MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: clay0305h

Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized.
Formats ams gms mod nl osil
Primal Bounds
8092.50000000 p1 ( gdx sol )
(infeas: 3e-12)
Dual Bounds
8092.50000000 (ALPHAECP)
8092.50000000 (ANTIGONE)
8092.49999200 (BARON)
8092.50000000 (BONMIN)
8092.50000000 (COUENNE)
3415.00000000 (LINDO)
8092.50000000 (SCIP)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source CLay0305H.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 275
#Binary Variables 55
#Integer Variables 0
#Nonlinear Variables 45
#Nonlinear Binary Variables 15
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 0
#Constraints 395
#Linear Constraints 335
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 60
Operands in Gen. Nonlin. Functions mul div sqr
Constraints curvature convex
#Nonzeros in Jacobian 1095
#Nonlinear Nonzeros in Jacobian 180
#Nonzeros in (Upper-Left) Hessian of Lagrangian 105
#Nonzeros in Diagonal of Hessian of Lagrangian 45
#Blocks in Hessian of Lagrangian 15
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 13.5
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
*        396       66       40      290        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        276      221       55        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*       1116      936      180        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,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,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,b201,b202,b203,b204,b205,b206,b207
          ,b208,b209,b210,b211,b212,b213,b214,b215,b216,b217,b218,b219,b220
          ,b221,b222,b223,b224,b225,b226,b227,b228,b229,b230,b231,b232,b233
          ,b234,b235,b236,b237,b238,b239,b240,b241,b242,b243,b244,b245,b246
          ,b247,b248,b249,b250,b251,b252,b253,b254,b255,x256,x257,x258,x259
          ,x260,x261,x262,x263,x264,x265,x266,x267,x268,x269,x270,x271,x272
          ,x273,x274,x275,objvar;

Positive Variables  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,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,x256,x257,x258,x259,x260,x261,x262,x263,x264,x265,x266
          ,x267,x268,x269,x270,x271,x272,x273,x274,x275;

Binary Variables  b201,b202,b203,b204,b205,b206,b207,b208,b209,b210,b211,b212
          ,b213,b214,b215,b216,b217,b218,b219,b220,b221,b222,b223,b224,b225
          ,b226,b227,b228,b229,b230,b231,b232,b233,b234,b235,b236,b237,b238
          ,b239,b240,b241,b242,b243,b244,b245,b246,b247,b248,b249,b250,b251
          ,b252,b253,b254,b255;

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;


e1..  - 300*x256 - 240*x257 - 210*x258 - 50*x259 - 100*x260 - 150*x261
      - 30*x262 - 120*x263 - 25*x264 - 60*x265 - 300*x266 - 240*x267 - 210*x268
      - 50*x269 - 100*x270 - 150*x271 - 30*x272 - 120*x273 - 25*x274 - 60*x275
      + objvar =E= 0;

e2..  - x1 + x2 + x256 =G= 0;

e3..  - x1 + x3 + x257 =G= 0;

e4..  - x1 + x4 + x258 =G= 0;

e5..  - x1 + x5 + x259 =G= 0;

e6..  - x2 + x3 + x260 =G= 0;

e7..  - x2 + x4 + x261 =G= 0;

e8..  - x2 + x5 + x262 =G= 0;

e9..  - x3 + x4 + x263 =G= 0;

e10..  - x3 + x5 + x264 =G= 0;

e11..  - x4 + x5 + x265 =G= 0;

e12..    x1 - x2 + x256 =G= 0;

e13..    x1 - x3 + x257 =G= 0;

e14..    x1 - x4 + x258 =G= 0;

e15..    x1 - x5 + x259 =G= 0;

e16..    x2 - x3 + x260 =G= 0;

e17..    x2 - x4 + x261 =G= 0;

e18..    x2 - x5 + x262 =G= 0;

e19..    x3 - x4 + x263 =G= 0;

e20..    x3 - x5 + x264 =G= 0;

e21..    x4 - x5 + x265 =G= 0;

e22..  - x6 + x7 + x266 =G= 0;

e23..  - x6 + x8 + x267 =G= 0;

e24..  - x6 + x9 + x268 =G= 0;

e25..  - x6 + x10 + x269 =G= 0;

e26..  - x7 + x8 + x270 =G= 0;

e27..  - x7 + x9 + x271 =G= 0;

e28..  - x7 + x10 + x272 =G= 0;

e29..  - x8 + x9 + x273 =G= 0;

e30..  - x8 + x10 + x274 =G= 0;

e31..  - x9 + x10 + x275 =G= 0;

e32..    x6 - x7 + x266 =G= 0;

e33..    x6 - x8 + x267 =G= 0;

e34..    x6 - x9 + x268 =G= 0;

e35..    x6 - x10 + x269 =G= 0;

e36..    x7 - x8 + x270 =G= 0;

e37..    x7 - x9 + x271 =G= 0;

e38..    x7 - x10 + x272 =G= 0;

e39..    x8 - x9 + x273 =G= 0;

e40..    x8 - x10 + x274 =G= 0;

e41..    x9 - x10 + x275 =G= 0;

e42..    x1 - x11 - x15 - x19 - x23 =E= 0;

e43..    x1 - x12 - x16 - x20 - x24 =E= 0;

e44..    x1 - x13 - x17 - x21 - x25 =E= 0;

e45..    x1 - x14 - x18 - x22 - x26 =E= 0;

e46..    x2 - x27 - x31 - x35 - x39 =E= 0;

e47..    x2 - x28 - x32 - x36 - x40 =E= 0;

e48..    x2 - x29 - x33 - x37 - x41 =E= 0;

e49..    x2 - x30 - x34 - x38 - x42 =E= 0;

e50..    x3 - x43 - x47 - x51 - x55 =E= 0;

e51..    x3 - x44 - x48 - x52 - x56 =E= 0;

e52..    x3 - x45 - x49 - x53 - x57 =E= 0;

e53..    x3 - x46 - x50 - x54 - x58 =E= 0;

e54..    x4 - x59 - x63 - x67 - x71 =E= 0;

e55..    x4 - x60 - x64 - x68 - x72 =E= 0;

e56..    x4 - x61 - x65 - x69 - x73 =E= 0;

e57..    x4 - x62 - x66 - x70 - x74 =E= 0;

e58..    x5 - x75 - x79 - x83 - x87 =E= 0;

e59..    x5 - x76 - x80 - x84 - x88 =E= 0;

e60..    x5 - x77 - x81 - x85 - x89 =E= 0;

e61..    x5 - x78 - x82 - x86 - x90 =E= 0;

e62..    x6 - x91 - x95 - x99 - x103 =E= 0;

e63..    x6 - x92 - x96 - x100 - x104 =E= 0;

e64..    x6 - x93 - x97 - x101 - x105 =E= 0;

e65..    x6 - x94 - x98 - x102 - x106 =E= 0;

e66..    x7 - x107 - x111 - x115 - x119 =E= 0;

e67..    x7 - x108 - x112 - x116 - x120 =E= 0;

e68..    x7 - x109 - x113 - x117 - x121 =E= 0;

e69..    x7 - x110 - x114 - x118 - x122 =E= 0;

e70..    x8 - x123 - x127 - x131 - x135 =E= 0;

e71..    x8 - x124 - x128 - x132 - x136 =E= 0;

e72..    x8 - x125 - x129 - x133 - x137 =E= 0;

e73..    x8 - x126 - x130 - x134 - x138 =E= 0;

e74..    x9 - x139 - x143 - x147 - x151 =E= 0;

e75..    x9 - x140 - x144 - x148 - x152 =E= 0;

e76..    x9 - x141 - x145 - x149 - x153 =E= 0;

e77..    x9 - x142 - x146 - x150 - x154 =E= 0;

e78..    x10 - x155 - x159 - x163 - x167 =E= 0;

e79..    x10 - x156 - x160 - x164 - x168 =E= 0;

e80..    x10 - x157 - x161 - x165 - x169 =E= 0;

e81..    x10 - x158 - x162 - x166 - x170 =E= 0;

e82..    x11 - 57.5*b201 =L= 0;

e83..    x12 - 57.5*b202 =L= 0;

e84..    x13 - 57.5*b203 =L= 0;

e85..    x14 - 57.5*b204 =L= 0;

e86..    x15 - 57.5*b211 =L= 0;

e87..    x16 - 57.5*b212 =L= 0;

e88..    x17 - 57.5*b213 =L= 0;

e89..    x18 - 57.5*b214 =L= 0;

e90..    x19 - 57.5*b221 =L= 0;

e91..    x20 - 57.5*b222 =L= 0;

e92..    x21 - 57.5*b223 =L= 0;

e93..    x22 - 57.5*b224 =L= 0;

e94..    x23 - 57.5*b231 =L= 0;

e95..    x24 - 57.5*b232 =L= 0;

e96..    x25 - 57.5*b233 =L= 0;

e97..    x26 - 57.5*b234 =L= 0;

e98..    x27 - 57.5*b201 =L= 0;

e99..    x28 - 56.5*b205 =L= 0;

e100..    x29 - 56.5*b206 =L= 0;

e101..    x30 - 56.5*b207 =L= 0;

e102..    x31 - 57.5*b211 =L= 0;

e103..    x32 - 56.5*b215 =L= 0;

e104..    x33 - 56.5*b216 =L= 0;

e105..    x34 - 56.5*b217 =L= 0;

e106..    x35 - 57.5*b221 =L= 0;

e107..    x36 - 56.5*b225 =L= 0;

e108..    x37 - 56.5*b226 =L= 0;

e109..    x38 - 56.5*b227 =L= 0;

e110..    x39 - 57.5*b231 =L= 0;

e111..    x40 - 56.5*b235 =L= 0;

e112..    x41 - 56.5*b236 =L= 0;

e113..    x42 - 56.5*b237 =L= 0;

e114..    x43 - 57.5*b202 =L= 0;

e115..    x44 - 56.5*b205 =L= 0;

e116..    x45 - 58.5*b208 =L= 0;

e117..    x46 - 58.5*b209 =L= 0;

e118..    x47 - 57.5*b212 =L= 0;

e119..    x48 - 56.5*b215 =L= 0;

e120..    x49 - 58.5*b218 =L= 0;

e121..    x50 - 58.5*b219 =L= 0;

e122..    x51 - 57.5*b222 =L= 0;

e123..    x52 - 56.5*b225 =L= 0;

e124..    x53 - 58.5*b228 =L= 0;

e125..    x54 - 58.5*b229 =L= 0;

e126..    x55 - 57.5*b232 =L= 0;

e127..    x56 - 56.5*b235 =L= 0;

e128..    x57 - 58.5*b238 =L= 0;

e129..    x58 - 58.5*b239 =L= 0;

e130..    x59 - 57.5*b203 =L= 0;

e131..    x60 - 56.5*b206 =L= 0;

e132..    x61 - 58.5*b208 =L= 0;

e133..    x62 - 59*b210 =L= 0;

e134..    x63 - 57.5*b213 =L= 0;

e135..    x64 - 56.5*b216 =L= 0;

e136..    x65 - 58.5*b218 =L= 0;

e137..    x66 - 59*b220 =L= 0;

e138..    x67 - 57.5*b223 =L= 0;

e139..    x68 - 56.5*b226 =L= 0;

e140..    x69 - 58.5*b228 =L= 0;

e141..    x70 - 59*b230 =L= 0;

e142..    x71 - 57.5*b233 =L= 0;

e143..    x72 - 56.5*b236 =L= 0;

e144..    x73 - 58.5*b238 =L= 0;

e145..    x74 - 59*b240 =L= 0;

e146..    x75 - 57.5*b204 =L= 0;

e147..    x76 - 56.5*b207 =L= 0;

e148..    x77 - 58.5*b209 =L= 0;

e149..    x78 - 59*b210 =L= 0;

e150..    x79 - 57.5*b214 =L= 0;

e151..    x80 - 56.5*b217 =L= 0;

e152..    x81 - 58.5*b219 =L= 0;

e153..    x82 - 59*b220 =L= 0;

e154..    x83 - 57.5*b224 =L= 0;

e155..    x84 - 56.5*b227 =L= 0;

e156..    x85 - 58.5*b229 =L= 0;

e157..    x86 - 59*b230 =L= 0;

e158..    x87 - 57.5*b234 =L= 0;

e159..    x88 - 56.5*b237 =L= 0;

e160..    x89 - 58.5*b239 =L= 0;

e161..    x90 - 59*b240 =L= 0;

e162..    x91 - 87*b201 =L= 0;

e163..    x92 - 87*b202 =L= 0;

e164..    x93 - 87*b203 =L= 0;

e165..    x94 - 87*b204 =L= 0;

e166..    x95 - 87*b211 =L= 0;

e167..    x96 - 87*b212 =L= 0;

e168..    x97 - 87*b213 =L= 0;

e169..    x98 - 87*b214 =L= 0;

e170..    x99 - 87*b221 =L= 0;

e171..    x100 - 87*b222 =L= 0;

e172..    x101 - 87*b223 =L= 0;

e173..    x102 - 87*b224 =L= 0;

e174..    x103 - 87*b231 =L= 0;

e175..    x104 - 87*b232 =L= 0;

e176..    x105 - 87*b233 =L= 0;

e177..    x106 - 87*b234 =L= 0;

e178..    x107 - 87*b201 =L= 0;

e179..    x108 - 87.5*b205 =L= 0;

e180..    x109 - 87.5*b206 =L= 0;

e181..    x110 - 87.5*b207 =L= 0;

e182..    x111 - 87*b211 =L= 0;

e183..    x112 - 87.5*b215 =L= 0;

e184..    x113 - 87.5*b216 =L= 0;

e185..    x114 - 87.5*b217 =L= 0;

e186..    x115 - 87*b221 =L= 0;

e187..    x116 - 87.5*b225 =L= 0;

e188..    x117 - 87.5*b226 =L= 0;

e189..    x118 - 87.5*b227 =L= 0;

e190..    x119 - 87*b231 =L= 0;

e191..    x120 - 87.5*b235 =L= 0;

e192..    x121 - 87.5*b236 =L= 0;

e193..    x122 - 87.5*b237 =L= 0;

e194..    x123 - 87*b202 =L= 0;

e195..    x124 - 87.5*b205 =L= 0;

e196..    x125 - 88.5*b208 =L= 0;

e197..    x126 - 88.5*b209 =L= 0;

e198..    x127 - 87*b212 =L= 0;

e199..    x128 - 87.5*b215 =L= 0;

e200..    x129 - 88.5*b218 =L= 0;

e201..    x130 - 88.5*b219 =L= 0;

e202..    x131 - 87*b222 =L= 0;

e203..    x132 - 87.5*b225 =L= 0;

e204..    x133 - 88.5*b228 =L= 0;

e205..    x134 - 88.5*b229 =L= 0;

e206..    x135 - 87*b232 =L= 0;

e207..    x136 - 87.5*b235 =L= 0;

e208..    x137 - 88.5*b238 =L= 0;

e209..    x138 - 88.5*b239 =L= 0;

e210..    x139 - 87*b203 =L= 0;

e211..    x140 - 87.5*b206 =L= 0;

e212..    x141 - 88.5*b208 =L= 0;

e213..    x142 - 88.5*b210 =L= 0;

e214..    x143 - 87*b213 =L= 0;

e215..    x144 - 87.5*b216 =L= 0;

e216..    x145 - 88.5*b218 =L= 0;

e217..    x146 - 88.5*b220 =L= 0;

e218..    x147 - 87*b223 =L= 0;

e219..    x148 - 87.5*b226 =L= 0;

e220..    x149 - 88.5*b228 =L= 0;

e221..    x150 - 88.5*b230 =L= 0;

e222..    x151 - 87*b233 =L= 0;

e223..    x152 - 87.5*b236 =L= 0;

e224..    x153 - 88.5*b238 =L= 0;

e225..    x154 - 88.5*b240 =L= 0;

e226..    x155 - 87*b204 =L= 0;

e227..    x156 - 87.5*b207 =L= 0;

e228..    x157 - 88.5*b209 =L= 0;

e229..    x158 - 88.5*b210 =L= 0;

e230..    x159 - 87*b214 =L= 0;

e231..    x160 - 87.5*b217 =L= 0;

e232..    x161 - 88.5*b219 =L= 0;

e233..    x162 - 88.5*b220 =L= 0;

e234..    x163 - 87*b224 =L= 0;

e235..    x164 - 87.5*b227 =L= 0;

e236..    x165 - 88.5*b229 =L= 0;

e237..    x166 - 88.5*b230 =L= 0;

e238..    x167 - 87*b234 =L= 0;

e239..    x168 - 87.5*b237 =L= 0;

e240..    x169 - 88.5*b239 =L= 0;

e241..    x170 - 88.5*b240 =L= 0;

e242..    x11 - x27 + 6*b201 =L= 0;

e243..    x12 - x43 + 4*b202 =L= 0;

e244..    x13 - x59 + 3.5*b203 =L= 0;

e245..    x14 - x75 + 7*b204 =L= 0;

e246..    x28 - x44 + 5*b205 =L= 0;

e247..    x29 - x60 + 4.5*b206 =L= 0;

e248..    x30 - x76 + 8*b207 =L= 0;

e249..    x45 - x61 + 2.5*b208 =L= 0;

e250..    x46 - x77 + 6*b209 =L= 0;

e251..    x62 - x78 + 5.5*b210 =L= 0;

e252..  - x15 + x31 + 6*b211 =L= 0;

e253..  - x16 + x47 + 4*b212 =L= 0;

e254..  - x17 + x63 + 3.5*b213 =L= 0;

e255..  - x18 + x79 + 7*b214 =L= 0;

e256..  - x32 + x48 + 5*b215 =L= 0;

e257..  - x33 + x64 + 4.5*b216 =L= 0;

e258..  - x34 + x80 + 8*b217 =L= 0;

e259..  - x49 + x65 + 2.5*b218 =L= 0;

e260..  - x50 + x81 + 6*b219 =L= 0;

e261..  - x66 + x82 + 5.5*b220 =L= 0;

e262..    x99 - x115 + 5.5*b221 =L= 0;

e263..    x100 - x131 + 4.5*b222 =L= 0;

e264..    x101 - x147 + 4.5*b223 =L= 0;

e265..    x102 - x163 + 6.5*b224 =L= 0;

e266..    x116 - x132 + 4*b225 =L= 0;

e267..    x117 - x148 + 4*b226 =L= 0;

e268..    x118 - x164 + 6*b227 =L= 0;

e269..    x133 - x149 + 3*b228 =L= 0;

e270..    x134 - x165 + 5*b229 =L= 0;

e271..    x150 - x166 + 5*b230 =L= 0;

e272..  - x103 + x119 + 5.5*b231 =L= 0;

e273..  - x104 + x135 + 4.5*b232 =L= 0;

e274..  - x105 + x151 + 4.5*b233 =L= 0;

e275..  - x106 + x167 + 6.5*b234 =L= 0;

e276..  - x120 + x136 + 4*b235 =L= 0;

e277..  - x121 + x152 + 4*b236 =L= 0;

e278..  - x122 + x168 + 6*b237 =L= 0;

e279..  - x137 + x153 + 3*b238 =L= 0;

e280..  - x138 + x169 + 5*b239 =L= 0;

e281..  - x154 + x170 + 5*b240 =L= 0;

e282..    b201 + b211 + b221 + b231 =E= 1;

e283..    b202 + b212 + b222 + b232 =E= 1;

e284..    b203 + b213 + b223 + b233 =E= 1;

e285..    b204 + b214 + b224 + b234 =E= 1;

e286..    b205 + b215 + b225 + b235 =E= 1;

e287..    b206 + b216 + b226 + b236 =E= 1;

e288..    b207 + b217 + b227 + b237 =E= 1;

e289..    b208 + b218 + b228 + b238 =E= 1;

e290..    b209 + b219 + b229 + b239 =E= 1;

e291..    b210 + b220 + b230 + b240 =E= 1;

e292..    x1 - x171 - x176 - x181 =E= 0;

e293..    x2 - x172 - x177 - x182 =E= 0;

e294..    x3 - x173 - x178 - x183 =E= 0;

e295..    x4 - x174 - x179 - x184 =E= 0;

e296..    x5 - x175 - x180 - x185 =E= 0;

e297..    x6 - x186 - x191 - x196 =E= 0;

e298..    x7 - x187 - x192 - x197 =E= 0;

e299..    x8 - x188 - x193 - x198 =E= 0;

e300..    x9 - x189 - x194 - x199 =E= 0;

e301..    x10 - x190 - x195 - x200 =E= 0;

e302..    x171 - 18.5*b241 =L= 0;

e303..    x172 - 17.5*b242 =L= 0;

e304..    x173 - 19.5*b243 =L= 0;

e305..    x174 - 20*b244 =L= 0;

e306..    x175 - 16.5*b245 =L= 0;

e307..    x176 - 57.5*b246 =L= 0;

e308..    x177 - 56.5*b247 =L= 0;

e309..    x178 - 58.5*b248 =L= 0;

e310..    x179 - 59*b249 =L= 0;

e311..    x180 - 55.5*b250 =L= 0;

e312..    x181 - 31.5*b251 =L= 0;

e313..    x182 - 30.5*b252 =L= 0;

e314..    x183 - 32.5*b253 =L= 0;

e315..    x184 - 33*b254 =L= 0;

e316..    x185 - 29.5*b255 =L= 0;

e317..    x186 - 13*b241 =L= 0;

e318..    x187 - 13.5*b242 =L= 0;

e319..    x188 - 14.5*b243 =L= 0;

e320..    x189 - 14.5*b244 =L= 0;

e321..    x190 - 12.5*b245 =L= 0;

e322..    x191 - 87*b246 =L= 0;

e323..    x192 - 87.5*b247 =L= 0;

e324..    x193 - 88.5*b248 =L= 0;

e325..    x194 - 88.5*b249 =L= 0;

e326..    x195 - 86.5*b250 =L= 0;

e327..    x196 - 51*b251 =L= 0;

e328..    x197 - 51.5*b252 =L= 0;

e329..    x198 - 52.5*b253 =L= 0;

e330..    x199 - 52.5*b254 =L= 0;

e331..    x200 - 50.5*b255 =L= 0;

e332.. (sqr(x171/(1e-6 + b241)) - 35*x171/(1e-6 + b241) + 306.25*b241 + sqr(
       x186/(1e-6 + b241)) - 14*x186/(1e-6 + b241) + 49*b241 - 36*b241)*(1e-6
        + b241) =L= 0;

e333.. (sqr(x172/(1e-6 + b242)) - 37*x172/(1e-6 + b242) + 342.25*b242 + sqr(
       x187/(1e-6 + b242)) - 15*x187/(1e-6 + b242) + 56.25*b242 - 36*b242)*(
       1e-6 + b242) =L= 0;

e334.. (sqr(x173/(1e-6 + b243)) - 33*x173/(1e-6 + b243) + 272.25*b243 + sqr(
       x188/(1e-6 + b243)) - 17*x188/(1e-6 + b243) + 72.25*b243 - 36*b243)*(
       1e-6 + b243) =L= 0;

e335.. (sqr(x174/(1e-6 + b244)) - 32*x174/(1e-6 + b244) + 256*b244 + sqr(x189/(
       1e-6 + b244)) - 17*x189/(1e-6 + b244) + 72.25*b244 - 36*b244)*(1e-6 + 
       b244) =L= 0;

e336.. (sqr(x175/(1e-6 + b245)) - 39*x175/(1e-6 + b245) + 380.25*b245 + sqr(
       x190/(1e-6 + b245)) - 13*x190/(1e-6 + b245) + 42.25*b245 - 36*b245)*(
       1e-6 + b245) =L= 0;

e337.. (sqr(x176/(1e-6 + b246)) - 105*x176/(1e-6 + b246) + 2756.25*b246 + sqr(
       x191/(1e-6 + b246)) - 154*x191/(1e-6 + b246) + 5929*b246 - 100*b246)*(
       1e-6 + b246) =L= 0;

e338.. (sqr(x177/(1e-6 + b247)) - 107*x177/(1e-6 + b247) + 2862.25*b247 + sqr(
       x192/(1e-6 + b247)) - 155*x192/(1e-6 + b247) + 6006.25*b247 - 100*b247)*
       (1e-6 + b247) =L= 0;

e339.. (sqr(x178/(1e-6 + b248)) - 103*x178/(1e-6 + b248) + 2652.25*b248 + sqr(
       x193/(1e-6 + b248)) - 157*x193/(1e-6 + b248) + 6162.25*b248 - 100*b248)*
       (1e-6 + b248) =L= 0;

e340.. (sqr(x179/(1e-6 + b249)) - 102*x179/(1e-6 + b249) + 2601*b249 + sqr(x194
       /(1e-6 + b249)) - 157*x194/(1e-6 + b249) + 6162.25*b249 - 100*b249)*(
       1e-6 + b249) =L= 0;

e341.. (sqr(x180/(1e-6 + b250)) - 109*x180/(1e-6 + b250) + 2970.25*b250 + sqr(
       x195/(1e-6 + b250)) - 153*x195/(1e-6 + b250) + 5852.25*b250 - 100*b250)*
       (1e-6 + b250) =L= 0;

e342.. (sqr(x181/(1e-6 + b251)) - 65*x181/(1e-6 + b251) + 1056.25*b251 + sqr(
       x196/(1e-6 + b251)) - 94*x196/(1e-6 + b251) + 2209*b251 - 16*b251)*(1e-6
        + b251) =L= 0;

e343.. (sqr(x182/(1e-6 + b252)) - 67*x182/(1e-6 + b252) + 1122.25*b252 + sqr(
       x197/(1e-6 + b252)) - 95*x197/(1e-6 + b252) + 2256.25*b252 - 16*b252)*(
       1e-6 + b252) =L= 0;

e344.. (sqr(x183/(1e-6 + b253)) - 63*x183/(1e-6 + b253) + 992.25*b253 + sqr(
       x198/(1e-6 + b253)) - 97*x198/(1e-6 + b253) + 2352.25*b253 - 16*b253)*(
       1e-6 + b253) =L= 0;

e345.. (sqr(x184/(1e-6 + b254)) - 62*x184/(1e-6 + b254) + 961*b254 + sqr(x199/(
       1e-6 + b254)) - 97*x199/(1e-6 + b254) + 2352.25*b254 - 16*b254)*(1e-6 + 
       b254) =L= 0;

e346.. (sqr(x185/(1e-6 + b255)) - 69*x185/(1e-6 + b255) + 1190.25*b255 + sqr(
       x200/(1e-6 + b255)) - 93*x200/(1e-6 + b255) + 2162.25*b255 - 16*b255)*(
       1e-6 + b255) =L= 0;

e347.. (sqr(x171/(1e-6 + b241)) - 35*x171/(1e-6 + b241) + 306.25*b241 + sqr(
       x186/(1e-6 + b241)) - 26*x186/(1e-6 + b241) + 169*b241 - 36*b241)*(1e-6
        + b241) =L= 0;

e348.. (sqr(x172/(1e-6 + b242)) - 37*x172/(1e-6 + b242) + 342.25*b242 + sqr(
       x187/(1e-6 + b242)) - 25*x187/(1e-6 + b242) + 156.25*b242 - 36*b242)*(
       1e-6 + b242) =L= 0;

e349.. (sqr(x173/(1e-6 + b243)) - 33*x173/(1e-6 + b243) + 272.25*b243 + sqr(
       x188/(1e-6 + b243)) - 23*x188/(1e-6 + b243) + 132.25*b243 - 36*b243)*(
       1e-6 + b243) =L= 0;

e350.. (sqr(x174/(1e-6 + b244)) - 32*x174/(1e-6 + b244) + 256*b244 + sqr(x189/(
       1e-6 + b244)) - 23*x189/(1e-6 + b244) + 132.25*b244 - 36*b244)*(1e-6 + 
       b244) =L= 0;

e351.. (sqr(x175/(1e-6 + b245)) - 39*x175/(1e-6 + b245) + 380.25*b245 + sqr(
       x190/(1e-6 + b245)) - 27*x190/(1e-6 + b245) + 182.25*b245 - 36*b245)*(
       1e-6 + b245) =L= 0;

e352.. (sqr(x176/(1e-6 + b246)) - 105*x176/(1e-6 + b246) + 2756.25*b246 + sqr(
       x191/(1e-6 + b246)) - 166*x191/(1e-6 + b246) + 6889*b246 - 100*b246)*(
       1e-6 + b246) =L= 0;

e353.. (sqr(x177/(1e-6 + b247)) - 107*x177/(1e-6 + b247) + 2862.25*b247 + sqr(
       x192/(1e-6 + b247)) - 165*x192/(1e-6 + b247) + 6806.25*b247 - 100*b247)*
       (1e-6 + b247) =L= 0;

e354.. (sqr(x178/(1e-6 + b248)) - 103*x178/(1e-6 + b248) + 2652.25*b248 + sqr(
       x193/(1e-6 + b248)) - 163*x193/(1e-6 + b248) + 6642.25*b248 - 100*b248)*
       (1e-6 + b248) =L= 0;

e355.. (sqr(x179/(1e-6 + b249)) - 102*x179/(1e-6 + b249) + 2601*b249 + sqr(x194
       /(1e-6 + b249)) - 163*x194/(1e-6 + b249) + 6642.25*b249 - 100*b249)*(
       1e-6 + b249) =L= 0;

e356.. (sqr(x180/(1e-6 + b250)) - 109*x180/(1e-6 + b250) + 2970.25*b250 + sqr(
       x195/(1e-6 + b250)) - 167*x195/(1e-6 + b250) + 6972.25*b250 - 100*b250)*
       (1e-6 + b250) =L= 0;

e357.. (sqr(x181/(1e-6 + b251)) - 65*x181/(1e-6 + b251) + 1056.25*b251 + sqr(
       x196/(1e-6 + b251)) - 106*x196/(1e-6 + b251) + 2809*b251 - 16*b251)*(
       1e-6 + b251) =L= 0;

e358.. (sqr(x182/(1e-6 + b252)) - 67*x182/(1e-6 + b252) + 1122.25*b252 + sqr(
       x197/(1e-6 + b252)) - 105*x197/(1e-6 + b252) + 2756.25*b252 - 16*b252)*(
       1e-6 + b252) =L= 0;

e359.. (sqr(x183/(1e-6 + b253)) - 63*x183/(1e-6 + b253) + 992.25*b253 + sqr(
       x198/(1e-6 + b253)) - 103*x198/(1e-6 + b253) + 2652.25*b253 - 16*b253)*(
       1e-6 + b253) =L= 0;

e360.. (sqr(x184/(1e-6 + b254)) - 62*x184/(1e-6 + b254) + 961*b254 + sqr(x199/(
       1e-6 + b254)) - 103*x199/(1e-6 + b254) + 2652.25*b254 - 16*b254)*(1e-6
        + b254) =L= 0;

e361.. (sqr(x185/(1e-6 + b255)) - 69*x185/(1e-6 + b255) + 1190.25*b255 + sqr(
       x200/(1e-6 + b255)) - 107*x200/(1e-6 + b255) + 2862.25*b255 - 16*b255)*(
       1e-6 + b255) =L= 0;

e362.. (sqr(x171/(1e-6 + b241)) - 25*x171/(1e-6 + b241) + 156.25*b241 + sqr(
       x186/(1e-6 + b241)) - 14*x186/(1e-6 + b241) + 49*b241 - 36*b241)*(1e-6
        + b241) =L= 0;

e363.. (sqr(x172/(1e-6 + b242)) - 23*x172/(1e-6 + b242) + 132.25*b242 + sqr(
       x187/(1e-6 + b242)) - 15*x187/(1e-6 + b242) + 56.25*b242 - 36*b242)*(
       1e-6 + b242) =L= 0;

e364.. (sqr(x173/(1e-6 + b243)) - 27*x173/(1e-6 + b243) + 182.25*b243 + sqr(
       x188/(1e-6 + b243)) - 17*x188/(1e-6 + b243) + 72.25*b243 - 36*b243)*(
       1e-6 + b243) =L= 0;

e365.. (sqr(x174/(1e-6 + b244)) - 28*x174/(1e-6 + b244) + 196*b244 + sqr(x189/(
       1e-6 + b244)) - 17*x189/(1e-6 + b244) + 72.25*b244 - 36*b244)*(1e-6 + 
       b244) =L= 0;

e366.. (sqr(x175/(1e-6 + b245)) - 21*x175/(1e-6 + b245) + 110.25*b245 + sqr(
       x190/(1e-6 + b245)) - 13*x190/(1e-6 + b245) + 42.25*b245 - 36*b245)*(
       1e-6 + b245) =L= 0;

e367.. (sqr(x176/(1e-6 + b246)) - 95*x176/(1e-6 + b246) + 2256.25*b246 + sqr(
       x191/(1e-6 + b246)) - 154*x191/(1e-6 + b246) + 5929*b246 - 100*b246)*(
       1e-6 + b246) =L= 0;

e368.. (sqr(x177/(1e-6 + b247)) - 93*x177/(1e-6 + b247) + 2162.25*b247 + sqr(
       x192/(1e-6 + b247)) - 155*x192/(1e-6 + b247) + 6006.25*b247 - 100*b247)*
       (1e-6 + b247) =L= 0;

e369.. (sqr(x178/(1e-6 + b248)) - 97*x178/(1e-6 + b248) + 2352.25*b248 + sqr(
       x193/(1e-6 + b248)) - 157*x193/(1e-6 + b248) + 6162.25*b248 - 100*b248)*
       (1e-6 + b248) =L= 0;

e370.. (sqr(x179/(1e-6 + b249)) - 98*x179/(1e-6 + b249) + 2401*b249 + sqr(x194/
       (1e-6 + b249)) - 157*x194/(1e-6 + b249) + 6162.25*b249 - 100*b249)*(1e-6
        + b249) =L= 0;

e371.. (sqr(x180/(1e-6 + b250)) - 91*x180/(1e-6 + b250) + 2070.25*b250 + sqr(
       x195/(1e-6 + b250)) - 153*x195/(1e-6 + b250) + 5852.25*b250 - 100*b250)*
       (1e-6 + b250) =L= 0;

e372.. (sqr(x181/(1e-6 + b251)) - 55*x181/(1e-6 + b251) + 756.25*b251 + sqr(
       x196/(1e-6 + b251)) - 94*x196/(1e-6 + b251) + 2209*b251 - 16*b251)*(1e-6
        + b251) =L= 0;

e373.. (sqr(x182/(1e-6 + b252)) - 53*x182/(1e-6 + b252) + 702.25*b252 + sqr(
       x197/(1e-6 + b252)) - 95*x197/(1e-6 + b252) + 2256.25*b252 - 16*b252)*(
       1e-6 + b252) =L= 0;

e374.. (sqr(x183/(1e-6 + b253)) - 57*x183/(1e-6 + b253) + 812.25*b253 + sqr(
       x198/(1e-6 + b253)) - 97*x198/(1e-6 + b253) + 2352.25*b253 - 16*b253)*(
       1e-6 + b253) =L= 0;

e375.. (sqr(x184/(1e-6 + b254)) - 58*x184/(1e-6 + b254) + 841*b254 + sqr(x199/(
       1e-6 + b254)) - 97*x199/(1e-6 + b254) + 2352.25*b254 - 16*b254)*(1e-6 + 
       b254) =L= 0;

e376.. (sqr(x185/(1e-6 + b255)) - 51*x185/(1e-6 + b255) + 650.25*b255 + sqr(
       x200/(1e-6 + b255)) - 93*x200/(1e-6 + b255) + 2162.25*b255 - 16*b255)*(
       1e-6 + b255) =L= 0;

e377.. (sqr(x171/(1e-6 + b241)) - 25*x171/(1e-6 + b241) + 156.25*b241 + sqr(
       x186/(1e-6 + b241)) - 26*x186/(1e-6 + b241) + 169*b241 - 36*b241)*(1e-6
        + b241) =L= 0;

e378.. (sqr(x172/(1e-6 + b242)) - 23*x172/(1e-6 + b242) + 132.25*b242 + sqr(
       x187/(1e-6 + b242)) - 25*x187/(1e-6 + b242) + 156.25*b242 - 36*b242)*(
       1e-6 + b242) =L= 0;

e379.. (sqr(x173/(1e-6 + b243)) - 27*x173/(1e-6 + b243) + 182.25*b243 + sqr(
       x188/(1e-6 + b243)) - 23*x188/(1e-6 + b243) + 132.25*b243 - 36*b243)*(
       1e-6 + b243) =L= 0;

e380.. (sqr(x174/(1e-6 + b244)) - 28*x174/(1e-6 + b244) + 196*b244 + sqr(x189/(
       1e-6 + b244)) - 23*x189/(1e-6 + b244) + 132.25*b244 - 36*b244)*(1e-6 + 
       b244) =L= 0;

e381.. (sqr(x175/(1e-6 + b245)) - 21*x175/(1e-6 + b245) + 110.25*b245 + sqr(
       x190/(1e-6 + b245)) - 27*x190/(1e-6 + b245) + 182.25*b245 - 36*b245)*(
       1e-6 + b245) =L= 0;

e382.. (sqr(x176/(1e-6 + b246)) - 95*x176/(1e-6 + b246) + 2256.25*b246 + sqr(
       x191/(1e-6 + b246)) - 166*x191/(1e-6 + b246) + 6889*b246 - 100*b246)*(
       1e-6 + b246) =L= 0;

e383.. (sqr(x177/(1e-6 + b247)) - 93*x177/(1e-6 + b247) + 2162.25*b247 + sqr(
       x192/(1e-6 + b247)) - 165*x192/(1e-6 + b247) + 6806.25*b247 - 100*b247)*
       (1e-6 + b247) =L= 0;

e384.. (sqr(x178/(1e-6 + b248)) - 97*x178/(1e-6 + b248) + 2352.25*b248 + sqr(
       x193/(1e-6 + b248)) - 163*x193/(1e-6 + b248) + 6642.25*b248 - 100*b248)*
       (1e-6 + b248) =L= 0;

e385.. (sqr(x179/(1e-6 + b249)) - 98*x179/(1e-6 + b249) + 2401*b249 + sqr(x194/
       (1e-6 + b249)) - 163*x194/(1e-6 + b249) + 6642.25*b249 - 100*b249)*(1e-6
        + b249) =L= 0;

e386.. (sqr(x180/(1e-6 + b250)) - 91*x180/(1e-6 + b250) + 2070.25*b250 + sqr(
       x195/(1e-6 + b250)) - 167*x195/(1e-6 + b250) + 6972.25*b250 - 100*b250)*
       (1e-6 + b250) =L= 0;

e387.. (sqr(x181/(1e-6 + b251)) - 55*x181/(1e-6 + b251) + 756.25*b251 + sqr(
       x196/(1e-6 + b251)) - 106*x196/(1e-6 + b251) + 2809*b251 - 16*b251)*(
       1e-6 + b251) =L= 0;

e388.. (sqr(x182/(1e-6 + b252)) - 53*x182/(1e-6 + b252) + 702.25*b252 + sqr(
       x197/(1e-6 + b252)) - 105*x197/(1e-6 + b252) + 2756.25*b252 - 16*b252)*(
       1e-6 + b252) =L= 0;

e389.. (sqr(x183/(1e-6 + b253)) - 57*x183/(1e-6 + b253) + 812.25*b253 + sqr(
       x198/(1e-6 + b253)) - 103*x198/(1e-6 + b253) + 2652.25*b253 - 16*b253)*(
       1e-6 + b253) =L= 0;

e390.. (sqr(x184/(1e-6 + b254)) - 58*x184/(1e-6 + b254) + 841*b254 + sqr(x199/(
       1e-6 + b254)) - 103*x199/(1e-6 + b254) + 2652.25*b254 - 16*b254)*(1e-6
        + b254) =L= 0;

e391.. (sqr(x185/(1e-6 + b255)) - 51*x185/(1e-6 + b255) + 650.25*b255 + sqr(
       x200/(1e-6 + b255)) - 107*x200/(1e-6 + b255) + 2862.25*b255 - 16*b255)*(
       1e-6 + b255) =L= 0;

e392..    b241 + b246 + b251 =E= 1;

e393..    b242 + b247 + b252 =E= 1;

e394..    b243 + b248 + b253 =E= 1;

e395..    b244 + b249 + b254 =E= 1;

e396..    b245 + b250 + b255 =E= 1;

* set non-default bounds
x1.lo = 11.5; x1.up = 57.5;
x2.lo = 12.5; x2.up = 56.5;
x3.lo = 10.5; x3.up = 58.5;
x4.lo = 10; x4.up = 59;
x5.lo = 13.5; x5.up = 55.5;
x6.lo = 7; x6.up = 87;
x7.lo = 6.5; x7.up = 87.5;
x8.lo = 5.5; x8.up = 88.5;
x9.lo = 5.5; x9.up = 88.5;
x10.lo = 7.5; x10.up = 86.5;

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: 2018-05-28 Git hash: ac4a64c1
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