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Instance syn15hfsg
Selection of optimal configuration and parameters for a processing system selected from a superstructure containing alternative processing units and interconnections. Equivalent perspective reformulation of syn15.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 853.28472920 (ALPHAECP) 853.28502380 (ANTIGONE) 853.28499290 (BARON) 853.28472920 (BONMIN) 853.28507850 (COUENNE) 853.28472930 (LINDO) 853.28482220 (SCIP) 2201.96649100 (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ⓘ | 121 |
| #Binary Variablesⓘ | 15 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 31 |
| #Nonlinear Binary Variablesⓘ | 10 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 22 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 181 |
| #Linear Constraintsⓘ | 170 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 11 |
| Operands in Gen. Nonlin. Functionsⓘ | div log mul |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 393 |
| #Nonlinear Nonzeros in Jacobianⓘ | 33 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 63 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 21 |
| #Blocks in Hessian of Lagrangianⓘ | 10 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 4 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.1 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-03 |
| Maximal coefficientⓘ | 5.0000e+02 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 182 85 20 77 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 122 107 15 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 416 383 33 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,b108,b109,b110,b111,b112,b113,b114,b115
,b116,b117,b118,b119,b120,b121,b122;
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;
Binary Variables b108,b109,b110,b111,b112,b113,b114,b115,b116,b117,b118,b119
,b120,b121,b122;
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;
e1.. objvar - 5*x8 - 500*x26 - 350*x27 - 200*x38 - 250*x39 - 200*x40
- 200*x41 + 5*b108 + 8*b109 + 6*b110 + 10*b111 + 6*b112 + 7*b113 + 4*b114
+ 5*b115 + 2*b116 + 4*b117 + 3*b118 + 7*b119 + 3*b120 + 2*b121 + 4*b122
=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.. (x46/(0.001 + 0.999*b108) - log(1 + x42/(0.001 + 0.999*b108)))*(0.001 +
0.999*b108) =L= 0;
e13.. x43 =E= 0;
e14.. x47 =E= 0;
e15.. x3 - x42 - x43 =E= 0;
e16.. x5 - x46 - x47 =E= 0;
e17.. x42 - 10*b108 =L= 0;
e18.. x43 + 10*b108 =L= 10;
e19.. x46 - 2.39789527279837*b108 =L= 0;
e20.. x47 + 2.39789527279837*b108 =L= 2.39789527279837;
e21.. (x48/(0.001 + 0.999*b109) - 1.2*log(1 + x44/(0.001 + 0.999*b109)))*(0.001
+ 0.999*b109) =L= 0;
e22.. x45 =E= 0;
e23.. x49 =E= 0;
e24.. x4 - x44 - x45 =E= 0;
e25.. x6 - x48 - x49 =E= 0;
e26.. x44 - 10*b109 =L= 0;
e27.. x45 + 10*b109 =L= 10;
e28.. x48 - 2.87747432735804*b109 =L= 0;
e29.. x49 + 2.87747432735804*b109 =L= 2.87747432735804;
e30.. - 0.75*x50 + x58 =E= 0;
e31.. x51 =E= 0;
e32.. x59 =E= 0;
e33.. x10 - x50 - x51 =E= 0;
e34.. x14 - x58 - x59 =E= 0;
e35.. x50 - 2.87747432735804*b110 =L= 0;
e36.. x51 + 2.87747432735804*b110 =L= 2.87747432735804;
e37.. x58 - 2.15810574551853*b110 =L= 0;
e38.. x59 + 2.15810574551853*b110 =L= 2.15810574551853;
e39.. (x60/(0.001 + 0.999*b111) - 1.5*log(1 + x52/(0.001 + 0.999*b111)))*(0.001
+ 0.999*b111) =L= 0;
e40.. x53 =E= 0;
e41.. x62 =E= 0;
e42.. x11 - x52 - x53 =E= 0;
e43.. x15 - x60 - x62 =E= 0;
e44.. x52 - 2.87747432735804*b111 =L= 0;
e45.. x53 + 2.87747432735804*b111 =L= 2.87747432735804;
e46.. x60 - 2.03277599268042*b111 =L= 0;
e47.. x62 + 2.03277599268042*b111 =L= 2.03277599268042;
e48.. - x54 + x64 =E= 0;
e49.. - 0.5*x56 + x64 =E= 0;
e50.. x55 =E= 0;
e51.. x57 =E= 0;
e52.. x65 =E= 0;
e53.. x12 - x54 - x55 =E= 0;
e54.. x13 - x56 - x57 =E= 0;
e55.. x16 - x64 - x65 =E= 0;
e56.. x54 - 2.87747432735804*b112 =L= 0;
e57.. x55 + 2.87747432735804*b112 =L= 2.87747432735804;
e58.. x56 - 7*b112 =L= 0;
e59.. x57 + 7*b112 =L= 7;
e60.. x64 - 3.5*b112 =L= 0;
e61.. x65 + 3.5*b112 =L= 3.5;
e62.. (x76/(0.001 + 0.999*b113) - 1.25*log(1 + x66/(0.001 + 0.999*b113)))*(
0.001 + 0.999*b113) =L= 0;
e63.. x67 =E= 0;
e64.. x78 =E= 0;
e65.. x17 - x66 - x67 =E= 0;
e66.. x22 - x76 - x78 =E= 0;
e67.. x66 - 2.15810574551853*b113 =L= 0;
e68.. x67 + 2.15810574551853*b113 =L= 2.15810574551853;
e69.. x76 - 1.43746550029693*b113 =L= 0;
e70.. x78 + 1.43746550029693*b113 =L= 1.43746550029693;
e71.. (x80/(0.001 + 0.999*b114) - 0.9*log(1 + x68/(0.001 + 0.999*b114)))*(0.001
+ 0.999*b114) =L= 0;
e72.. x69 =E= 0;
e73.. x82 =E= 0;
e74.. x18 - x68 - x69 =E= 0;
e75.. x23 - x80 - x82 =E= 0;
e76.. x68 - 2.15810574551853*b114 =L= 0;
e77.. x69 + 2.15810574551853*b114 =L= 2.15810574551853;
e78.. x80 - 1.03497516021379*b114 =L= 0;
e79.. x82 + 1.03497516021379*b114 =L= 1.03497516021379;
e80.. (x84/(0.001 + 0.999*b115) - log(1 + x61/(0.001 + 0.999*b115)))*(0.001 +
0.999*b115) =L= 0;
e81.. x63 =E= 0;
e82.. x85 =E= 0;
e83.. x15 - x61 - x63 =E= 0;
e84.. x24 - x84 - x85 =E= 0;
e85.. x61 - 2.03277599268042*b115 =L= 0;
e86.. x63 + 2.03277599268042*b115 =L= 2.03277599268042;
e87.. x84 - 1.10947836929589*b115 =L= 0;
e88.. x85 + 1.10947836929589*b115 =L= 1.10947836929589;
e89.. - 0.9*x70 + x86 =E= 0;
e90.. x71 =E= 0;
e91.. x87 =E= 0;
e92.. x19 - x70 - x71 =E= 0;
e93.. x25 - x86 - x87 =E= 0;
e94.. x70 - 3.5*b116 =L= 0;
e95.. x71 + 3.5*b116 =L= 3.5;
e96.. x86 - 3.15*b116 =L= 0;
e97.. x87 + 3.15*b116 =L= 3.15;
e98.. - 0.6*x72 + x88 =E= 0;
e99.. x73 =E= 0;
e100.. x89 =E= 0;
e101.. x20 - x72 - x73 =E= 0;
e102.. x26 - x88 - x89 =E= 0;
e103.. x72 - 3.5*b117 =L= 0;
e104.. x73 + 3.5*b117 =L= 3.5;
e105.. x88 - 2.1*b117 =L= 0;
e106.. x89 + 2.1*b117 =L= 2.1;
e107.. (x90/(0.001 + 0.999*b118) - 1.1*log(1 + x74/(0.001 + 0.999*b118)))*(
0.001 + 0.999*b118) =L= 0;
e108.. x75 =E= 0;
e109.. x91 =E= 0;
e110.. x21 - x74 - x75 =E= 0;
e111.. x27 - x90 - x91 =E= 0;
e112.. x74 - 3.5*b118 =L= 0;
e113.. x75 + 3.5*b118 =L= 3.5;
e114.. x90 - 1.6544851364539*b118 =L= 0;
e115.. x91 + 1.6544851364539*b118 =L= 1.6544851364539;
e116.. - 0.9*x77 + x100 =E= 0;
e117.. - x96 + x100 =E= 0;
e118.. x79 =E= 0;
e119.. x97 =E= 0;
e120.. x101 =E= 0;
e121.. x22 - x77 - x79 =E= 0;
e122.. x30 - x96 - x97 =E= 0;
e123.. x38 - x100 - x101 =E= 0;
e124.. x77 - 1.43746550029693*b119 =L= 0;
e125.. x79 + 1.43746550029693*b119 =L= 1.43746550029693;
e126.. x96 - 5*b119 =L= 0;
e127.. x97 + 5*b119 =L= 5;
e128.. x100 - 5*b119 =L= 0;
e129.. x101 + 5*b119 =L= 5;
e130.. (x102/(0.001 + 0.999*b120) - log(1 + x81/(0.001 + 0.999*b120)))*(0.001
+ 0.999*b120) =L= 0;
e131.. x83 =E= 0;
e132.. x103 =E= 0;
e133.. x23 - x81 - x83 =E= 0;
e134.. x39 - x102 - x103 =E= 0;
e135.. x81 - 1.03497516021379*b120 =L= 0;
e136.. x83 + 1.03497516021379*b120 =L= 1.03497516021379;
e137.. x102 - 0.710483612536911*b120 =L= 0;
e138.. x103 + 0.710483612536911*b120 =L= 0.710483612536911;
e139.. (x104/(0.001 + 0.999*b121) - 0.7*log(1 + x92/(0.001 + 0.999*b121)))*(
0.001 + 0.999*b121) =L= 0;
e140.. x93 =E= 0;
e141.. x105 =E= 0;
e142.. x28 - x92 - x93 =E= 0;
e143.. x40 - x104 - x105 =E= 0;
e144.. x92 - 1.10947836929589*b121 =L= 0;
e145.. x93 + 1.10947836929589*b121 =L= 1.10947836929589;
e146.. x104 - 0.522508489006913*b121 =L= 0;
e147.. x105 + 0.522508489006913*b121 =L= 0.522508489006913;
e148.. (x106/(0.001 + 0.999*b122) - 0.65*log(1 + x94/(0.001 + 0.999*b122)))*(
0.001 + 0.999*b122) =L= 0;
e149.. (x106/(0.001 + 0.999*b122) - 0.65*log(1 + x98/(0.001 + 0.999*b122)))*(
0.001 + 0.999*b122) =L= 0;
e150.. x95 =E= 0;
e151.. x99 =E= 0;
e152.. x107 =E= 0;
e153.. x29 - x94 - x95 =E= 0;
e154.. x32 - x98 - x99 =E= 0;
e155.. x41 - x106 - x107 =E= 0;
e156.. x94 - 1.10947836929589*b122 =L= 0;
e157.. x95 + 1.10947836929589*b122 =L= 1.10947836929589;
e158.. x98 - 8.15*b122 =L= 0;
e159.. x99 + 8.15*b122 =L= 8.15;
e160.. x106 - 1.43894002153683*b122 =L= 0;
e161.. x107 + 1.43894002153683*b122 =L= 1.43894002153683;
e162.. b108 + b109 =E= 1;
e163.. - b110 + b113 + b114 =G= 0;
e164.. - b113 + b119 =G= 0;
e165.. - b114 + b120 =G= 0;
e166.. - b111 + b115 =G= 0;
e167.. - b115 + b121 + b122 =G= 0;
e168.. - b112 + b116 + b117 + b118 =G= 0;
e169.. - b116 + b122 =G= 0;
e170.. b108 + b109 - b110 =G= 0;
e171.. b108 + b109 - b111 =G= 0;
e172.. b108 + b109 - b112 =G= 0;
e173.. b110 - b113 =G= 0;
e174.. b110 - b114 =G= 0;
e175.. b111 - b115 =G= 0;
e176.. b112 - b116 =G= 0;
e177.. b112 - b117 =G= 0;
e178.. b112 - b118 =G= 0;
e179.. b113 - b119 =G= 0;
e180.. b114 - b120 =G= 0;
e181.. b115 - b121 =G= 0;
e182.. b115 - b122 =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