MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance wager
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 20339.43182000 (ANTIGONE) 20339.43182000 (BARON) 20339.43184000 (COUENNE) 15879.20271000 (LINDO) 20339.43184000 (SCIP) 13180.91374000 (SHOT) |
| Sourceⓘ | AIMMS clients |
| Added to libraryⓘ | 06 Feb 2017 |
| Problem typeⓘ | MINLP |
| #Variablesⓘ | 156 |
| #Binary Variablesⓘ | 30 |
| #Integer Variablesⓘ | 54 |
| #Nonlinear Variablesⓘ | 84 |
| #Nonlinear Binary Variablesⓘ | 30 |
| #Nonlinear Integer Variablesⓘ | 26 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 6 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 142 |
| #Linear Constraintsⓘ | 99 |
| #Quadratic Constraintsⓘ | 9 |
| #Polynomial Constraintsⓘ | 18 |
| #Signomial Constraintsⓘ | 10 |
| #General Nonlinear Constraintsⓘ | 6 |
| Operands in Gen. Nonlin. Functionsⓘ | div |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 526 |
| #Nonlinear Nonzeros in Jacobianⓘ | 240 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 664 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 36 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 84 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 84 |
| Average blocksize in Hessian of Lagrangianⓘ | 84.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 7.8663e-04 |
| Maximal coefficientⓘ | 1.0000e+06 |
| Infeasibility of initial pointⓘ | 1.211e+08 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 143 85 43 15 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 157 73 30 54 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 533 293 240 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,b29,b30,i31,i32,i33,i34,i35,i36
,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53
,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,i64,i65,i66,i67,i68,i69,i70
,i71,i72,i73,i74,i75,i76,i77,i78,i79,i80,i81,i82,i83,i84,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,x146,x147,x148,x149,x150,x151,x152,x153,x154,x155
,x156,objvar;
Positive Variables 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;
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,b29,b30;
Integer Variables i31,i32,i33,i34,i35,i36,i37,i38,i39,i40,i41,i42,i43,i44,i45
,i46,i47,i48,i49,i50,i51,i52,i53,i54,i55,i56,i57,i58,i59,i60,i61,i62
,i63,i64,i65,i66,i67,i68,i69,i70,i71,i72,i73,i74,i75,i76,i77,i78,i79
,i80,i81,i82,i83,i84;
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;
e1.. b2 + b8 + b14 =E= 1;
e2.. b3 + b9 + b15 =E= 1;
e3.. b4 + b10 + b16 =E= 1;
e4.. b5 + b11 + b17 =E= 1;
e5.. b6 + b12 + b18 =E= 1;
e6.. b25 + b28 =E= 1;
e7.. b26 + b29 =E= 1;
e8.. b27 + b30 =E= 1;
e9.. b19 + b22 =E= 1;
e10.. b20 + b23 =E= 1;
e11.. b21 + b24 =E= 1;
e12.. -1.11111111111111*x91*(2025*b1 + 4420*b7 + 7050*b13)/i48 + x151 =E= -2100
;
e13.. -1.11111111111111*x92*(2025*b2 + 4420*b8 + 7050*b14)/i49 + x152 =E= -2100
;
e14.. -1.11111111111111*x93*(2025*b3 + 4420*b9 + 7050*b15)/i50 + x153 =E= -2100
;
e15.. -1.11111111111111*x94*(2025*b4 + 4420*b10 + 7050*b16)/i52 + x154
=E= -2100;
e16.. -1.11111111111111*x95*(2025*b5 + 4420*b11 + 7050*b17)/i53 + x155
=E= -2100;
e17.. -1.11111111111111*x96*(2025*b6 + 4420*b12 + 7050*b18)/i54 + x156
=E= -2100;
e18.. -(480*b25 + 360*b28)*(1 + 0.1*b1 + 0.1*b7 + 0.1*b13)*(1 + x85) + x91
=E= 0;
e19.. -(480*b26 + 360*b29)*(1 + 0.1*b2 + 0.1*b8 + 0.1*b14)*(1 + x86) + x92
=E= 0;
e20.. -(480*b27 + 360*b30)*(1 + 0.1*b3 + 0.1*b9 + 0.1*b15)*(1 + x87) + x93
=E= 0;
e21.. -(450*b19 + 400*b22)*(1 + 0.1*b4 + 0.1*b10 + 0.1*b16)*(1 + x88) + x94
=E= 0;
e22.. -(450*b20 + 400*b23)*(1 + 0.1*b5 + 0.1*b11 + 0.1*b17)*(1 + x89) + x95
=E= 0;
e23.. -(450*b21 + 400*b24)*(1 + 0.1*b6 + 0.1*b12 + 0.1*b18)*(1 + x90) + x96
=E= 0;
e24.. x121 - x151 =E= 0;
e25.. (-x121*i48/i49) - (x121*i56 + x124*i62)/i49 + (x121*i56 + x121*i59)/i49
+ x122 - x152 =E= 0;
e26.. (-x122*i49/i50) - (x122*i57 + x125*i63)/i50 + (x122*i57 + x122*i60)/i50
+ x123 - x153 =E= 0;
e27.. x124 - x154 =E= 0;
e28.. (-x124*i52/i53) - (x121*i59 + x124*i65)/i53 + (x124*i62 + x124*i65)/i53
+ x125 - x155 =E= 0;
e29.. (-x125*i53/i54) - (x122*i60 + x125*i66)/i54 + (x125*i63 + x125*i66)/i54
+ x126 - x156 =E= 0;
e30.. i31 =E= 1100;
e31.. - i31 + i32 + i58 - i61 - i73 =E= 0;
e32.. - i32 + i33 + i59 - i62 - i74 =E= 0;
e33.. - i33 + i34 + i60 - i63 - i75 =E= 0;
e34.. i35 =E= 2200;
e35.. - i35 + i36 - i58 + i61 - i76 =E= 0;
e36.. - i36 + i37 - i59 + i62 - i77 =E= 0;
e37.. - i37 + i38 - i60 + i63 - i78 =E= 0;
e38.. i39 =E= 150;
e39.. - i39 + i40 - i79 =E= 0;
e40.. - i40 + i41 - i80 =E= 0;
e41.. - i41 + i42 - i81 =E= 0;
e42.. i43 =E= 100;
e43.. - i43 + i44 - i82 =E= 0;
e44.. - i44 + i45 - i83 =E= 0;
e45.. - i45 + i46 - i84 =E= 0;
e46.. - i31 - i39 + i47 =E= 0;
e47.. - i32 - i40 + i48 =E= 0;
e48.. - i33 - i41 + i49 =E= 0;
e49.. - i34 - i42 + i50 =E= 0;
e50.. - i35 - i43 + i51 =E= 0;
e51.. - i36 - i44 + i52 =E= 0;
e52.. - i37 - i45 + i53 =E= 0;
e53.. - i38 - i46 + i54 =E= 0;
e54.. (-1.11111111111*x91*b1) - 2.22222222222*x91*b7 - 3.33333333333*x91*b13
+ i48 =G= 0;
e55.. (-1.11111111111*x92*b2) - 2.22222222222*x92*b8 - 3.33333333333*x92*b14
+ i49 =G= 0;
e56.. (-1.11111111111*x93*b3) - 2.22222222222*x93*b9 - 3.33333333333*x93*b15
+ i50 =G= 0;
e57.. (-1.11111111111*x94*b4) - 2.22222222222*x94*b10 - 3.33333333333*x94*b16
+ i52 =G= 0;
e58.. (-1.11111111111*x95*b5) - 2.22222222222*x95*b11 - 3.33333333333*x95*b17
+ i53 =G= 0;
e59.. (-1.11111111111*x96*b6) - 2.22222222222*x96*b12 - 3.33333333333*x96*b18
+ i54 =G= 0;
e60.. i73 =G= 0;
e61.. i74 =G= 0;
e62.. i75 =G= 0;
e63.. i76 =G= 0;
e64.. i77 =G= 0;
e65.. i78 =G= 0;
e66.. - i73 + x115 =G= 0;
e67.. - i74 + x116 =G= 0;
e68.. - i75 + x117 =G= 0;
e69.. - i76 + x118 =G= 0;
e70.. - i77 + x119 =G= 0;
e71.. - i78 + x120 =G= 0;
e72.. - i79 + x109 =G= 0;
e73.. - i80 + x110 =G= 0;
e74.. - i81 + x111 =G= 0;
e75.. - i82 + x112 =G= 0;
e76.. - i83 + x113 =G= 0;
e77.. - i84 + x114 =G= 0;
e78.. - x109 - x112 - x115 - x118 =G= -100;
e79.. - x110 - x113 - x116 - x119 =G= -100;
e80.. - x111 - x114 - x117 - x120 =G= -100;
e81.. i40 - 0.2*i48 =L= 0;
e82.. i41 - 0.2*i49 =L= 0;
e83.. i42 - 0.2*i50 =L= 0;
e84.. i44 - 0.2*i52 =L= 0;
e85.. i45 - 0.2*i53 =L= 0;
e86.. i46 - 0.2*i54 =L= 0;
e87.. i55 =E= 0;
e88.. i56 =E= 0;
e89.. i57 =E= 0;
e90.. i64 =E= 0;
e91.. i65 =E= 0;
e92.. i66 =E= 0;
e93.. i67 + i70 =L= 2739;
e94.. i68 + i71 =L= 2739;
e95.. i69 + i72 =L= 2607;
e96.. i67 + i70 =G= 2241;
e97.. i68 + i71 =G= 2241;
e98.. i69 + i72 =G= 2133;
e99.. i67 + i68 + i69 + i70 + i71 + i72 =G= 7350;
e100.. -(1950*b1 + 4200*b7 + 6600*b13)/(4*b25 + 7*b28) + i67 =L= 0;
e101.. -(1950*b2 + 4200*b8 + 6600*b14)/(4*b26 + 7*b29) + i68 =L= 0;
e102.. -(1950*b3 + 4200*b9 + 6600*b15)/(4*b27 + 7*b30) + i69 =L= 0;
e103.. -(1950*b4 + 4200*b10 + 6600*b16)/(5*b19 + 6*b22) + i70 =L= 0;
e104.. -(1950*b5 + 4200*b11 + 6600*b17)/(5*b20 + 6*b23) + i71 =L= 0;
e105.. -(1950*b6 + 4200*b12 + 6600*b18)/(5*b21 + 6*b24) + i72 =L= 0;
e106.. sqr(b1 - b2 + 2*b7 - 2*b8 + 3*b13 - 3*b14)*x97 - 10000*sqr(b1 - b2 + 2*
b7 - 2*b8 + 3*b13 - 3*b14) =G= 0;
e107.. sqr(b2 - b3 + 2*b8 - 2*b9 + 3*b14 - 3*b15)*x98 - 10000*sqr(b2 - b3 + 2*
b8 - 2*b9 + 3*b14 - 3*b15) =G= 0;
e108.. sqr(b3 + 2*b9 + 3*b15)*x99 - 10000*sqr(b3 + 2*b9 + 3*b15) =G= 0;
e109.. sqr(b4 - b5 + 2*b10 - 2*b11 + 3*b16 - 3*b17)*x100 - 10000*sqr(b4 - b5 +
2*b10 - 2*b11 + 3*b16 - 3*b17) =G= 0;
e110.. sqr(b5 - b6 + 2*b11 - 2*b12 + 3*b17 - 3*b18)*x101 - 10000*sqr(b5 - b6 +
2*b11 - 2*b12 + 3*b17 - 3*b18) =G= 0;
e111.. sqr(b6 + 2*b12 + 3*b18)*x102 - 10000*sqr(b6 + 2*b12 + 3*b18) =G= 0;
e112.. sqr(4*b25 - 4*b26 + 7*b28 - 7*b29)*x103 - sqr(4*b25 - 4*b26 + 7*b28 - 7*
b29)*(1000000 + 1000*i48) =G= 0;
e113.. sqr(4*b26 - 4*b27 + 7*b29 - 7*b30)*x104 - sqr(4*b26 - 4*b27 + 7*b29 - 7*
b30)*(1000000 + 1000*i49) =G= 0;
e114.. sqr(4*b27 + 7*b30)*x105 - sqr(4*b27 + 7*b30)*(1000000 + 1000*i50) =G= 0;
e115.. sqr(5*b19 - 5*b20 + 6*b22 - 6*b23)*x106 - sqr(5*b19 - 5*b20 + 6*b22 - 6*
b23)*(1000000 + 1000*i52) =G= 0;
e116.. sqr(5*b20 - 5*b21 + 6*b23 - 6*b24)*x107 - sqr(5*b20 - 5*b21 + 6*b23 - 6*
b24)*(1000000 + 1000*i53) =G= 0;
e117.. sqr(5*b21 + 6*b24)*x108 - sqr(5*b21 + 6*b24)*(1000000 + 1000*i54) =G= 0;
e118.. x145 =E= 0;
e119.. x146 =E= 0;
e120.. x147 =E= 0;
e121.. x148 =E= 0;
e122.. x149 =E= 0;
e123.. x150 =E= 0;
e124.. x139 =E= 0;
e125.. x140 =E= 0;
e126.. x141 =E= 0;
e127.. x142 =E= 0;
e128.. x143 =E= 0;
e129.. x144 =E= 0;
e130.. - 1000*i55 - 1000*i61 + x133 =E= 0;
e131.. - 1000*i56 - 1000*i62 + x134 =E= 0;
e132.. - 1000*i57 - 1000*i63 + x135 =E= 0;
e133.. - 1000*i58 - 1000*i64 + x136 =E= 0;
e134.. - 1000*i59 - 1000*i65 + x137 =E= 0;
e135.. - 1000*i60 - 1000*i66 + x138 =E= 0;
e136.. - x97 - x100 - x103 - x106 + x130 - x133 - x136 - x139 - x142 - x145
- x148 =E= 0;
e137.. - x98 - x101 - x104 - x107 + x131 - x134 - x137 - x140 - x143 - x146
- x149 =E= 0;
e138.. - x99 - x102 - x105 - x108 + x132 - x135 - x138 - x141 - x144 - x147
- x150 =E= 0;
e139.. (-315*i40*b7) - 2100*i40 - 420*i40*b13 - 315*i44*b10 - 2100*i44 - 420*
i44*b16 - 210*i32*b7 - 1400*i32 - 280*i32*b13 - 210*i36*b10 - 1400*i36
- 280*i36*b16 + x127 =E= 0;
e140.. (-315*i41*b8) - 2100*i41 - 420*i41*b14 - 315*i45*b11 - 2100*i45 - 420*
i45*b17 - 210*i33*b8 - 1400*i33 - 280*i33*b14 - 210*i37*b11 - 1400*i37
- 280*i37*b17 + x128 =E= 0;
e141.. (-315*i42*b9) - 2100*i42 - 420*i42*b15 - 315*i46*b12 - 2100*i46 - 420*
i46*b18 - 210*i34*b9 - 1400*i34 - 280*i34*b15 - 210*i38*b12 - 1400*i38
- 280*i38*b18 + x129 =E= 0;
e142.. b1 + b7 + b13 =E= 1;
e143.. - 0.0009231163463866*x127 - 0.0008521437889662*x128
- 0.0007866278610666*x129 - 0.0009231163463866*x130
- 0.0008521437889662*x131 - 0.0007866278610666*x132 + objvar =E= 0;
* set non-default bounds
i31.up = 2147483647;
i32.up = 2147483647;
i33.up = 2147483647;
i34.up = 2147483647;
i35.up = 2147483647;
i36.up = 2147483647;
i37.up = 2147483647;
i38.up = 2147483647;
i39.up = 2147483647;
i40.up = 2147483647;
i41.up = 2147483647;
i42.up = 2147483647;
i43.up = 2147483647;
i44.up = 2147483647;
i45.up = 2147483647;
i46.up = 2147483647;
i47.lo = 1;
i48.lo = 1;
i49.lo = 1;
i50.lo = 1;
i51.lo = 1;
i52.lo = 1;
i53.lo = 1;
i54.lo = 1;
i67.up = 2147483647;
i68.up = 2147483647;
i69.up = 2147483647;
i70.up = 2147483647;
i71.up = 2147483647;
i72.up = 2147483647;
x121.lo = -12000; x121.up = 12000;
x122.lo = -12000; x122.up = 12000;
x123.lo = -12000; x123.up = 12000;
x124.lo = -12000; x124.up = 12000;
x125.lo = -12000; x125.up = 12000;
x126.lo = -12000; x126.up = 12000;
* set non-default levels
b19.l = 1;
b20.l = 1;
b21.l = 1;
b22.l = 1;
b23.l = 1;
b24.l = 1;
b25.l = 1;
b26.l = 1;
b27.l = 1;
b28.l = 1;
b29.l = 1;
b30.l = 1;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if gamsversion 242 option intvarup = 0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc