MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance util
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 999.57875020 (ANTIGONE) 999.57875020 (BARON) 999.57875020 (COUENNE) 999.57875020 (GUROBI) 999.57875020 (LINDO) 999.57875020 (SCIP) 536.64529300 (SHOT) |
| Sourceⓘ | Aldo Vecchietti's Model Collection |
| Applicationⓘ | Argentina utility plant |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 145 |
| #Binary Variablesⓘ | 28 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 7 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 17 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 167 |
| #Linear Constraintsⓘ | 163 |
| #Quadratic Constraintsⓘ | 4 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 449 |
| #Nonlinear Nonzeros in Jacobianⓘ | 10 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 10 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 2 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 5 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.5 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 6.4100e-03 |
| Maximal coefficientⓘ | 4.4500e+02 |
| Infeasibility of initial pointⓘ | 4117 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 168 116 1 51 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 146 118 28 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 467 457 10 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,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,x133,x134,x135,x136,x137,x138,x139,x140,x141,x142
,x143,x144,x145,objvar;
Positive Variables 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,x59,x60
,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x77,x78
,x79,x80,x81,x82,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92,x94,x95,x96
,x98,x99,x100,x101,x102,x103,x104,x105,x106,x107,x108,x109,x111,x112
,x113,x114,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125
,x126,x127,x128,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138
,x139,x140,x141,x142,x143,x144,x145;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28;
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;
e1.. x53*x49 + x52*x51 - 0.5439*x44 - 0.5439*x46 - 1.22963*x47 - 2.74289*x48
- 6.94492*x50 =E= 0;
e2.. x53*x54 - 3.22692*x55 - 9.05971*x56 + x57 - x58 =E= 0;
e3.. x53*x59 + 7.32917*x60 + 7.70075*x61 - 7.31039*x62 - 7.31039*x63
- 7.31039*x64 - 7.31039*x65 - 7.31039*x66 - 7.31039*x67 - 7.31039*x68
- 7.31039*x69 - 7.31039*x70 - 7.31039*x71 - 7.31039*x72 - 7.31039*x73
- 7.31039*x74 - 7.31039*x75 - 7.31039*x76 =E= 0;
e4.. x53*x77 - 6.94492*x50 + 7.31039*x62 + 7.03739*x78 + 7.03739*x79
+ 6.91604*x80 + 6.91604*x81 + 6.91604*x82 + 6.91604*x83 + 6.91604*x84
+ 6.91604*x85 + 6.91604*x86 + 6.91604*x87 + 6.91604*x88 + 6.91604*x89
+ 6.91604*x90 + 6.91604*x91 - 6.94492*x92 - 6.94492*x93 =E= 0;
e5.. - x44 - x46 - x47 - x48 + x49 - x50 + x51 =E= 0;
e6.. x44 - x94 - x95 =E= 0;
e7.. - 0.08*x50 + x51 =E= 0;
e8.. 0.05391*x96 - x97 =E= 4.45329;
e9.. x52 - 0.34851*x53 =E= 6.04388;
e10.. x53 - 0.18673*x97 =E= 0.82639;
e11.. x49 - x54 - x59 - x77 - x98 =E= 0;
e12.. x98 =G= 104.21999;
e13.. - 0.5*x49 + x99 =E= 0;
e14.. - 1.89474*x99 + x100 =E= 230;
e15.. x100 - x101 =E= 0;
e16.. x54 - x55 - x56 =E= 0;
e17.. - 0.05*x54 + x55 =E= 0;
e18.. - 116.41403*x29 + x57 =E= 0;
e19.. x29 - x102 =E= 4.035;
e20.. - 23.39292*x102 + x103 =E= 0;
e21.. - 3.61341*x103 + x104 =E= 0;
e22.. x56 - x61 + x105 - x106 - x107 - x108 - x109 - x110 =E= 0;
e23.. x59 + x60 + x61 - x62 - x63 - x64 - x65 - x66 - x67 - x68 - x69 - x70
- x71 - x72 - x73 - x74 - x75 - x76 =E= 0;
e24.. - x50 + x62 + x77 + x78 + x79 + x80 + x81 + x82 + x83 + x84 + x85 + x86
+ x87 + x88 + x89 + x90 + x91 - x92 - x93 =E= 0;
e25.. - x46 + x111 + x112 =E= 0;
e26.. x106 - x113 =E= 0;
e27.. - x60 + x107 =E= 0;
e28.. - x78 + x108 =E= 0;
e29.. - x79 + x109 =E= 0;
e30.. 7.70075*x106 - 6.08959*x113 - 0.00641*x114 =E= 0;
e31.. - 7.32917*x60 + 7.70075*x107 - 0.00641*x115 =E= 0;
e32.. - 7.03739*x78 + 7.70075*x108 - 0.00641*x116 =E= 0;
e33.. - 7.03739*x79 + 7.70075*x109 - 0.00641*x117 =E= 0;
e34.. x63 - x80 =E= 0;
e35.. x64 - x81 =E= 0;
e36.. x65 - x82 =E= 0;
e37.. x66 - x118 =E= 0;
e38.. x67 - x83 =E= 0;
e39.. x68 - x84 =E= 0;
e40.. x69 - x85 =E= 0;
e41.. x70 - x86 =E= 0;
e42.. x71 - x87 =E= 0;
e43.. x72 - x88 =E= 0;
e44.. x73 - x89 =E= 0;
e45.. x74 - x90 =E= 0;
e46.. x75 - x91 =E= 0;
e47.. 7.31039*x63 - 6.91604*x80 - 0.00641*x119 =E= 0;
e48.. 7.31039*x64 - 6.91604*x81 - 0.00641*x120 =E= 0;
e49.. 7.31039*x65 - 6.91604*x82 - 0.00641*x121 =E= 0;
e50.. 7.31039*x66 - 5.77083*x118 - 0.00641*x122 =E= 0;
e51.. 7.31039*x67 - 6.91604*x83 - 0.00641*x123 =E= 0;
e52.. 7.31039*x68 - 6.91604*x84 - 0.00641*x124 =E= 0;
e53.. 7.31039*x69 - 6.91604*x85 - 0.00641*x125 =E= 0;
e54.. 7.31039*x70 - 6.91604*x86 - 0.00641*x126 =E= 0;
e55.. 7.31039*x71 - 6.91604*x87 - 0.00641*x127 =E= 0;
e56.. 7.31039*x72 - 6.91604*x88 - 0.00641*x128 =E= 0;
e57.. 7.31039*x73 - 6.91604*x89 - 0.00641*x129 =E= 0;
e58.. 7.31039*x74 - 6.91604*x90 - 0.00641*x130 =E= 0;
e59.. 7.31039*x75 - 6.91604*x91 - 0.00641*x131 =E= 0;
e60.. x111 - x113 =E= 0;
e61.. x112 - x118 =E= 0;
e62.. 5.6972*x111 - 0.12983*x132 =E= 0;
e63.. 5.6972*x112 - 0.12983*x133 =E= 0;
e64.. x45 - x132 - x133 =E= 4117;
e65.. - 0.33333*x45 + x134 =E= 0;
e66.. - 0.20286*x134 + x135 =E= 0;
e67.. x135 - x136 =E= 0;
e68.. x135 - x137 =E= 0;
e69.. x138 =E= 1;
e70.. x139 =E= 1;
e71.. x140 =E= 1;
e72.. x141 =E= 1;
e73.. x138 - x142 =E= 0;
e74.. x138 - x143 =E= 0;
e75.. x139 - x144 =E= 0;
e76.. 0.01*x111 - 100*x144 =L= 0;
e77.. x141 - x145 =E= 0;
e78.. 0.01*x112 - 100*x145 =L= 0;
e79.. 0.1*x49 - 100*x142 =L= 0;
e80.. 0.1*x103 - 100*x143 =L= 0;
e81.. 0.1*x56 - 100*x138 =L= 0;
e82.. 0.1*x106 - 100*x139 =L= 0;
e83.. 0.1*x107 - 100*x140 =L= 0;
e84.. - 100*b1 + 0.1*x108 =L= 0;
e85.. - 100*b2 + 0.1*x109 =L= 0;
e86.. 0.1*x60 - 100*x140 =L= 0;
e87.. - 100*b1 + 0.1*x78 =L= 0;
e88.. - 100*b2 + 0.1*x79 =L= 0;
e89.. 0.1*x113 - 100*x139 =L= 0;
e90.. - 100*b3 + 0.1*x63 =L= 0;
e91.. - 100*b4 + 0.1*x64 =L= 0;
e92.. - b5 + 0.1*x65 =L= 0;
e93.. 0.1*x66 - 100*x141 =L= 0;
e94.. - 100*b6 + 0.1*x67 =L= 0;
e95.. - 100*b7 + 0.1*x68 =L= 0;
e96.. - 100*b8 + 0.1*x69 =L= 0;
e97.. - 100*b9 + 0.1*x70 =L= 0;
e98.. - 100*b10 + 0.1*x71 =L= 0;
e99.. - 100*b11 + 0.1*x72 =L= 0;
e100.. - 100*b12 + 0.1*x73 =L= 0;
e101.. - 100*b13 + 0.1*x74 =L= 0;
e102.. - 100*b14 + 0.1*x75 =L= 0;
e103.. - 100*b3 + 0.1*x80 =L= 0;
e104.. - 100*b4 + 0.1*x81 =L= 0;
e105.. - 100*b5 + 0.1*x82 =L= 0;
e106.. - 100*b6 + 0.1*x83 =L= 0;
e107.. - 100*b7 + 0.1*x84 =L= 0;
e108.. - 100*b8 + 0.1*x85 =L= 0;
e109.. - 100*b9 + 0.1*x86 =L= 0;
e110.. - 100*b10 + 0.1*x87 =L= 0;
e111.. - 100*b11 + 0.1*x88 =L= 0;
e112.. - 100*b12 + 0.1*x89 =L= 0;
e113.. - 100*b13 + 0.1*x90 =L= 0;
e114.. - 100*b14 + 0.1*x91 =L= 0;
e115.. 0.1*x118 - 100*x141 =L= 0;
e116.. 0.01*x114 - 163.03*x139 =E= 0;
e117.. 0.01*x115 - 56*x140 =E= 0;
e118.. - 444*b3 + x119 =E= 0;
e119.. - 100*b4 + x120 =E= 0;
e120.. - 125*b5 + x121 =E= 0;
e121.. 0.01*x122 - 94.5*x141 =E= 0;
e122.. - 75*b6 + x123 =E= 0;
e123.. - 60*b7 + x124 =E= 0;
e124.. - 36*b8 + x125 =E= 0;
e125.. - 26*b9 + x126 =E= 0;
e126.. - 445*b10 + x127 =E= 0;
e127.. - 444*b15 + x30 =E= 0;
e128.. - 100*b16 + x31 =E= 0;
e129.. - 125*b17 + x32 =E= 0;
e130.. - 75*b18 + x33 =E= 0;
e131.. - 60*b19 + x34 =E= 0;
e132.. - 36*b20 + x35 =E= 0;
e133.. - 26*b21 + x36 =E= 0;
e134.. - 445*b22 + x37 =E= 0;
e135.. - 300*b1 + 0.01*x116 =L= 0;
e136.. - 300*b2 + 0.01*x117 =L= 0;
e137.. - 300*b11 + 0.01*x128 =L= 0;
e138.. - 300*b12 + 0.01*x129 =L= 0;
e139.. - 300*b13 + 0.01*x130 =L= 0;
e140.. - 300*b14 + 0.01*x131 =L= 0;
e141.. - 300*b23 + 0.01*x38 =L= 0;
e142.. - 300*b24 + 0.01*x39 =L= 0;
e143.. - 300*b25 + 0.01*x40 =L= 0;
e144.. - 300*b26 + 0.01*x41 =L= 0;
e145.. - 300*b27 + 0.01*x42 =L= 0;
e146.. - 300*b28 + 0.01*x43 =L= 0;
e147.. x38 - x100 + x116 =E= 0;
e148.. x39 - x101 + x117 =E= 0;
e149.. x40 - x104 + x128 =E= 0;
e150.. x41 + x129 - x135 =E= 0;
e151.. x42 + x130 - x136 =E= 0;
e152.. x43 + x131 - x137 =E= 0;
e153.. b1 + b23 =E= 1;
e154.. b2 + b24 =E= 1;
e155.. b3 + b15 =E= 1;
e156.. b4 + b16 =E= 1;
e157.. b5 + b17 =E= 1;
e158.. b6 + b18 =E= 1;
e159.. b7 + b19 =E= 1;
e160.. b8 + b20 =E= 1;
e161.. b9 + b21 =E= 1;
e162.. b10 + b22 =E= 1;
e163.. b11 + b25 =E= 1;
e164.. b12 + b26 =E= 1;
e165.. b13 + b27 =E= 1;
e166.. b14 + b28 =E= 1;
e167.. b14 + b24 =E= 0;
e168.. - 87.3969*x29 - 0.03781*x30 - 0.03781*x31 - 0.03781*x32 - 0.03781*x33
- 0.03781*x34 - 0.03781*x35 - 0.03781*x36 - 0.03781*x37 - 0.03781*x38
- 0.03781*x39 - 0.03781*x40 - 0.03781*x41 - 0.03781*x42 - 0.03781*x43
- 0.3*x44 - 0.017*x45 + objvar =E= 0;
* set non-default bounds
x47.up = 29.2;
x48.up = 1.2;
x58.lo = 353.66;
x76.lo = 32.8;
x93.lo = 24.1;
x95.up = 21;
x97.lo = 1.2; x97.up = 2.2;
x105.up = 98.72;
x110.lo = 8.7;
* set non-default levels
x49.l = 215.581;
x53.l = 1.237;
x54.l = 109.57;
x59.l = 1.854;
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% minimizing objvar;
Last updated: 2024-12-17 Git hash: 8eaceb91