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)
999.57875020 p1 ( gdx sol )
(infeas: 2e-13)
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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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: 2022-08-11 Git hash: f176bd52
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