MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance waterno2_02
| Formatsⓘ | ams gms mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 39.57141794 (ANTIGONE) 39.57132962 (BARON) 39.57142150 (COUENNE) 39.57140768 (LINDO) 39.57142193 (SCIP) 0.00000000 (SHOT) |
| Referencesⓘ | Huang, Wei, Operative Planning of Water Supply Networks by Mixed Integer Nonlinear Programming, Masters thesis, Freie Universität Berlin, 2011. Gleixner, Ambros M, 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ⓘ | 332 |
| #Binary Variablesⓘ | 18 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 84 |
| #Nonlinear Binary Variablesⓘ | 18 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 18 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 410 |
| #Linear Constraintsⓘ | 280 |
| #Quadratic Constraintsⓘ | 104 |
| #Polynomial Constraintsⓘ | 26 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 1070 |
| #Nonlinear Nonzeros in Jacobianⓘ | 202 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 176 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 32 |
| #Blocks in Hessian of Lagrangianⓘ | 22 |
| 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
* 411 244 69 98 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 333 315 18 0 0 0 0 0
* FX 5
*
* Nonzero counts
* Total const NL DLL
* 1089 887 202 0
*
* Solve m using MINLP minimizing objvar;
Variables objvar,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18
,b19,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
,x168,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180
,x181,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192,x193
,x194,x195,x196,x197,x198,x199,x200,x201,x202,x203,x204,x205,x206
,x207,x208,x209,x210,x211,x212,x213,x214,x215,x216,x217,x218,x219
,x220,x221,x222,x223,x224,x225,x226,x227,x228,x229,x230,x231,x232
,x233,x234,x235,x236,x237,x238,x239,x240,x241,x242,x243,x244,x245
,x246,x247,x248,x249,x250,x251,x252,x253,x254,x255,x256,x257,x258
,x259,x260,x261,x262,x263,x264,x265,x266,x267,x268,x269,x270,x271
,x272,x273,x274,x275,x276,x277,x278,x279,x280,x281,x282,x283,x284
,x285,x286,x287,x288,x289,x290,x291,x292,x293,x294,x295,x296,x297
,x298,x299,x300,x301,x302,x303,x304,x305,x306,x307,x308,x309,x310
,x311,x312,x313,x314,x315,x316,x317,x318,x319,x320,x321,x322,x323
,x324,x325,x326,x327,x328,x329,x330,x331,x332,x333;
Positive Variables x64,x65,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77
,x78,x79,x80,x81,x94,x96,x98,x100,x102,x104,x106,x108,x110,x112,x114
,x116,x118,x120,x122,x124,x126,x128,x136,x138,x140,x141,x143,x144
,x146,x148,x188,x195,x196,x202,x206,x211,x216,x221,x226,x231,x236
,x241,x246,x251,x256,x261,x266,x272,x276,x277,x278,x279,x280,x281
,x282,x283,x284,x285,x286,x287,x288,x289,x290,x291,x292,x293,x294
,x295,x296,x297,x298,x299,x300,x301,x302,x303,x304,x305,x306,x307
,x308,x309,x310,x311,x312,x313,x314,x315,x316,x317;
Binary Variables b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18
,b19;
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,e206,e207
,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284,e285
,e286,e287,e288,e289,e290,e291,e292,e293,e294,e295,e296,e297,e298
,e299,e300,e301,e302,e303,e304,e305,e306,e307,e308,e309,e310,e311
,e312,e313,e314,e315,e316,e317,e318,e319,e320,e321,e322,e323,e324
,e325,e326,e327,e328,e329,e330,e331,e332,e333,e334,e335,e336,e337
,e338,e339,e340,e341,e342,e343,e344,e345,e346,e347,e348,e349,e350
,e351,e352,e353,e354,e355,e356,e357,e358,e359,e360,e361,e362,e363
,e364,e365,e366,e367,e368,e369,e370,e371,e372,e373,e374,e375,e376
,e377,e378,e379,e380,e381,e382,e383,e384,e385,e386,e387,e388,e389
,e390,e391,e392,e393,e394,e395,e396,e397,e398,e399,e400,e401,e402
,e403,e404,e405,e406,e407,e408,e409,e410,e411;
e1.. objvar - x188 - x195 - x196 - x202 - x206 - x211 - x216 - x221 - x226
- x231 - x236 - x241 - x246 - x251 - x256 - x261 - x266 - x272 =E= 0;
e2.. x95 + 27.42831624*x97 - 57.2814121*x99 + 37.5407324*x101 =E= 0;
e3.. x103 + 37.5407324*x105 + 27.42831624*x107 - 57.2814121*x109 =E= 0;
e4.. - 57.2814121*x99 + x111 + 27.42831624*x113 + 37.5407324*x115 =E= 0;
e5.. - 57.2814121*x109 + x117 + 37.5407324*x119 + 27.42831624*x121 =E= 0;
e6.. - 57.2814121*x99 + x123 + 27.42831624*x125 + 37.5407324*x127 =E= 0;
e7.. 27.42831624*x20 + 37.5407324*x21 - 57.2814121*x109 + x129 =E= 0;
e8.. x22 - 76.45219958*x23 + 43.14087708*x24 + 50.37356589*x25 =E= 0;
e9.. x26 + 43.14087708*x27 - 76.45219958*x28 + 50.37356589*x29 =E= 0;
e10.. - 76.45219958*x23 + x30 + 50.37356589*x31 + 43.14087708*x32 =E= 0;
e11.. - 76.45219958*x28 + x33 + 50.37356589*x34 + 43.14087708*x35 =E= 0;
e12.. x36 - 69.39622571*x37 + 58.31011875*x38 - 25.39911174*x39 =E= 0;
e13.. x40 - 25.39911174*x41 + 58.31011875*x42 - 69.39622571*x43 =E= 0;
e14.. - 69.39622571*x37 + x44 - 25.39911174*x45 + 58.31011875*x46 =E= 0;
e15.. - 69.39622571*x43 + x47 - 25.39911174*x48 + 58.31011875*x49 =E= 0;
e16.. x50 + 63.61644904*x51 - 34.92732674*x52 - 2.03724124*x53 =E= 0;
e17.. x54 - 34.92732674*x55 - 2.03724124*x56 + 63.61644904*x57 =E= 0;
e18.. - 34.92732674*x52 + x58 + 63.61644904*x59 - 2.03724124*x60 =E= 0;
e19.. - 34.92732674*x55 + x61 + 63.61644904*x62 - 2.03724124*x63 =E= 0;
e20.. x64 + x65 =G= 0.591111111;
e21.. - x66 + x67 =E= 0;
e22.. - x68 + x69 =E= 0;
e23.. - x70 + x71 =E= 0;
e24.. - x72 + x73 =E= 0;
e25.. x70 - x74 =E= 0;
e26.. x72 - x75 =E= 0;
e27.. - x76 + x77 =E= 0;
e28.. - x78 + x79 =E= 0;
e29.. x80 =E= 0.296666667;
e30.. x81 =E= 0.294444444;
e31.. x64 - x67 =E= 0;
e32.. x65 - x69 =E= 0;
e33.. 3600*x66 - 3600*x71 + 1800*x82 - 1800*x83 =E= 0;
e34.. 3600*x68 - 3600*x73 + 1800*x84 - 1800*x85 =E= 0;
e35.. 3600*x74 - 3600*x77 + 720*x86 - 720*x87 =E= 0;
e36.. 3600*x75 - 3600*x79 + 720*x88 - 720*x89 =E= 0;
e37.. 3600*x76 - 3600*x80 + 1600*x90 - 1600*x91 =E= 0;
e38.. 3600*x78 - 3600*x81 + 1600*x92 - 1600*x93 =E= 0;
e39.. - x83 + x84 =E= 0;
e40.. - x87 + x88 =E= 0;
e41.. - x91 + x92 =E= 0;
e42.. - 0.2*b2 + x94 =G= 0;
e43.. - 0.2*b3 + x96 =G= 0;
e44.. - 0.2*b4 + x98 =G= 0;
e45.. - 0.2*b5 + x100 =G= 0;
e46.. - 0.2*b6 + x102 =G= 0;
e47.. - 0.2*b7 + x104 =G= 0;
e48.. - 0.25*b8 + x106 =G= 0;
e49.. - 0.25*b9 + x108 =G= 0;
e50.. - 0.25*b10 + x110 =G= 0;
e51.. - 0.25*b11 + x112 =G= 0;
e52.. - 0.4*b12 + x114 =G= 0;
e53.. - 0.4*b13 + x116 =G= 0;
e54.. - 0.4*b14 + x118 =G= 0;
e55.. - 0.4*b15 + x120 =G= 0;
e56.. - 0.24*b16 + x122 =G= 0;
e57.. - 0.24*b17 + x124 =G= 0;
e58.. - 0.24*b18 + x126 =G= 0;
e59.. - 0.24*b19 + x128 =G= 0;
e60.. - 0.8*b2 + x94 =L= 0;
e61.. - 0.8*b3 + x96 =L= 0;
e62.. - 0.8*b4 + x98 =L= 0;
e63.. - 0.8*b5 + x100 =L= 0;
e64.. - 0.8*b6 + x102 =L= 0;
e65.. - 0.8*b7 + x104 =L= 0;
e66.. - 0.5*b8 + x106 =L= 0;
e67.. - 0.5*b9 + x108 =L= 0;
e68.. - 0.5*b10 + x110 =L= 0;
e69.. - 0.5*b11 + x112 =L= 0;
e70.. - 0.7*b12 + x114 =L= 0;
e71.. - 0.7*b13 + x116 =L= 0;
e72.. - 0.7*b14 + x118 =L= 0;
e73.. - 0.7*b15 + x120 =L= 0;
e74.. - 0.58*b16 + x122 =L= 0;
e75.. - 0.58*b17 + x124 =L= 0;
e76.. - 0.58*b18 + x126 =L= 0;
e77.. - 0.58*b19 + x128 =L= 0;
e78.. - x82 + x130 =E= 60;
e79.. - x84 + x131 =E= 60;
e80.. - x86 + x132 =E= 90;
e81.. - x88 + x133 =E= 90;
e82.. - x90 + x134 =E= 103;
e83.. - x92 + x135 =E= 103;
e84.. - x130 + x136 - x137 =E= 0;
e85.. - x131 + x138 - x139 =E= 0;
e86.. x140 - x141 - x142 =E= 0;
e87.. x143 - x144 - x145 =E= 0;
e88.. - x134 + x146 - x147 =E= 0;
e89.. - x135 + x148 - x149 =E= 0;
e90.. x136 - x150 - x151 =E= 0;
e91.. x138 - x152 - x153 =E= 0;
e92.. - x130 + x140 - x154 =E= 0;
e93.. - x131 + x143 - x155 =E= 0;
e94.. - x132 + x146 - x156 =E= 0;
e95.. - x133 + x148 - x157 =E= 0;
e96.. 0.2*b2 - x94 + x158 =L= 0.2;
e97.. 0.2*b3 - x96 + x159 =L= 0.2;
e98.. 0.2*b4 - x98 + x160 =L= 0.2;
e99.. 0.2*b5 - x100 + x161 =L= 0.2;
e100.. 0.2*b6 - x102 + x162 =L= 0.2;
e101.. 0.2*b7 - x104 + x163 =L= 0.2;
e102.. 0.25*b8 - x106 + x164 =L= 0.25;
e103.. 0.25*b9 - x108 + x165 =L= 0.25;
e104.. 0.25*b10 - x110 + x166 =L= 0.25;
e105.. 0.25*b11 - x112 + x167 =L= 0.25;
e106.. 0.4*b12 - x114 + x168 =L= 0.4;
e107.. 0.4*b13 - x116 + x169 =L= 0.4;
e108.. 0.4*b14 - x118 + x170 =L= 0.4;
e109.. 0.4*b15 - x120 + x171 =L= 0.4;
e110.. 0.24*b16 - x122 + x172 =L= 0.24;
e111.. 0.24*b17 - x124 + x173 =L= 0.24;
e112.. 0.24*b18 - x126 + x174 =L= 0.24;
e113.. 0.24*b19 - x128 + x175 =L= 0.24;
e114.. - x94 + x158 =G= 0;
e115.. - x96 + x159 =G= 0;
e116.. - x98 + x160 =G= 0;
e117.. - x100 + x161 =G= 0;
e118.. - x102 + x162 =G= 0;
e119.. - x104 + x163 =G= 0;
e120.. - x106 + x164 =G= 0;
e121.. - x108 + x165 =G= 0;
e122.. - x110 + x166 =G= 0;
e123.. - x112 + x167 =G= 0;
e124.. - x114 + x168 =G= 0;
e125.. - x116 + x169 =G= 0;
e126.. - x118 + x170 =G= 0;
e127.. - x120 + x171 =G= 0;
e128.. - x122 + x172 =G= 0;
e129.. - x124 + x173 =G= 0;
e130.. - x126 + x174 =G= 0;
e131.. - x128 + x175 =G= 0;
e132.. - 0.6*b2 + x158 =L= 0.2;
e133.. - 0.6*b3 + x159 =L= 0.2;
e134.. - 0.6*b4 + x160 =L= 0.2;
e135.. - 0.6*b5 + x161 =L= 0.2;
e136.. - 0.6*b6 + x162 =L= 0.2;
e137.. - 0.6*b7 + x163 =L= 0.2;
e138.. - 0.25*b8 + x164 =L= 0.25;
e139.. - 0.25*b9 + x165 =L= 0.25;
e140.. - 0.25*b10 + x166 =L= 0.25;
e141.. - 0.25*b11 + x167 =L= 0.25;
e142.. - 0.3*b12 + x168 =L= 0.4;
e143.. - 0.3*b13 + x169 =L= 0.4;
e144.. - 0.3*b14 + x170 =L= 0.4;
e145.. - 0.3*b15 + x171 =L= 0.4;
e146.. - 0.34*b16 + x172 =L= 0.24;
e147.. - 0.34*b17 + x173 =L= 0.24;
e148.. - 0.34*b18 + x174 =L= 0.24;
e149.. - 0.34*b19 + x175 =L= 0.24;
e150.. - 0.4*b2 + x176 =L= 0.6;
e151.. - 0.4*b3 + x177 =L= 0.6;
e152.. - 0.2*b8 + x178 =L= 0.8;
e153.. - 0.2*b9 + x179 =L= 0.8;
e154.. - 0.15*b12 + x180 =L= 0.85;
e155.. - 0.15*b13 + x181 =L= 0.85;
e156.. - 0.3*b16 + x182 =L= 0.7;
e157.. - 0.3*b17 + x183 =L= 0.7;
e158.. b2 - b4 =G= 0;
e159.. b3 - b5 =G= 0;
e160.. b4 - b6 =G= 0;
e161.. b5 - b7 =G= 0;
e162.. b8 - b10 =G= 0;
e163.. b9 - b11 =G= 0;
e164.. b12 - b14 =G= 0;
e165.. b13 - b15 =G= 0;
e166.. b16 - b18 =G= 0;
e167.. b17 - b19 =G= 0;
e168.. x67 - x94 - x98 - x102 =E= 0;
e169.. x69 - x96 - x100 - x104 =E= 0;
e170.. x71 - x106 - x110 - x114 - x118 =E= 0;
e171.. x73 - x108 - x112 - x116 - x120 =E= 0;
e172.. x77 - x122 - x126 =E= 0;
e173.. x79 - x124 - x128 =E= 0;
e174.. - 2000*b2 + x95 - x151 =G= -2000;
e175.. - 2000*b3 + x103 - x153 =G= -2000;
e176.. - 2000*b4 + x111 - x151 =G= -2000;
e177.. - 2000*b5 + x117 - x153 =G= -2000;
e178.. - 2000*b6 + x123 - x151 =G= -2000;
e179.. - 2000*b7 + x129 - x153 =G= -2000;
e180.. - 2000*b8 + x22 - x154 =G= -2000;
e181.. - 2000*b9 + x26 - x155 =G= -2000;
e182.. - 2000*b10 + x30 - x154 =G= -2000;
e183.. - 2000*b11 + x33 - x155 =G= -2000;
e184.. - 2000*b12 + x36 - x154 =G= -2000;
e185.. - 2000*b13 + x40 - x155 =G= -2000;
e186.. - 2000*b14 + x44 - x154 =G= -2000;
e187.. - 2000*b15 + x47 - x155 =G= -2000;
e188.. - 2000*b16 + x50 - x156 =G= -2000;
e189.. - 2000*b17 + x54 - x157 =G= -2000;
e190.. - 2000*b18 + x58 - x156 =G= -2000;
e191.. - 2000*b19 + x61 - x157 =G= -2000;
e192.. 1049*b2 + x95 - x151 =L= 1049;
e193.. 1049*b3 + x103 - x153 =L= 1049;
e194.. 1049*b4 + x111 - x151 =L= 1049;
e195.. 1049*b5 + x117 - x153 =L= 1049;
e196.. 1049*b6 + x123 - x151 =L= 1049;
e197.. 1049*b7 + x129 - x153 =L= 1049;
e198.. 1065*b8 + x22 - x154 =L= 1065;
e199.. 1065*b9 + x26 - x155 =L= 1065;
e200.. 1065*b10 + x30 - x154 =L= 1065;
e201.. 1065*b11 + x33 - x155 =L= 1065;
e202.. 1065*b12 + x36 - x154 =L= 1065;
e203.. 1065*b13 + x40 - x155 =L= 1065;
e204.. 1065*b14 + x44 - x154 =L= 1065;
e205.. 1065*b15 + x47 - x155 =L= 1065;
e206.. 1095*b16 + x50 - x156 =L= 1095;
e207.. 1095*b17 + x54 - x157 =L= 1095;
e208.. 1095*b18 + x58 - x156 =L= 1095;
e209.. 1095*b19 + x61 - x157 =L= 1095;
e210.. - x132 + x141 =G= 0;
e211.. - x133 + x144 =G= 0;
e212.. x134 - x184 =G= 0;
e213.. x135 - x185 =G= 0;
e214.. - 7.28623839*x186 - 23.57687014*x187 - 0.309838295393634*x188
+ 13.94696158*x189 + 24.46510819*x190 =L= 0;
e215.. 13.94696158*x191 + 24.46510819*x192 - 7.28623839*x193
- 23.57687014*x194 - 0.309838295393634*x195 =L= 0;
e216.. - 0.309838295393634*x196 + 13.94696158*x197 + 24.46510819*x198
- 7.28623839*x199 - 23.57687014*x200 =L= 0;
e217.. - 23.57687014*x201 - 0.309838295393634*x202 + 13.94696158*x203
+ 24.46510819*x204 - 7.28623839*x205 =L= 0;
e218.. - 0.309838295393634*x206 + 13.94696158*x207 + 24.46510819*x208
- 7.28623839*x209 - 23.57687014*x210 =L= 0;
e219.. - 0.309838295393634*x211 + 13.94696158*x212 + 24.46510819*x213
- 7.28623839*x214 - 23.57687014*x215 =L= 0;
e220.. - 0.309838295393634*x216 + 29.29404529*x217 - 108.39408287*x218
+ 442.21990639*x219 - 454.58448169*x220 =L= 0;
e221.. - 0.309838295393634*x221 + 29.29404529*x222 - 108.39408287*x223
+ 442.21990639*x224 - 454.58448169*x225 =L= 0;
e222.. - 0.309838295393634*x226 + 29.29404529*x227 - 108.39408287*x228
+ 442.21990639*x229 - 454.58448169*x230 =L= 0;
e223.. - 0.309838295393634*x231 + 29.29404529*x232 - 108.39408287*x233
+ 442.21990639*x234 - 454.58448169*x235 =L= 0;
e224.. - 0.309838295393634*x236 + 25.92674585*x237 + 18.13482123*x238
+ 22.12766012*x239 - 42.68950769*x240 =L= 0;
e225.. - 0.309838295393634*x241 + 25.92674585*x242 + 18.13482123*x243
+ 22.12766012*x244 - 42.68950769*x245 =L= 0;
e226.. - 0.309838295393634*x246 + 25.92674585*x247 + 18.13482123*x248
+ 22.12766012*x249 - 42.68950769*x250 =L= 0;
e227.. - 0.309838295393634*x251 + 25.92674585*x252 + 18.13482123*x253
+ 22.12766012*x254 - 42.68950769*x255 =L= 0;
e228.. - 0.309838295393634*x256 + 17.4714791*x257 - 39.98407808*x258
+ 134.55943082*x259 - 135.88441782*x260 =L= 0;
e229.. - 0.309838295393634*x261 + 17.4714791*x262 - 39.98407808*x263
+ 134.55943082*x264 - 135.88441782*x265 =L= 0;
e230.. - 0.309838295393634*x266 + 17.4714791*x267 - 39.98407808*x268
+ 134.55943082*x269 - 135.88441782*x270 =L= 0;
e231.. - 135.88441782*x271 - 0.309838295393634*x272 + 17.4714791*x273
- 39.98407808*x274 + 134.55943082*x275 =L= 0;
e232.. sqr(x66) - x276 =E= 0;
e233.. x137 - 5*x276 =E= 0;
e234.. sqr(x68) - x277 =E= 0;
e235.. x139 - 5*x277 =E= 0;
e236.. sqr(x70) - x278 =E= 0;
e237.. x142 - 4*x278 =E= 0;
e238.. sqr(x72) - x279 =E= 0;
e239.. x145 - 4*x279 =E= 0;
e240.. sqr(x76) - x280 =E= 0;
e241.. x147 - 5*x280 =E= 0;
e242.. sqr(x78) - x281 =E= 0;
e243.. x149 - 5*x281 =E= 0;
e244.. sqr(x94) - x282 =E= 0;
e245.. x97 - x282 =E= 0;
e246.. POWER(x94,3) - x283 =E= 0;
e247.. x187 - x283 =E= 0;
e248.. sqr(x96) - x284 =E= 0;
e249.. x107 - x284 =E= 0;
e250.. POWER(x96,3) - x285 =E= 0;
e251.. x194 - x285 =E= 0;
e252.. sqr(x98) - x286 =E= 0;
e253.. x113 - x286 =E= 0;
e254.. POWER(x98,3) - x287 =E= 0;
e255.. x200 - x287 =E= 0;
e256.. sqr(x100) - x288 =E= 0;
e257.. x121 - x288 =E= 0;
e258.. POWER(x100,3) - x289 =E= 0;
e259.. x201 - x289 =E= 0;
e260.. sqr(x102) - x290 =E= 0;
e261.. x125 - x290 =E= 0;
e262.. POWER(x102,3) - x291 =E= 0;
e263.. x210 - x291 =E= 0;
e264.. sqr(x104) - x292 =E= 0;
e265.. x20 - x292 =E= 0;
e266.. POWER(x104,3) - x293 =E= 0;
e267.. x215 - x293 =E= 0;
e268.. sqr(x106) - x294 =E= 0;
e269.. x25 - x294 =E= 0;
e270.. POWER(x106,3) - x295 =E= 0;
e271.. x220 - x295 =E= 0;
e272.. sqr(x108) - x296 =E= 0;
e273.. x29 - x296 =E= 0;
e274.. POWER(x108,3) - x297 =E= 0;
e275.. x225 - x297 =E= 0;
e276.. sqr(x110) - x298 =E= 0;
e277.. x31 - x298 =E= 0;
e278.. POWER(x110,3) - x299 =E= 0;
e279.. x230 - x299 =E= 0;
e280.. sqr(x112) - x300 =E= 0;
e281.. x34 - x300 =E= 0;
e282.. POWER(x112,3) - x301 =E= 0;
e283.. x235 - x301 =E= 0;
e284.. sqr(x114) - x302 =E= 0;
e285.. x39 - x302 =E= 0;
e286.. POWER(x114,3) - x303 =E= 0;
e287.. x240 - x303 =E= 0;
e288.. sqr(x116) - x304 =E= 0;
e289.. x41 - x304 =E= 0;
e290.. POWER(x116,3) - x305 =E= 0;
e291.. x245 - x305 =E= 0;
e292.. sqr(x118) - x306 =E= 0;
e293.. x45 - x306 =E= 0;
e294.. POWER(x118,3) - x307 =E= 0;
e295.. x250 - x307 =E= 0;
e296.. sqr(x120) - x308 =E= 0;
e297.. x48 - x308 =E= 0;
e298.. POWER(x120,3) - x309 =E= 0;
e299.. x255 - x309 =E= 0;
e300.. sqr(x122) - x310 =E= 0;
e301.. x51 - x310 =E= 0;
e302.. POWER(x122,3) - x311 =E= 0;
e303.. x260 - x311 =E= 0;
e304.. sqr(x124) - x312 =E= 0;
e305.. x57 - x312 =E= 0;
e306.. POWER(x124,3) - x313 =E= 0;
e307.. x265 - x313 =E= 0;
e308.. sqr(x126) - x314 =E= 0;
e309.. x59 - x314 =E= 0;
e310.. POWER(x126,3) - x315 =E= 0;
e311.. x270 - x315 =E= 0;
e312.. sqr(x128) - x316 =E= 0;
e313.. x62 - x316 =E= 0;
e314.. POWER(x128,3) - x317 =E= 0;
e315.. x271 - x317 =E= 0;
e316.. x94*x176 - x101 =E= 0;
e317.. x176*x282 - x186 =E= 0;
e318.. x98*x176 - x115 =E= 0;
e319.. x176*x286 - x199 =E= 0;
e320.. x102*x176 - x127 =E= 0;
e321.. x176*x290 - x209 =E= 0;
e322.. sqr(x176) - x318 =E= 0;
e323.. x99 - x318 =E= 0;
e324.. x94*x318 - x190 =E= 0;
e325.. x98*x318 - x198 =E= 0;
e326.. x102*x318 - x208 =E= 0;
e327.. POWER(x176,3) - x319 =E= 0;
e328.. b2*x319 - x189 =E= 0;
e329.. b4*x319 - x197 =E= 0;
e330.. b6*x319 - x207 =E= 0;
e331.. x96*x177 - x105 =E= 0;
e332.. x177*x284 - x193 =E= 0;
e333.. x100*x177 - x119 =E= 0;
e334.. x177*x288 - x205 =E= 0;
e335.. x104*x177 - x21 =E= 0;
e336.. x177*x292 - x214 =E= 0;
e337.. sqr(x177) - x320 =E= 0;
e338.. x109 - x320 =E= 0;
e339.. x96*x320 - x192 =E= 0;
e340.. x100*x320 - x204 =E= 0;
e341.. x104*x320 - x213 =E= 0;
e342.. POWER(x177,3) - x321 =E= 0;
e343.. b3*x321 - x191 =E= 0;
e344.. b5*x321 - x203 =E= 0;
e345.. b7*x321 - x212 =E= 0;
e346.. x106*x178 - x24 =E= 0;
e347.. x178*x294 - x219 =E= 0;
e348.. x110*x178 - x32 =E= 0;
e349.. x178*x298 - x229 =E= 0;
e350.. sqr(x178) - x322 =E= 0;
e351.. x23 - x322 =E= 0;
e352.. x106*x322 - x218 =E= 0;
e353.. x110*x322 - x228 =E= 0;
e354.. POWER(x178,3) - x323 =E= 0;
e355.. b8*x323 - x217 =E= 0;
e356.. b10*x323 - x227 =E= 0;
e357.. x108*x179 - x27 =E= 0;
e358.. x179*x296 - x224 =E= 0;
e359.. x112*x179 - x35 =E= 0;
e360.. x179*x300 - x234 =E= 0;
e361.. sqr(x179) - x324 =E= 0;
e362.. x28 - x324 =E= 0;
e363.. x108*x324 - x223 =E= 0;
e364.. x112*x324 - x233 =E= 0;
e365.. POWER(x179,3) - x325 =E= 0;
e366.. b9*x325 - x222 =E= 0;
e367.. b11*x325 - x232 =E= 0;
e368.. x114*x180 - x38 =E= 0;
e369.. x180*x302 - x239 =E= 0;
e370.. x118*x180 - x46 =E= 0;
e371.. x180*x306 - x249 =E= 0;
e372.. sqr(x180) - x326 =E= 0;
e373.. x37 - x326 =E= 0;
e374.. x114*x326 - x238 =E= 0;
e375.. x118*x326 - x248 =E= 0;
e376.. POWER(x180,3) - x327 =E= 0;
e377.. b12*x327 - x237 =E= 0;
e378.. b14*x327 - x247 =E= 0;
e379.. x116*x181 - x42 =E= 0;
e380.. x181*x304 - x244 =E= 0;
e381.. x120*x181 - x49 =E= 0;
e382.. x181*x308 - x254 =E= 0;
e383.. sqr(x181) - x328 =E= 0;
e384.. x43 - x328 =E= 0;
e385.. x116*x328 - x243 =E= 0;
e386.. x120*x328 - x253 =E= 0;
e387.. POWER(x181,3) - x329 =E= 0;
e388.. b13*x329 - x242 =E= 0;
e389.. b15*x329 - x252 =E= 0;
e390.. x122*x182 - x53 =E= 0;
e391.. x182*x310 - x259 =E= 0;
e392.. x126*x182 - x60 =E= 0;
e393.. x182*x314 - x269 =E= 0;
e394.. sqr(x182) - x330 =E= 0;
e395.. x52 - x330 =E= 0;
e396.. x122*x330 - x258 =E= 0;
e397.. x126*x330 - x268 =E= 0;
e398.. POWER(x182,3) - x331 =E= 0;
e399.. b16*x331 - x257 =E= 0;
e400.. b18*x331 - x267 =E= 0;
e401.. x124*x183 - x56 =E= 0;
e402.. x183*x312 - x264 =E= 0;
e403.. x128*x183 - x63 =E= 0;
e404.. x183*x316 - x275 =E= 0;
e405.. sqr(x183) - x332 =E= 0;
e406.. x55 - x332 =E= 0;
e407.. x124*x332 - x263 =E= 0;
e408.. x128*x332 - x274 =E= 0;
e409.. POWER(x183,3) - x333 =E= 0;
e410.. b17*x333 - x262 =E= 0;
e411.. b19*x333 - x273 =E= 0;
* set non-default bounds
x22.lo = -1000; x22.up = 1000;
x26.lo = -1000; x26.up = 1000;
x30.lo = -1000; x30.up = 1000;
x33.lo = -1000; x33.up = 1000;
x36.lo = -1000; x36.up = 1000;
x40.lo = -1000; x40.up = 1000;
x44.lo = -1000; x44.up = 1000;
x47.lo = -1000; x47.up = 1000;
x50.lo = -1000; x50.up = 1000;
x54.lo = -1000; x54.up = 1000;
x58.lo = -1000; x58.up = 1000;
x61.lo = -1000; x61.up = 1000;
x64.up = 5;
x65.up = 5;
x66.up = 5;
x67.up = 2.4;
x68.up = 5;
x69.up = 2.4;
x70.up = 5;
x71.up = 2.4;
x72.up = 5;
x73.up = 2.4;
x74.up = 5;
x75.up = 5;
x76.up = 5;
x77.up = 1.16;
x78.up = 5;
x79.up = 1.16;
x80.up = 5;
x81.up = 5;
x82.fx = 3.5;
x83.lo = 2; x83.up = 5;
x84.lo = 2; x84.up = 5;
x85.lo = 2; x85.up = 5;
x86.fx = 4.1;
x87.lo = 2.5; x87.up = 5;
x88.lo = 2.5; x88.up = 5;
x89.lo = 2.5; x89.up = 5;
x90.fx = 4;
x91.lo = 2; x91.up = 6;
x92.lo = 2; x92.up = 6;
x93.lo = 2; x93.up = 6;
x94.up = 0.8;
x95.lo = -1000; x95.up = 1000;
x96.up = 0.8;
x98.up = 0.8;
x100.up = 0.8;
x102.up = 0.8;
x103.lo = -1000; x103.up = 1000;
x104.up = 0.8;
x106.up = 0.5;
x108.up = 0.5;
x110.up = 0.5;
x111.lo = -1000; x111.up = 1000;
x112.up = 0.5;
x114.up = 0.7;
x116.up = 0.7;
x117.lo = -1000; x117.up = 1000;
x118.up = 0.7;
x120.up = 0.7;
x122.up = 0.58;
x123.lo = -1000; x123.up = 1000;
x124.up = 0.58;
x126.up = 0.58;
x128.up = 0.58;
x129.lo = -1000; x129.up = 1000;
x130.lo = 62; x130.up = 65;
x131.lo = 62; x131.up = 65;
x132.lo = 92.5; x132.up = 95;
x133.lo = 92.5; x133.up = 95;
x134.lo = 105; x134.up = 109;
x135.lo = 105; x135.up = 109;
x136.up = 1000;
x137.lo = -125; x137.up = 125;
x138.up = 1000;
x139.lo = -125; x139.up = 125;
x140.up = 1000;
x141.up = 1000;
x142.lo = -100; x142.up = 100;
x143.up = 1000;
x144.up = 1000;
x145.lo = -100; x145.up = 100;
x146.up = 1000;
x147.lo = -125; x147.up = 125;
x148.up = 1000;
x149.lo = -125; x149.up = 125;
x150.fx = 49;
x151.lo = -49; x151.up = 1000;
x152.fx = 49;
x153.lo = -49; x153.up = 1000;
x154.lo = -65; x154.up = 1000;
x155.lo = -65; x155.up = 1000;
x156.lo = -95; x156.up = 1000;
x157.lo = -95; x157.up = 1000;
x158.lo = 0.2; x158.up = 0.8;
x159.lo = 0.2; x159.up = 0.8;
x160.lo = 0.2; x160.up = 0.8;
x161.lo = 0.2; x161.up = 0.8;
x162.lo = 0.2; x162.up = 0.8;
x163.lo = 0.2; x163.up = 0.8;
x164.lo = 0.25; x164.up = 0.5;
x165.lo = 0.25; x165.up = 0.5;
x166.lo = 0.25; x166.up = 0.5;
x167.lo = 0.25; x167.up = 0.5;
x168.lo = 0.4; x168.up = 0.7;
x169.lo = 0.4; x169.up = 0.7;
x170.lo = 0.4; x170.up = 0.7;
x171.lo = 0.4; x171.up = 0.7;
x172.lo = 0.24; x172.up = 0.58;
x173.lo = 0.24; x173.up = 0.58;
x174.lo = 0.24; x174.up = 0.58;
x175.lo = 0.24; x175.up = 0.58;
x176.lo = 0.6; x176.up = 1;
x177.lo = 0.6; x177.up = 1;
x178.lo = 0.8; x178.up = 1;
x179.lo = 0.8; x179.up = 1;
x180.lo = 0.85; x180.up = 1;
x181.lo = 0.85; x181.up = 1;
x182.lo = 0.7; x182.up = 1;
x183.lo = 0.7; x183.up = 1;
x184.lo = 100; x184.up = 1000;
x185.lo = 100; x185.up = 1000;
x188.up = 54.1717996137183;
x195.up = 54.1717996137183;
x196.up = 54.1717996137183;
x202.up = 54.1717996137183;
x206.up = 54.1717996137183;
x211.up = 54.1717996137183;
x216.up = 93.045051789432;
x221.up = 93.045051789432;
x226.up = 93.045051789432;
x231.up = 93.045051789432;
x236.up = 112.384987749469;
x241.up = 112.384987749469;
x246.up = 112.384987749469;
x251.up = 112.384987749469;
x256.up = 42.066542469172;
x261.up = 42.066542469172;
x266.up = 42.066542469172;
x272.up = 42.066542469172;
x276.up = 25;
x277.up = 25;
x278.up = 25;
x279.up = 25;
x280.up = 25;
x281.up = 25;
x282.up = 0.64;
x283.up = 0.512;
x284.up = 0.64;
x285.up = 0.512;
x286.up = 0.64;
x287.up = 0.512;
x288.up = 0.64;
x289.up = 0.512;
x290.up = 0.64;
x291.up = 0.512;
x292.up = 0.64;
x293.up = 0.512;
x294.up = 0.25;
x295.up = 0.125;
x296.up = 0.25;
x297.up = 0.125;
x298.up = 0.25;
x299.up = 0.125;
x300.up = 0.25;
x301.up = 0.125;
x302.up = 0.49;
x303.up = 0.343;
x304.up = 0.49;
x305.up = 0.343;
x306.up = 0.49;
x307.up = 0.343;
x308.up = 0.49;
x309.up = 0.343;
x310.up = 0.3364;
x311.up = 0.195112;
x312.up = 0.3364;
x313.up = 0.195112;
x314.up = 0.3364;
x315.up = 0.195112;
x316.up = 0.3364;
x317.up = 0.195112;
x318.lo = 0.36; x318.up = 1;
x319.lo = 0.216; x319.up = 1;
x320.lo = 0.36; x320.up = 1;
x321.lo = 0.216; x321.up = 1;
x322.lo = 0.64; x322.up = 1;
x323.lo = 0.512; x323.up = 1;
x324.lo = 0.64; x324.up = 1;
x325.lo = 0.512; x325.up = 1;
x326.lo = 0.7225; x326.up = 1;
x327.lo = 0.614125; x327.up = 1;
x328.lo = 0.7225; x328.up = 1;
x329.lo = 0.614125; x329.up = 1;
x330.lo = 0.49; x330.up = 1;
x331.lo = 0.343; x331.up = 1;
x332.lo = 0.49; x332.up = 1;
x333.lo = 0.343; x333.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: 2025-08-07 Git hash: e62cedfc