139)))*(
0.001 + 0.999*b139) =L= 0;
e98.. x95 =E= 0;
e99.. x96 =E= 0;
e100.. x97 =E= 0;
e101.. x119 =E= 0;
e102.. x120 =E= 0;
e103.. x121 =E= 0;
e104.. x44 - x92 - x95 =E= 0;
e105.. x45 - x93 - x96 =E= 0;
e106.. x46 - x94 - x97 =E= 0;
e107.. x56 - x116 - x119 =E= 0;
e108.. x57 - x117 - x120 =E= 0;
e109.. x58 - x118 - x121 =E= 0;
e110.. x92 - 4.45628648004517*b137 =L= 0;
e111.. x93 - 4.45628648004517*b138 =L= 0;
e112.. x94 - 4.45628648004517*b139 =L= 0;
e113.. x95 + 4.45628648004517*b137 =L= 4.45628648004517;
e114.. x96 + 4.45628648004517*b138 =L= 4.45628648004517;
e115.. x97 + 4.45628648004517*b139 =L= 4.45628648004517;
e116.. x116 - 2.54515263975353*b137 =L= 0;
e117.. x117 - 2.54515263975353*b138 =L= 0;
e118.. x118 - 2.54515263975353*b139 =L= 0;
e119.. x119 + 2.54515263975353*b137 =L= 2.54515263975353;
e120.. x120 + 2.54515263975353*b138 =L= 2.54515263975353;
e121.. x121 + 2.54515263975353*b139 =L= 2.54515263975353;
e122.. - x98 + x122 =E= 0;
e123.. - x99 + x123 =E= 0;
e124.. - x100 + x124 =E= 0;
e125.. - 0.5*x104 + x122 =E= 0;
e126.. - 0.5*x105 + x123 =E= 0;
e127.. - 0.5*x106 + x124 =E= 0;
e128.. x101 =E= 0;
e129.. x102 =E= 0;
e130.. x103 =E= 0;
e131.. x107 =E= 0;
e132.. x108 =E= 0;
e133.. x109 =E= 0;
e134.. x125 =E= 0;
e135.. x126 =E= 0;
e136.. x127 =E= 0;
e137.. x47 - x98 - x101 =E= 0;
e138.. x48 - x99 - x102 =E= 0;
e139.. x49 - x100 - x103 =E= 0;
e140.. x50 - x104 - x107 =E= 0;
e141.. x51 - x105 - x108 =E= 0;
e142.. x52 - x106 - x109 =E= 0;
e143.. x59 - x122 - x125 =E= 0;
e144.. x60 - x123 - x126 =E= 0;
e145.. x61 - x124 - x127 =E= 0;
e146.. x98 - 4.45628648004517*b140 =L= 0;
e147.. x99 - 4.45628648004517*b141 =L= 0;
e148.. x100 - 4.45628648004517*b142 =L= 0;
e149.. x101 + 4.45628648004517*b140 =L= 4.45628648004517;
e150.. x102 + 4.45628648004517*b141 =L= 4.45628648004517;
e151.. x103 + 4.45628648004517*b142 =L= 4.45628648004517;
e152.. x104 - 30*b140 =L= 0;
e153.. x105 - 30*b141 =L= 0;
e154.. x106 - 30*b142 =L= 0;
e155.. x107 + 30*b140 =L= 30;
e156.. x108 + 30*b141 =L= 30;
e157.. x109 + 30*b142 =L= 30;
e158.. x122 - 15*b140 =L= 0;
e159.. x123 - 15*b141 =L= 0;
e160.. x124 - 15*b142 =L= 0;
e161.. x125 + 15*b140 =L= 15;
e162.. x126 + 15*b141 =L= 15;
e163.. x127 + 15*b142 =L= 15;
e164.. x2 + 5*b143 =E= 0;
e165.. x3 + 4*b144 =E= 0;
e166.. x4 + 6*b145 =E= 0;
e167.. x5 + 8*b146 =E= 0;
e168.. x6 + 7*b147 =E= 0;
e169.. x7 + 6*b148 =E= 0;
e170.. x8 + 6*b149 =E= 0;
e171.. x9 + 9*b150 =E= 0;
e172.. x10 + 4*b151 =E= 0;
e173.. x11 + 10*b152 =E= 0;
e174.. x12 + 9*b153 =E= 0;
e175.. x13 + 5*b154 =E= 0;
e176.. x14 + 6*b155 =E= 0;
e177.. x15 + 10*b156 =E= 0;
e178.. x16 + 6*b157 =E= 0;
e179.. b128 - b129 =L= 0;
e180.. b128 - b130 =L= 0;
e181.. b129 - b130 =L= 0;
e182.. b131 - b132 =L= 0;
e183.. b131 - b133 =L= 0;
e184.. b132 - b133 =L= 0;
e185.. b134 - b135 =L= 0;
e186.. b134 - b136 =L= 0;
e187.. b135 - b136 =L= 0;
e188.. b137 - b138 =L= 0;
e189.. b137 - b139 =L= 0;
e190.. b138 - b139 =L= 0;
e191.. b140 - b141 =L= 0;
e192.. b140 - b142 =L= 0;
e193.. b141 - b142 =L= 0;
e194.. b143 + b144 =L= 1;
e195.. b143 + b145 =L= 1;
e196.. b143 + b144 =L= 1;
e197.. b144 + b145 =L= 1;
e198.. b143 + b145 =L= 1;
e199.. b144 + b145 =L= 1;
e200.. b146 + b147 =L= 1;
e201.. b146 + b148 =L= 1;
e202.. b146 + b147 =L= 1;
e203.. b147 + b148 =L= 1;
e204.. b146 + b148 =L= 1;
e205.. b147 + b148 =L= 1;
e206.. b149 + b150 =L= 1;
e207.. b149 + b151 =L= 1;
e208.. b149 + b150 =L= 1;
e209.. b150 + b151 =L= 1;
e210.. b149 + b151 =L= 1;
e211.. b150 + b151 =L= 1;
e212.. b152 + b153 =L= 1;
e213.. b152 + b154 =L= 1;
e214.. b152 + b153 =L= 1;
e215.. b153 + b154 =L= 1;
e216.. b152 + b154 =L= 1;
e217.. b153 + b154 =L= 1;
e218.. b155 + b156 =L= 1;
e219.. b155 + b157 =L= 1;
e220.. b155 + b156 =L= 1;
e221.. b156 + b157 =L= 1;
e222.. b155 + b157 =L= 1;
e223.. b156 + b157 =L= 1;
e224.. b128 - b143 =L= 0;
e225.. - b128 + b129 - b144 =L= 0;
e226.. - b128 - b129 + b130 - b145 =L= 0;
e227.. b131 - b146 =L= 0;
e228.. - b131 + b132 - b147 =L= 0;
e229.. - b131 - b132 + b133 - b148 =L= 0;
e230.. b134 - b149 =L= 0;
e231.. - b134 + b135 - b150 =L= 0;
e232.. - b134 - b135 + b136 - b151 =L= 0;
e233.. b137 - b152 =L= 0;
e234.. - b137 + b138 - b153 =L= 0;
e235.. - b137 - b138 + b139 - b154 =L= 0;
e236.. b140 - b155 =L= 0;
e237.. - b140 + b141 - b156 =L= 0;
e238.. - b140 - b141 + b142 - b157 =L= 0;
e239.. b128 + b131 =E= 1;
e240.. b129 + b132 =E= 1;
e241.. b130 + b133 =E= 1;
e242.. b128 + b131 - b134 =G= 0;
e243.. b129 + b132 - b135 =G= 0;
e244.. b130 + b133 - b136 =G= 0;
e245.. b128 + b131 - b137 =G= 0;
e246.. b129 + b132 - b138 =G= 0;
e247.. b130 + b133 - b139 =G= 0;
e248.. b128 + b131 - b140 =G= 0;
e249.. b129 + b132 - b141 =G= 0;
e250.. b130 + b133 - b142 =G= 0;
* set non-default bounds
x17.up = 40;
x18.up = 40;
x19.up = 40;
x50.up = 30;
x51.up = 30;
x52.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: 2024-08-26 Git hash: 6cc1607f