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Instance syn20hfsg
Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections. Equivalent perspective reformulation of syn20.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 925.14445060 (ALPHAECP) 924.58556370 (ANTIGONE) 924.26331140 (BARON) 924.26331070 (BONMIN) 924.26340200 (COUENNE) 924.26331060 (LINDO) 924.26405550 (SCIP) 3666.71143600 (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ⓘ | 151 |
| #Binary Variablesⓘ | 20 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 40 |
| #Nonlinear Binary Variablesⓘ | 13 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 30 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 233 |
| #Linear Constraintsⓘ | 219 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 14 |
| Operands in Gen. Nonlin. Functionsⓘ | div log mul |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 503 |
| #Nonlinear Nonzeros in Jacobianⓘ | 42 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 81 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 27 |
| #Blocks in Hessian of Lagrangianⓘ | 13 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 4 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.076923 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-03 |
| Maximal coefficientⓘ | 7.0000e+02 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 234 107 27 100 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 152 132 20 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 534 492 42 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,x128
,x129,x130,x131,x132,b133,b134,b135,b136,b137,b138,b139,b140,b141
,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152;
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,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
,x128,x129,x130,x131,x132;
Binary Variables b133,b134,b135,b136,b137,b138,b139,b140,b141,b142,b143,b144
,b145,b146,b147,b148,b149,b150,b151,b152;
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;
e1.. objvar - 5*x8 - 200*x38 - 250*x39 - 200*x40 - 700*x41 - 400*x42
- 500*x43 - 400*x44 - 600*x45 - 700*x46 + 5*b133 + 8*b134 + 6*b135
+ 10*b136 + 6*b137 + 7*b138 + 4*b139 + 5*b140 + 2*b141 + 4*b142 + 3*b143
+ 7*b144 + 3*b145 + 2*b146 + 4*b147 + 2*b148 + 3*b149 + 5*b150 + 2*b151
+ 8*b152 =E= 0;
e2.. x2 - x3 - x4 =E= 0;
e3.. - x5 - x6 + x7 =E= 0;
e4.. x7 - x8 - x9 =E= 0;
e5.. x9 - x10 - x11 - x12 =E= 0;
e6.. x14 - x17 - x18 =E= 0;
e7.. x16 - x19 - x20 - x21 =E= 0;
e8.. x24 - x28 - x29 =E= 0;
e9.. - x25 - x31 + x32 =E= 0;
e10.. x26 - x33 - x34 =E= 0;
e11.. x27 - x35 - x36 - x37 =E= 0;
e12.. (x51/(0.001 + 0.999*b133) - log(1 + x47/(0.001 + 0.999*b133)))*(0.001 +
0.999*b133) =L= 0;
e13.. x48 =E= 0;
e14.. x52 =E= 0;
e15.. x3 - x47 - x48 =E= 0;
e16.. x5 - x51 - x52 =E= 0;
e17.. x47 - 10*b133 =L= 0;
e18.. x48 + 10*b133 =L= 10;
e19.. x51 - 2.39789527279837*b133 =L= 0;
e20.. x52 + 2.39789527279837*b133 =L= 2.39789527279837;
e21.. (x53/(0.001 + 0.999*b134) - 1.2*log(1 + x49/(0.001 + 0.999*b134)))*(0.001
+ 0.999*b134) =L= 0;
e22.. x50 =E= 0;
e23.. x54 =E= 0;
e24.. x4 - x49 - x50 =E= 0;
e25.. x6 - x53 - x54 =E= 0;
e26.. x49 - 10*b134 =L= 0;
e27.. x50 + 10*b134 =L= 10;
e28.. x53 - 2.87747432735804*b134 =L= 0;
e29.. x54 + 2.87747432735804*b134 =L= 2.87747432735804;
e30.. - 0.75*x55 + x63 =E= 0;
e31.. x56 =E= 0;
e32.. x64 =E= 0;
e33.. x10 - x55 - x56 =E= 0;
e34.. x14 - x63 - x64 =E= 0;
e35.. x55 - 2.87747432735804*b135 =L= 0;
e36.. x56 + 2.87747432735804*b135 =L= 2.87747432735804;
e37.. x63 - 2.15810574551853*b135 =L= 0;
e38.. x64 + 2.15810574551853*b135 =L= 2.15810574551853;
e39.. (x65/(0.001 + 0.999*b136) - 1.5*log(1 + x57/(0.001 + 0.999*b136)))*(0.001
+ 0.999*b136) =L= 0;
e40.. x58 =E= 0;
e41.. x67 =E= 0;
e42.. x11 - x57 - x58 =E= 0;
e43.. x15 - x65 - x67 =E= 0;
e44.. x57 - 2.87747432735804*b136 =L= 0;
e45.. x58 + 2.87747432735804*b136 =L= 2.87747432735804;
e46.. x65 - 2.03277599268042*b136 =L= 0;
e47.. x67 + 2.03277599268042*b136 =L= 2.03277599268042;
e48.. - x59 + x69 =E= 0;
e49.. - 0.5*x61 + x69 =E= 0;
e50.. x60 =E= 0;
e51.. x62 =E= 0;
e52.. x70 =E= 0;
e53.. x12 - x59 - x60 =E= 0;
e54.. x13 - x61 - x62 =E= 0;
e55.. x16 - x69 - x70 =E= 0;
e56.. x59 - 2.87747432735804*b137 =L= 0;
e57.. x60 + 2.87747432735804*b137 =L= 2.87747432735804;
e58.. x61 - 7*b137 =L= 0;
e59.. x62 + 7*b137 =L= 7;
e60.. x69 - 3.5*b137 =L= 0;
e61.. x70 + 3.5*b137 =L= 3.5;
e62.. (x81/(0.001 + 0.999*b138) - 1.25*log(1 + x71/(0.001 + 0.999*b138)))*(
0.001 + 0.999*b138) =L= 0;
e63.. x72 =E= 0;
e64.. x83 =E= 0;
e65.. x17 - x71 - x72 =E= 0;
e66.. x22 - x81 - x83 =E= 0;
e67.. x71 - 2.15810574551853*b138 =L= 0;
e68.. x72 + 2.15810574551853*b138 =L= 2.15810574551853;
e69.. x81 - 1.43746550029693*b138 =L= 0;
e70.. x83 + 1.43746550029693*b138 =L= 1.43746550029693;
e71.. (x85/(0.001 + 0.999*b139) - 0.9*log(1 + x73/(0.001 + 0.999*b139)))*(0.001
+ 0.999*b139) =L= 0;
e72.. x74 =E= 0;
e73.. x87 =E= 0;
e74.. x18 - x73 - x74 =E= 0;
e75.. x23 - x85 - x87 =E= 0;
e76.. x73 - 2.15810574551853*b139 =L= 0;
e77.. x74 + 2.15810574551853*b139 =L= 2.15810574551853;
e78.. x85 - 1.03497516021379*b139 =L= 0;
e79.. x87 + 1.03497516021379*b139 =L= 1.03497516021379;
e80.. (x89/(0.001 + 0.999*b140) - log(1 + x66/(0.001 + 0.999*b140)))*(0.001 +
0.999*b140) =L= 0;
e81.. x68 =E= 0;
e82.. x90 =E= 0;
e83.. x15 - x66 - x68 =E= 0;
e84.. x24 - x89 - x90 =E= 0;
e85.. x66 - 2.03277599268042*b140 =L= 0;
e86.. x68 + 2.03277599268042*b140 =L= 2.03277599268042;
e87.. x89 - 1.10947836929589*b140 =L= 0;
e88.. x90 + 1.10947836929589*b140 =L= 1.10947836929589;
e89.. - 0.9*x75 + x91 =E= 0;
e90.. x76 =E= 0;
e91.. x92 =E= 0;
e92.. x19 - x75 - x76 =E= 0;
e93.. x25 - x91 - x92 =E= 0;
e94.. x75 - 3.5*b141 =L= 0;
e95.. x76 + 3.5*b141 =L= 3.5;
e96.. x91 - 3.15*b141 =L= 0;
e97.. x92 + 3.15*b141 =L= 3.15;
e98.. - 0.6*x77 + x93 =E= 0;
e99.. x78 =E= 0;
e100.. x94 =E= 0;
e101.. x20 - x77 - x78 =E= 0;
e102.. x26 - x93 - x94 =E= 0;
e103.. x77 - 3.5*b142 =L= 0;
e104.. x78 + 3.5*b142 =L= 3.5;
e105.. x93 - 2.1*b142 =L= 0;
e106.. x94 + 2.1*b142 =L= 2.1;
e107.. (x95/(0.001 + 0.999*b143) - 1.1*log(1 + x79/(0.001 + 0.999*b143)))*(
0.001 + 0.999*b143) =L= 0;
e108.. x80 =E= 0;
e109.. x96 =E= 0;
e110.. x21 - x79 - x80 =E= 0;
e111.. x27 - x95 - x96 =E= 0;
e112.. x79 - 3.5*b143 =L= 0;
e113.. x80 + 3.5*b143 =L= 3.5;
e114.. x95 - 1.6544851364539*b143 =L= 0;
e115.. x96 + 1.6544851364539*b143 =L= 1.6544851364539;
e116.. - 0.9*x82 + x115 =E= 0;
e117.. - x101 + x115 =E= 0;
e118.. x84 =E= 0;
e119.. x102 =E= 0;
e120.. x116 =E= 0;
e121.. x22 - x82 - x84 =E= 0;
e122.. x30 - x101 - x102 =E= 0;
e123.. x38 - x115 - x116 =E= 0;
e124.. x82 - 1.43746550029693*b144 =L= 0;
e125.. x84 + 1.43746550029693*b144 =L= 1.43746550029693;
e126.. x101 - 5*b144 =L= 0;
e127.. x102 + 5*b144 =L= 5;
e128.. x115 - 5*b144 =L= 0;
e129.. x116 + 5*b144 =L= 5;
e130.. (x117/(0.001 + 0.999*b145) - log(1 + x86/(0.001 + 0.999*b145)))*(0.001
+ 0.999*b145) =L= 0;
e131.. x88 =E= 0;
e132.. x118 =E= 0;
e133.. x23 - x86 - x88 =E= 0;
e134.. x39 - x117 - x118 =E= 0;
e135.. x86 - 1.03497516021379*b145 =L= 0;
e136.. x88 + 1.03497516021379*b145 =L= 1.03497516021379;
e137.. x117 - 0.710483612536911*b145 =L= 0;
e138.. x118 + 0.710483612536911*b145 =L= 0.710483612536911;
e139.. (x119/(0.001 + 0.999*b146) - 0.7*log(1 + x97/(0.001 + 0.999*b146)))*(
0.001 + 0.999*b146) =L= 0;
e140.. x98 =E= 0;
e141.. x120 =E= 0;
e142.. x28 - x97 - x98 =E= 0;
e143.. x40 - x119 - x120 =E= 0;
e144.. x97 - 1.10947836929589*b146 =L= 0;
e145.. x98 + 1.10947836929589*b146 =L= 1.10947836929589;
e146.. x119 - 0.522508489006913*b146 =L= 0;
e147.. x120 + 0.522508489006913*b146 =L= 0.522508489006913;
e148.. (x121/(0.001 + 0.999*b147) - 0.65*log(1 + x99/(0.001 + 0.999*b147)))*(
0.001 + 0.999*b147) =L= 0;
e149.. (x121/(0.001 + 0.999*b147) - 0.65*log(1 + x103/(0.001 + 0.999*b147)))*(
0.001 + 0.999*b147) =L= 0;
e150.. x100 =E= 0;
e151.. x104 =E= 0;
e152.. x122 =E= 0;
e153.. x29 - x99 - x100 =E= 0;
e154.. x32 - x103 - x104 =E= 0;
e155.. x41 - x121 - x122 =E= 0;
e156.. x99 - 1.10947836929589*b147 =L= 0;
e157.. x100 + 1.10947836929589*b147 =L= 1.10947836929589;
e158.. x103 - 8.15*b147 =L= 0;
e159.. x104 + 8.15*b147 =L= 8.15;
e160.. x121 - 1.43894002153683*b147 =L= 0;
e161.. x122 + 1.43894002153683*b147 =L= 1.43894002153683;
e162.. - x105 + x123 =E= 0;
e163.. x106 =E= 0;
e164.. x124 =E= 0;
e165.. x33 - x105 - x106 =E= 0;
e166.. x42 - x123 - x124 =E= 0;
e167.. x105 - 2.1*b148 =L= 0;
e168.. x106 + 2.1*b148 =L= 2.1;
e169.. x123 - 2.1*b148 =L= 0;
e170.. x124 + 2.1*b148 =L= 2.1;
e171.. - x107 + x125 =E= 0;
e172.. x108 =E= 0;
e173.. x126 =E= 0;
e174.. x34 - x107 - x108 =E= 0;
e175.. x43 - x125 - x126 =E= 0;
e176.. x107 - 2.1*b149 =L= 0;
e177.. x108 + 2.1*b149 =L= 2.1;
e178.. x125 - 2.1*b149 =L= 0;
e179.. x126 + 2.1*b149 =L= 2.1;
e180.. (x127/(0.001 + 0.999*b150) - 0.75*log(1 + x109/(0.001 + 0.999*b150)))*(
0.001 + 0.999*b150) =L= 0;
e181.. x110 =E= 0;
e182.. x128 =E= 0;
e183.. x35 - x109 - x110 =E= 0;
e184.. x44 - x127 - x128 =E= 0;
e185.. x109 - 1.6544851364539*b150 =L= 0;
e186.. x110 + 1.6544851364539*b150 =L= 1.6544851364539;
e187.. x127 - 0.732188035236726*b150 =L= 0;
e188.. x128 + 0.732188035236726*b150 =L= 0.732188035236726;
e189.. (x129/(0.001 + 0.999*b151) - 0.8*log(1 + x111/(0.001 + 0.999*b151)))*(
0.001 + 0.999*b151) =L= 0;
e190.. x112 =E= 0;
e191.. x130 =E= 0;
e192.. x36 - x111 - x112 =E= 0;
e193.. x45 - x129 - x130 =E= 0;
e194.. x111 - 1.6544851364539*b151 =L= 0;
e195.. x112 + 1.6544851364539*b151 =L= 1.6544851364539;
e196.. x129 - 0.781000570919175*b151 =L= 0;
e197.. x130 + 0.781000570919175*b151 =L= 0.781000570919175;
e198.. (x131/(0.001 + 0.999*b152) - 0.85*log(1 + x113/(0.001 + 0.999*b152)))*(
0.001 + 0.999*b152) =L= 0;
e199.. x114 =E= 0;
e200.. x132 =E= 0;
e201.. x37 - x113 - x114 =E= 0;
e202.. x46 - x131 - x132 =E= 0;
e203.. x113 - 1.6544851364539*b152 =L= 0;
e204.. x114 + 1.6544851364539*b152 =L= 1.6544851364539;
e205.. x131 - 0.829813106601623*b152 =L= 0;
e206.. x132 + 0.829813106601623*b152 =L= 0.829813106601623;
e207.. b133 + b134 =E= 1;
e208.. - b135 + b138 + b139 =G= 0;
e209.. - b138 + b144 =G= 0;
e210.. - b139 + b145 =G= 0;
e211.. - b136 + b140 =G= 0;
e212.. - b140 + b146 + b147 =G= 0;
e213.. - b137 + b141 + b142 + b143 =G= 0;
e214.. - b141 + b147 =G= 0;
e215.. - b142 + b148 + b149 =G= 0;
e216.. - b143 + b150 + b151 + b152 =G= 0;
e217.. b133 + b134 - b135 =G= 0;
e218.. b133 + b134 - b136 =G= 0;
e219.. b133 + b134 - b137 =G= 0;
e220.. b135 - b138 =G= 0;
e221.. b135 - b139 =G= 0;
e222.. b136 - b140 =G= 0;
e223.. b137 - b141 =G= 0;
e224.. b137 - b142 =G= 0;
e225.. b137 - b143 =G= 0;
e226.. b138 - b144 =G= 0;
e227.. b139 - b145 =G= 0;
e228.. b140 - b146 =G= 0;
e229.. b140 - b147 =G= 0;
e230.. b142 - b148 =G= 0;
e231.. b142 - b149 =G= 0;
e232.. b143 - b150 =G= 0;
e233.. b143 - b151 =G= 0;
e234.. b143 - b152 =G= 0;
* set non-default bounds
x2.up = 10;
x13.up = 7;
x30.up = 5;
x31.up = 5;
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