MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance waterno2_01
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 19.45668044 (ANTIGONE) 19.45667362 (BARON) 19.45668046 (COUENNE) 19.45667923 (LINDO) 19.45667979 (SCIP) 0. (SHOT) |
| Referencesⓘ | Huang, Wei, Operative Planning of Water Supply Networks by Mixed Integer Nonlinear Programming, Masters thesis, Freie Universität Berlin, 2011. Gleixner, Ambros, Held, Harald, Huang, Wei, and Vigerske, Stefan, Towards globally optimal operation of water supply networks, Numerical Algebra, Control and Optimization, 2:4, 2012, 695-711. |
| Applicationⓘ | Water Network Operation |
| Added to libraryⓘ | 12 Aug 2014 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 166 |
| #Binary Variablesⓘ | 9 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 42 |
| #Nonlinear Binary Variablesⓘ | 9 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 9 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 204 |
| #Linear Constraintsⓘ | 139 |
| #Quadratic Constraintsⓘ | 52 |
| #Polynomial Constraintsⓘ | 13 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 532 |
| #Nonlinear Nonzeros in Jacobianⓘ | 101 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 88 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 16 |
| #Blocks in Hessian of Lagrangianⓘ | 11 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
| Average blocksize in Hessian of Lagrangianⓘ | 3.818182 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.5000e-01 |
| Maximal coefficientⓘ | 3.6000e+03 |
| Infeasibility of initial pointⓘ | 3200 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 205 121 35 49 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 167 158 9 0 0 0 0 0
* FX 4
*
* Nonzero counts
* Total const NL DLL
* 542 441 101 0
*
* Solve m using MINLP minimizing objvar;
Variables objvar,b2,b3,b4,b5,b6,b7,b8,b9,b10,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,x133,x134,x135,x136,x137,x138,x139,x140,x141
,x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154
,x155,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167;
Positive Variables x33,x34,x35,x36,x37,x38,x39,x40,x41,x48,x50,x52,x54,x56
,x58,x60,x62,x64,x69,x71,x72,x74,x94,x99,x104,x109,x114,x119,x124
,x129,x134,x139,x140,x141,x142,x143,x144,x145,x146,x147,x148,x149
,x150,x151,x152,x153,x154,x155,x156,x157,x158,x159;
Binary Variables b2,b3,b4,b5,b6,b7,b8,b9,b10;
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;
e1.. objvar - x94 - x99 - x104 - x109 - x114 - x119 - x124 - x129 - x134
=E= 0;
e2.. x49 + 27.42831624*x51 + 37.5407324*x53 - 57.2814121*x55 =E= 0;
e3.. - 57.2814121*x55 + x57 + 27.42831624*x59 + 37.5407324*x61 =E= 0;
e4.. 37.5407324*x11 - 57.2814121*x55 + x63 + 27.42831624*x65 =E= 0;
e5.. x12 + 50.37356589*x13 + 43.14087708*x14 - 76.45219958*x15 =E= 0;
e6.. - 76.45219958*x15 + x16 + 50.37356589*x17 + 43.14087708*x18 =E= 0;
e7.. x19 - 25.39911174*x20 + 58.31011875*x21 - 69.39622571*x22 =E= 0;
e8.. - 69.39622571*x22 + x23 - 25.39911174*x24 + 58.31011875*x25 =E= 0;
e9.. x26 + 63.61644904*x27 - 2.03724124*x28 - 34.92732674*x29 =E= 0;
e10.. - 34.92732674*x29 + x30 + 63.61644904*x31 - 2.03724124*x32 =E= 0;
e11.. x33 =G= 0.296666667;
e12.. - x34 + x35 =E= 0;
e13.. - x36 + x37 =E= 0;
e14.. x36 - x38 =E= 0;
e15.. - x39 + x40 =E= 0;
e16.. x41 =E= 0.296666667;
e17.. x33 - x35 =E= 0;
e18.. 3600*x34 - 3600*x37 + 1800*x42 - 1800*x43 =E= 0;
e19.. 3600*x38 - 3600*x40 + 720*x44 - 720*x45 =E= 0;
e20.. 3600*x39 - 3600*x41 + 1600*x46 - 1600*x47 =E= 0;
e21.. - 0.2*b2 + x48 =G= 0;
e22.. - 0.2*b3 + x50 =G= 0;
e23.. - 0.2*b4 + x52 =G= 0;
e24.. - 0.25*b5 + x54 =G= 0;
e25.. - 0.25*b6 + x56 =G= 0;
e26.. - 0.4*b7 + x58 =G= 0;
e27.. - 0.4*b8 + x60 =G= 0;
e28.. - 0.24*b9 + x62 =G= 0;
e29.. - 0.24*b10 + x64 =G= 0;
e30.. - 0.8*b2 + x48 =L= 0;
e31.. - 0.8*b3 + x50 =L= 0;
e32.. - 0.8*b4 + x52 =L= 0;
e33.. - 0.5*b5 + x54 =L= 0;
e34.. - 0.5*b6 + x56 =L= 0;
e35.. - 0.7*b7 + x58 =L= 0;
e36.. - 0.7*b8 + x60 =L= 0;
e37.. - 0.58*b9 + x62 =L= 0;
e38.. - 0.58*b10 + x64 =L= 0;
e39.. - x42 + x66 =E= 60;
e40.. - x44 + x67 =E= 90;
e41.. - x46 + x68 =E= 103;
e42.. - x66 + x69 - x70 =E= 0;
e43.. x71 - x72 - x73 =E= 0;
e44.. - x68 + x74 - x75 =E= 0;
e45.. x69 - x76 - x77 =E= 0;
e46.. - x66 + x71 - x78 =E= 0;
e47.. - x67 + x74 - x79 =E= 0;
e48.. 0.2*b2 - x48 + x80 =L= 0.2;
e49.. 0.2*b3 - x50 + x81 =L= 0.2;
e50.. 0.2*b4 - x52 + x82 =L= 0.2;
e51.. 0.25*b5 - x54 + x83 =L= 0.25;
e52.. 0.25*b6 - x56 + x84 =L= 0.25;
e53.. 0.4*b7 - x58 + x85 =L= 0.4;
e54.. 0.4*b8 - x60 + x86 =L= 0.4;
e55.. 0.24*b9 - x62 + x87 =L= 0.24;
e56.. 0.24*b10 - x64 + x88 =L= 0.24;
e57.. - x48 + x80 =G= 0;
e58.. - x50 + x81 =G= 0;
e59.. - x52 + x82 =G= 0;
e60.. - x54 + x83 =G= 0;
e61.. - x56 + x84 =G= 0;
e62.. - x58 + x85 =G= 0;
e63.. - x60 + x86 =G= 0;
e64.. - x62 + x87 =G= 0;
e65.. - x64 + x88 =G= 0;
e66.. - 0.6*b2 + x80 =L= 0.2;
e67.. - 0.6*b3 + x81 =L= 0.2;
e68.. - 0.6*b4 + x82 =L= 0.2;
e69.. - 0.25*b5 + x83 =L= 0.25;
e70.. - 0.25*b6 + x84 =L= 0.25;
e71.. - 0.3*b7 + x85 =L= 0.4;
e72.. - 0.3*b8 + x86 =L= 0.4;
e73.. - 0.34*b9 + x87 =L= 0.24;
e74.. - 0.34*b10 + x88 =L= 0.24;
e75.. - 0.4*b2 + x89 =L= 0.6;
e76.. - 0.2*b5 + x90 =L= 0.8;
e77.. - 0.15*b7 + x91 =L= 0.85;
e78.. - 0.3*b9 + x92 =L= 0.7;
e79.. b2 - b3 =G= 0;
e80.. b3 - b4 =G= 0;
e81.. b5 - b6 =G= 0;
e82.. b7 - b8 =G= 0;
e83.. b9 - b10 =G= 0;
e84.. x35 - x48 - x50 - x52 =E= 0;
e85.. x37 - x54 - x56 - x58 - x60 =E= 0;
e86.. x40 - x62 - x64 =E= 0;
e87.. - 2000*b2 + x49 - x77 =G= -2000;
e88.. - 2000*b3 + x57 - x77 =G= -2000;
e89.. - 2000*b4 + x63 - x77 =G= -2000;
e90.. - 2000*b5 + x12 - x78 =G= -2000;
e91.. - 2000*b6 + x16 - x78 =G= -2000;
e92.. - 2000*b7 + x19 - x78 =G= -2000;
e93.. - 2000*b8 + x23 - x78 =G= -2000;
e94.. - 2000*b9 + x26 - x79 =G= -2000;
e95.. - 2000*b10 + x30 - x79 =G= -2000;
e96.. 1049*b2 + x49 - x77 =L= 1049;
e97.. 1049*b3 + x57 - x77 =L= 1049;
e98.. 1049*b4 + x63 - x77 =L= 1049;
e99.. 1065*b5 + x12 - x78 =L= 1065;
e100.. 1065*b6 + x16 - x78 =L= 1065;
e101.. 1065*b7 + x19 - x78 =L= 1065;
e102.. 1065*b8 + x23 - x78 =L= 1065;
e103.. 1095*b9 + x26 - x79 =L= 1095;
e104.. 1095*b10 + x30 - x79 =L= 1095;
e105.. - x67 + x72 =G= 0;
e106.. x68 - x93 =G= 0;
e107.. - 0.309838295393634*x94 + 13.94696158*x95 + 24.46510819*x96
- 7.28623839*x97 - 23.57687014*x98 =L= 0;
e108.. - 0.309838295393634*x99 + 13.94696158*x100 + 24.46510819*x101
- 7.28623839*x102 - 23.57687014*x103 =L= 0;
e109.. - 0.309838295393634*x104 + 13.94696158*x105 + 24.46510819*x106
- 7.28623839*x107 - 23.57687014*x108 =L= 0;
e110.. - 0.309838295393634*x109 + 29.29404529*x110 - 108.39408287*x111
+ 442.21990639*x112 - 454.58448169*x113 =L= 0;
e111.. - 0.309838295393634*x114 + 29.29404529*x115 - 108.39408287*x116
+ 442.21990639*x117 - 454.58448169*x118 =L= 0;
e112.. - 0.309838295393634*x119 + 25.92674585*x120 + 18.13482123*x121
+ 22.12766012*x122 - 42.68950769*x123 =L= 0;
e113.. - 0.309838295393634*x124 + 25.92674585*x125 + 18.13482123*x126
+ 22.12766012*x127 - 42.68950769*x128 =L= 0;
e114.. - 0.309838295393634*x129 + 17.4714791*x130 - 39.98407808*x131
+ 134.55943082*x132 - 135.88441782*x133 =L= 0;
e115.. - 0.309838295393634*x134 + 17.4714791*x135 - 39.98407808*x136
+ 134.55943082*x137 - 135.88441782*x138 =L= 0;
e116.. sqr(x34) - x139 =E= 0;
e117.. x70 - 5*x139 =E= 0;
e118.. sqr(x36) - x140 =E= 0;
e119.. x73 - 4*x140 =E= 0;
e120.. sqr(x39) - x141 =E= 0;
e121.. x75 - 5*x141 =E= 0;
e122.. sqr(x48) - x142 =E= 0;
e123.. x51 - x142 =E= 0;
e124.. POWER(x48,3) - x143 =E= 0;
e125.. x98 - x143 =E= 0;
e126.. sqr(x50) - x144 =E= 0;
e127.. x59 - x144 =E= 0;
e128.. POWER(x50,3) - x145 =E= 0;
e129.. x103 - x145 =E= 0;
e130.. sqr(x52) - x146 =E= 0;
e131.. x65 - x146 =E= 0;
e132.. POWER(x52,3) - x147 =E= 0;
e133.. x108 - x147 =E= 0;
e134.. sqr(x54) - x148 =E= 0;
e135.. x13 - x148 =E= 0;
e136.. POWER(x54,3) - x149 =E= 0;
e137.. x113 - x149 =E= 0;
e138.. sqr(x56) - x150 =E= 0;
e139.. x17 - x150 =E= 0;
e140.. POWER(x56,3) - x151 =E= 0;
e141.. x118 - x151 =E= 0;
e142.. sqr(x58) - x152 =E= 0;
e143.. x20 - x152 =E= 0;
e144.. POWER(x58,3) - x153 =E= 0;
e145.. x123 - x153 =E= 0;
e146.. sqr(x60) - x154 =E= 0;
e147.. x24 - x154 =E= 0;
e148.. POWER(x60,3) - x155 =E= 0;
e149.. x128 - x155 =E= 0;
e150.. sqr(x62) - x156 =E= 0;
e151.. x27 - x156 =E= 0;
e152.. POWER(x62,3) - x157 =E= 0;
e153.. x133 - x157 =E= 0;
e154.. sqr(x64) - x158 =E= 0;
e155.. x31 - x158 =E= 0;
e156.. POWER(x64,3) - x159 =E= 0;
e157.. x138 - x159 =E= 0;
e158.. x48*x89 - x53 =E= 0;
e159.. x89*x142 - x97 =E= 0;
e160.. x50*x89 - x61 =E= 0;
e161.. x89*x144 - x102 =E= 0;
e162.. x52*x89 - x11 =E= 0;
e163.. x89*x146 - x107 =E= 0;
e164.. sqr(x89) - x160 =E= 0;
e165.. x55 - x160 =E= 0;
e166.. x48*x160 - x96 =E= 0;
e167.. x50*x160 - x101 =E= 0;
e168.. x52*x160 - x106 =E= 0;
e169.. POWER(x89,3) - x161 =E= 0;
e170.. b2*x161 - x95 =E= 0;
e171.. b3*x161 - x100 =E= 0;
e172.. b4*x161 - x105 =E= 0;
e173.. x54*x90 - x14 =E= 0;
e174.. x90*x148 - x112 =E= 0;
e175.. x56*x90 - x18 =E= 0;
e176.. x90*x150 - x117 =E= 0;
e177.. sqr(x90) - x162 =E= 0;
e178.. x15 - x162 =E= 0;
e179.. x54*x162 - x111 =E= 0;
e180.. x56*x162 - x116 =E= 0;
e181.. POWER(x90,3) - x163 =E= 0;
e182.. b5*x163 - x110 =E= 0;
e183.. b6*x163 - x115 =E= 0;
e184.. x58*x91 - x21 =E= 0;
e185.. x91*x152 - x122 =E= 0;
e186.. x60*x91 - x25 =E= 0;
e187.. x91*x154 - x127 =E= 0;
e188.. sqr(x91) - x164 =E= 0;
e189.. x22 - x164 =E= 0;
e190.. x58*x164 - x121 =E= 0;
e191.. x60*x164 - x126 =E= 0;
e192.. POWER(x91,3) - x165 =E= 0;
e193.. b7*x165 - x120 =E= 0;
e194.. b8*x165 - x125 =E= 0;
e195.. x62*x92 - x28 =E= 0;
e196.. x92*x156 - x132 =E= 0;
e197.. x64*x92 - x32 =E= 0;
e198.. x92*x158 - x137 =E= 0;
e199.. sqr(x92) - x166 =E= 0;
e200.. x29 - x166 =E= 0;
e201.. x62*x166 - x131 =E= 0;
e202.. x64*x166 - x136 =E= 0;
e203.. POWER(x92,3) - x167 =E= 0;
e204.. b9*x167 - x130 =E= 0;
e205.. b10*x167 - x135 =E= 0;
* set non-default bounds
x12.lo = -1000; x12.up = 1000;
x16.lo = -1000; x16.up = 1000;
x19.lo = -1000; x19.up = 1000;
x23.lo = -1000; x23.up = 1000;
x26.lo = -1000; x26.up = 1000;
x30.lo = -1000; x30.up = 1000;
x33.up = 5;
x34.up = 5;
x35.up = 2.4;
x36.up = 5;
x37.up = 2.4;
x38.up = 5;
x39.up = 5;
x40.up = 1.16;
x41.up = 5;
x42.fx = 3.5;
x43.lo = 2; x43.up = 5;
x44.fx = 4.1;
x45.lo = 2.5; x45.up = 5;
x46.fx = 4;
x47.lo = 2; x47.up = 6;
x48.up = 0.8;
x49.lo = -1000; x49.up = 1000;
x50.up = 0.8;
x52.up = 0.8;
x54.up = 0.5;
x56.up = 0.5;
x57.lo = -1000; x57.up = 1000;
x58.up = 0.7;
x60.up = 0.7;
x62.up = 0.58;
x63.lo = -1000; x63.up = 1000;
x64.up = 0.58;
x66.lo = 62; x66.up = 65;
x67.lo = 92.5; x67.up = 95;
x68.lo = 105; x68.up = 109;
x69.up = 1000;
x70.lo = -125; x70.up = 125;
x71.up = 1000;
x72.up = 1000;
x73.lo = -100; x73.up = 100;
x74.up = 1000;
x75.lo = -125; x75.up = 125;
x76.fx = 49;
x77.lo = -49; x77.up = 1000;
x78.lo = -65; x78.up = 1000;
x79.lo = -95; x79.up = 1000;
x80.lo = 0.2; x80.up = 0.8;
x81.lo = 0.2; x81.up = 0.8;
x82.lo = 0.2; x82.up = 0.8;
x83.lo = 0.25; x83.up = 0.5;
x84.lo = 0.25; x84.up = 0.5;
x85.lo = 0.4; x85.up = 0.7;
x86.lo = 0.4; x86.up = 0.7;
x87.lo = 0.24; x87.up = 0.58;
x88.lo = 0.24; x88.up = 0.58;
x89.lo = 0.6; x89.up = 1;
x90.lo = 0.8; x90.up = 1;
x91.lo = 0.85; x91.up = 1;
x92.lo = 0.7; x92.up = 1;
x93.lo = 100; x93.up = 1000;
x94.up = 54.1717996137183;
x99.up = 54.1717996137183;
x104.up = 54.1717996137183;
x109.up = 93.045051789432;
x114.up = 93.045051789432;
x119.up = 112.384987749469;
x124.up = 112.384987749469;
x129.up = 42.066542469172;
x134.up = 42.066542469172;
x139.up = 25;
x140.up = 25;
x141.up = 25;
x142.up = 0.64;
x143.up = 0.512;
x144.up = 0.64;
x145.up = 0.512;
x146.up = 0.64;
x147.up = 0.512;
x148.up = 0.25;
x149.up = 0.125;
x150.up = 0.25;
x151.up = 0.125;
x152.up = 0.49;
x153.up = 0.343;
x154.up = 0.49;
x155.up = 0.343;
x156.up = 0.3364;
x157.up = 0.195112;
x158.up = 0.3364;
x159.up = 0.195112;
x160.lo = 0.36; x160.up = 1;
x161.lo = 0.216; x161.up = 1;
x162.lo = 0.64; x162.up = 1;
x163.lo = 0.512; x163.up = 1;
x164.lo = 0.7225; x164.up = 1;
x165.lo = 0.614125; x165.up = 1;
x166.lo = 0.49; x166.up = 1;
x167.lo = 0.343; x167.up = 1;
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: 2026-09-14 Git hash: 9472b011