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Instance slay06h
Determine the optimal placement of a set of units with fixed width and length such that the Euclidean distance between their center point and a predefined "safety point" is minimized.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 32757.02000000 (ALPHAECP) 32757.01960000 (ANTIGONE) 32757.02015000 (BARON) 32757.02000000 (BONMIN) 32757.02000000 (COUENNE) 32757.02018000 (CPLEX) 32757.02018000 (GUROBI) 32757.02018000 (LINDO) 32757.02018000 (SCIP) 32757.02018000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | SLay06H.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQP |
| #Variablesⓘ | 342 |
| #Binary Variablesⓘ | 60 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 12 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 42 |
| #Nonlinear Nonzeros in Objectiveⓘ | 12 |
| #Constraintsⓘ | 435 |
| #Linear Constraintsⓘ | 435 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 1200 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 12 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 12 |
| #Blocks in Hessian of Lagrangianⓘ | 12 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 3.9000e+02 |
| Infeasibility of initial pointⓘ | 3.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 436 76 60 300 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 343 283 60 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1243 1231 12 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,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,b253,b254,b255,b256,b257,b258,b259
,b260,b261,b262,b263,b264,b265,b266,b267,b268,b269,b270,b271,b272
,b273,b274,b275,b276,b277,b278,b279,b280,b281,b282,b283,b284,b285
,b286,b287,b288,b289,b290,b291,b292,b293,b294,b295,b296,b297,b298
,b299,b300,b301,b302,b303,b304,b305,b306,b307,b308,b309,b310,b311
,b312,x313,x314,x315,x316,x317,x318,x319,x320,x321,x322,x323,x324
,x325,x326,x327,x328,x329,x330,x331,x332,x333,x334,x335,x336,x337
,x338,x339,x340,x341,x342,objvar;
Positive Variables 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,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,x313,x314,x315,x316,x317,x318,x319,x320,x321,x322,x323,x324
,x325,x326,x327,x328,x329,x330,x331,x332,x333,x334,x335,x336,x337
,x338,x339,x340,x341,x342;
Binary Variables b253,b254,b255,b256,b257,b258,b259,b260,b261,b262,b263,b264
,b265,b266,b267,b268,b269,b270,b271,b272,b273,b274,b275,b276,b277
,b278,b279,b280,b281,b282,b283,b284,b285,b286,b287,b288,b289,b290
,b291,b292,b293,b294,b295,b296,b297,b298,b299,b300,b301,b302,b303
,b304,b305,b306,b307,b308,b309,b310,b311,b312;
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,e412,e413,e414,e415
,e416,e417,e418,e419,e420,e421,e422,e423,e424,e425,e426,e427,e428
,e429,e430,e431,e432,e433,e434,e435,e436;
e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x7)) + 390*(sqr((-10) + x2) + sqr((-15
) + x8)) + 240*(sqr((-7) + x3) + sqr((-9) + x9)) + 70*(sqr((-3) + x4) +
sqr((-3) + x10)) + 165*(sqr((-20) + x5) + sqr((-17) + x11)) + 100*(sqr((-
18) + x6) + sqr((-8) + x12))) - 300*x313 - 240*x314 - 210*x315 - 140*x316
- 300*x317 - 100*x318 - 150*x319 - 220*x320 - 200*x321 - 120*x322
- 300*x323 - 150*x324 - 100*x325 - 120*x326 - 130*x327 - 300*x328
- 240*x329 - 210*x330 - 140*x331 - 300*x332 - 100*x333 - 150*x334
- 220*x335 - 200*x336 - 120*x337 - 300*x338 - 150*x339 - 100*x340
- 120*x341 - 130*x342 + objvar =E= 0;
e2.. - x1 + x2 + x313 =G= 0;
e3.. - x1 + x3 + x314 =G= 0;
e4.. - x1 + x4 + x315 =G= 0;
e5.. - x1 + x5 + x316 =G= 0;
e6.. - x1 + x6 + x317 =G= 0;
e7.. - x2 + x3 + x318 =G= 0;
e8.. - x2 + x4 + x319 =G= 0;
e9.. - x2 + x5 + x320 =G= 0;
e10.. - x2 + x6 + x321 =G= 0;
e11.. - x3 + x4 + x322 =G= 0;
e12.. - x3 + x5 + x323 =G= 0;
e13.. - x3 + x6 + x324 =G= 0;
e14.. - x4 + x5 + x325 =G= 0;
e15.. - x4 + x6 + x326 =G= 0;
e16.. - x5 + x6 + x327 =G= 0;
e17.. x1 - x2 + x313 =G= 0;
e18.. x1 - x3 + x314 =G= 0;
e19.. x1 - x4 + x315 =G= 0;
e20.. x1 - x5 + x316 =G= 0;
e21.. x1 - x6 + x317 =G= 0;
e22.. x2 - x3 + x318 =G= 0;
e23.. x2 - x4 + x319 =G= 0;
e24.. x2 - x5 + x320 =G= 0;
e25.. x2 - x6 + x321 =G= 0;
e26.. x3 - x4 + x322 =G= 0;
e27.. x3 - x5 + x323 =G= 0;
e28.. x3 - x6 + x324 =G= 0;
e29.. x4 - x5 + x325 =G= 0;
e30.. x4 - x6 + x326 =G= 0;
e31.. x5 - x6 + x327 =G= 0;
e32.. - x7 + x8 + x328 =G= 0;
e33.. - x7 + x9 + x329 =G= 0;
e34.. - x7 + x10 + x330 =G= 0;
e35.. - x7 + x11 + x331 =G= 0;
e36.. - x7 + x12 + x332 =G= 0;
e37.. - x8 + x9 + x333 =G= 0;
e38.. - x8 + x10 + x334 =G= 0;
e39.. - x8 + x11 + x335 =G= 0;
e40.. - x8 + x12 + x336 =G= 0;
e41.. - x9 + x10 + x337 =G= 0;
e42.. - x9 + x11 + x338 =G= 0;
e43.. - x9 + x12 + x339 =G= 0;
e44.. - x10 + x11 + x340 =G= 0;
e45.. - x10 + x12 + x341 =G= 0;
e46.. - x11 + x12 + x342 =G= 0;
e47.. x7 - x8 + x328 =G= 0;
e48.. x7 - x9 + x329 =G= 0;
e49.. x7 - x10 + x330 =G= 0;
e50.. x7 - x11 + x331 =G= 0;
e51.. x7 - x12 + x332 =G= 0;
e52.. x8 - x9 + x333 =G= 0;
e53.. x8 - x10 + x334 =G= 0;
e54.. x8 - x11 + x335 =G= 0;
e55.. x8 - x12 + x336 =G= 0;
e56.. x9 - x10 + x337 =G= 0;
e57.. x9 - x11 + x338 =G= 0;
e58.. x9 - x12 + x339 =G= 0;
e59.. x10 - x11 + x340 =G= 0;
e60.. x10 - x12 + x341 =G= 0;
e61.. x11 - x12 + x342 =G= 0;
e62.. x1 - x13 - x18 - x23 - x28 =E= 0;
e63.. x1 - x14 - x19 - x24 - x29 =E= 0;
e64.. x1 - x15 - x20 - x25 - x30 =E= 0;
e65.. x1 - x16 - x21 - x26 - x31 =E= 0;
e66.. x1 - x17 - x22 - x27 - x32 =E= 0;
e67.. x2 - x33 - x38 - x43 - x48 =E= 0;
e68.. x2 - x34 - x39 - x44 - x49 =E= 0;
e69.. x2 - x35 - x40 - x45 - x50 =E= 0;
e70.. x2 - x36 - x41 - x46 - x51 =E= 0;
e71.. x2 - x37 - x42 - x47 - x52 =E= 0;
e72.. x3 - x53 - x58 - x63 - x68 =E= 0;
e73.. x3 - x54 - x59 - x64 - x69 =E= 0;
e74.. x3 - x55 - x60 - x65 - x70 =E= 0;
e75.. x3 - x56 - x61 - x66 - x71 =E= 0;
e76.. x3 - x57 - x62 - x67 - x72 =E= 0;
e77.. x4 - x73 - x78 - x83 - x88 =E= 0;
e78.. x4 - x74 - x79 - x84 - x89 =E= 0;
e79.. x4 - x75 - x80 - x85 - x90 =E= 0;
e80.. x4 - x76 - x81 - x86 - x91 =E= 0;
e81.. x4 - x77 - x82 - x87 - x92 =E= 0;
e82.. x5 - x93 - x98 - x103 - x108 =E= 0;
e83.. x5 - x94 - x99 - x104 - x109 =E= 0;
e84.. x5 - x95 - x100 - x105 - x110 =E= 0;
e85.. x5 - x96 - x101 - x106 - x111 =E= 0;
e86.. x5 - x97 - x102 - x107 - x112 =E= 0;
e87.. x6 - x113 - x118 - x123 - x128 =E= 0;
e88.. x6 - x114 - x119 - x124 - x129 =E= 0;
e89.. x6 - x115 - x120 - x125 - x130 =E= 0;
e90.. x6 - x116 - x121 - x126 - x131 =E= 0;
e91.. x6 - x117 - x122 - x127 - x132 =E= 0;
e92.. x7 - x133 - x138 - x143 - x148 =E= 0;
e93.. x7 - x134 - x139 - x144 - x149 =E= 0;
e94.. x7 - x135 - x140 - x145 - x150 =E= 0;
e95.. x7 - x136 - x141 - x146 - x151 =E= 0;
e96.. x7 - x137 - x142 - x147 - x152 =E= 0;
e97.. x8 - x153 - x158 - x163 - x168 =E= 0;
e98.. x8 - x154 - x159 - x164 - x169 =E= 0;
e99.. x8 - x155 - x160 - x165 - x170 =E= 0;
e100.. x8 - x156 - x161 - x166 - x171 =E= 0;
e101.. x8 - x157 - x162 - x167 - x172 =E= 0;
e102.. x9 - x173 - x178 - x183 - x188 =E= 0;
e103.. x9 - x174 - x179 - x184 - x189 =E= 0;
e104.. x9 - x175 - x180 - x185 - x190 =E= 0;
e105.. x9 - x176 - x181 - x186 - x191 =E= 0;
e106.. x9 - x177 - x182 - x187 - x192 =E= 0;
e107.. x10 - x193 - x198 - x203 - x208 =E= 0;
e108.. x10 - x194 - x199 - x204 - x209 =E= 0;
e109.. x10 - x195 - x200 - x205 - x210 =E= 0;
e110.. x10 - x196 - x201 - x206 - x211 =E= 0;
e111.. x10 - x197 - x202 - x207 - x212 =E= 0;
e112.. x11 - x213 - x218 - x223 - x228 =E= 0;
e113.. x11 - x214 - x219 - x224 - x229 =E= 0;
e114.. x11 - x215 - x220 - x225 - x230 =E= 0;
e115.. x11 - x216 - x221 - x226 - x231 =E= 0;
e116.. x11 - x217 - x222 - x227 - x232 =E= 0;
e117.. x12 - x233 - x238 - x243 - x248 =E= 0;
e118.. x12 - x234 - x239 - x244 - x249 =E= 0;
e119.. x12 - x235 - x240 - x245 - x250 =E= 0;
e120.. x12 - x236 - x241 - x246 - x251 =E= 0;
e121.. x12 - x237 - x242 - x247 - x252 =E= 0;
e122.. x13 - 27.5*b253 =L= 0;
e123.. x14 - 27.5*b254 =L= 0;
e124.. x15 - 27.5*b255 =L= 0;
e125.. x16 - 27.5*b256 =L= 0;
e126.. x17 - 27.5*b257 =L= 0;
e127.. x18 - 27.5*b268 =L= 0;
e128.. x19 - 27.5*b269 =L= 0;
e129.. x20 - 27.5*b270 =L= 0;
e130.. x21 - 27.5*b271 =L= 0;
e131.. x22 - 27.5*b272 =L= 0;
e132.. x23 - 27.5*b283 =L= 0;
e133.. x24 - 27.5*b284 =L= 0;
e134.. x25 - 27.5*b285 =L= 0;
e135.. x26 - 27.5*b286 =L= 0;
e136.. x27 - 27.5*b287 =L= 0;
e137.. x28 - 27.5*b298 =L= 0;
e138.. x29 - 27.5*b299 =L= 0;
e139.. x30 - 27.5*b300 =L= 0;
e140.. x31 - 27.5*b301 =L= 0;
e141.. x32 - 27.5*b302 =L= 0;
e142.. x33 - 27.5*b253 =L= 0;
e143.. x34 - 26.5*b258 =L= 0;
e144.. x35 - 26.5*b259 =L= 0;
e145.. x36 - 26.5*b260 =L= 0;
e146.. x37 - 26.5*b261 =L= 0;
e147.. x38 - 27.5*b268 =L= 0;
e148.. x39 - 26.5*b273 =L= 0;
e149.. x40 - 26.5*b274 =L= 0;
e150.. x41 - 26.5*b275 =L= 0;
e151.. x42 - 26.5*b276 =L= 0;
e152.. x43 - 27.5*b283 =L= 0;
e153.. x44 - 26.5*b288 =L= 0;
e154.. x45 - 26.5*b289 =L= 0;
e155.. x46 - 26.5*b290 =L= 0;
e156.. x47 - 26.5*b291 =L= 0;
e157.. x48 - 27.5*b298 =L= 0;
e158.. x49 - 26.5*b303 =L= 0;
e159.. x50 - 26.5*b304 =L= 0;
e160.. x51 - 26.5*b305 =L= 0;
e161.. x52 - 26.5*b306 =L= 0;
e162.. x53 - 27.5*b254 =L= 0;
e163.. x54 - 26.5*b258 =L= 0;
e164.. x55 - 28.5*b262 =L= 0;
e165.. x56 - 28.5*b263 =L= 0;
e166.. x57 - 28.5*b264 =L= 0;
e167.. x58 - 27.5*b269 =L= 0;
e168.. x59 - 26.5*b273 =L= 0;
e169.. x60 - 28.5*b277 =L= 0;
e170.. x61 - 28.5*b278 =L= 0;
e171.. x62 - 28.5*b279 =L= 0;
e172.. x63 - 27.5*b284 =L= 0;
e173.. x64 - 26.5*b288 =L= 0;
e174.. x65 - 28.5*b292 =L= 0;
e175.. x66 - 28.5*b293 =L= 0;
e176.. x67 - 28.5*b294 =L= 0;
e177.. x68 - 27.5*b299 =L= 0;
e178.. x69 - 26.5*b303 =L= 0;
e179.. x70 - 28.5*b307 =L= 0;
e180.. x71 - 28.5*b308 =L= 0;
e181.. x72 - 28.5*b309 =L= 0;
e182.. x73 - 27.5*b255 =L= 0;
e183.. x74 - 26.5*b259 =L= 0;
e184.. x75 - 28.5*b262 =L= 0;
e185.. x76 - 29*b265 =L= 0;
e186.. x77 - 29*b266 =L= 0;
e187.. x78 - 27.5*b270 =L= 0;
e188.. x79 - 26.5*b274 =L= 0;
e189.. x80 - 28.5*b277 =L= 0;
e190.. x81 - 29*b280 =L= 0;
e191.. x82 - 29*b281 =L= 0;
e192.. x83 - 27.5*b285 =L= 0;
e193.. x84 - 26.5*b289 =L= 0;
e194.. x85 - 28.5*b292 =L= 0;
e195.. x86 - 29*b295 =L= 0;
e196.. x87 - 29*b296 =L= 0;
e197.. x88 - 27.5*b300 =L= 0;
e198.. x89 - 26.5*b304 =L= 0;
e199.. x90 - 28.5*b307 =L= 0;
e200.. x91 - 29*b310 =L= 0;
e201.. x92 - 29*b311 =L= 0;
e202.. x93 - 27.5*b256 =L= 0;
e203.. x94 - 26.5*b260 =L= 0;
e204.. x95 - 28.5*b263 =L= 0;
e205.. x96 - 29*b265 =L= 0;
e206.. x97 - 28*b267 =L= 0;
e207.. x98 - 27.5*b271 =L= 0;
e208.. x99 - 26.5*b275 =L= 0;
e209.. x100 - 28.5*b278 =L= 0;
e210.. x101 - 29*b280 =L= 0;
e211.. x102 - 28*b282 =L= 0;
e212.. x103 - 27.5*b286 =L= 0;
e213.. x104 - 26.5*b290 =L= 0;
e214.. x105 - 28.5*b293 =L= 0;
e215.. x106 - 29*b295 =L= 0;
e216.. x107 - 28*b297 =L= 0;
e217.. x108 - 27.5*b301 =L= 0;
e218.. x109 - 26.5*b305 =L= 0;
e219.. x110 - 28.5*b308 =L= 0;
e220.. x111 - 29*b310 =L= 0;
e221.. x112 - 28*b312 =L= 0;
e222.. x113 - 27.5*b257 =L= 0;
e223.. x114 - 26.5*b261 =L= 0;
e224.. x115 - 28.5*b264 =L= 0;
e225.. x116 - 29*b266 =L= 0;
e226.. x117 - 28*b267 =L= 0;
e227.. x118 - 27.5*b272 =L= 0;
e228.. x119 - 26.5*b276 =L= 0;
e229.. x120 - 28.5*b279 =L= 0;
e230.. x121 - 29*b281 =L= 0;
e231.. x122 - 28*b282 =L= 0;
e232.. x123 - 27.5*b287 =L= 0;
e233.. x124 - 26.5*b291 =L= 0;
e234.. x125 - 28.5*b294 =L= 0;
e235.. x126 - 29*b296 =L= 0;
e236.. x127 - 28*b297 =L= 0;
e237.. x128 - 27.5*b302 =L= 0;
e238.. x129 - 26.5*b306 =L= 0;
e239.. x130 - 28.5*b309 =L= 0;
e240.. x131 - 29*b311 =L= 0;
e241.. x132 - 28*b312 =L= 0;
e242.. x133 - 27*b253 =L= 0;
e243.. x134 - 27*b254 =L= 0;
e244.. x135 - 27*b255 =L= 0;
e245.. x136 - 27*b256 =L= 0;
e246.. x137 - 27*b257 =L= 0;
e247.. x138 - 27*b268 =L= 0;
e248.. x139 - 27*b269 =L= 0;
e249.. x140 - 27*b270 =L= 0;
e250.. x141 - 27*b271 =L= 0;
e251.. x142 - 27*b272 =L= 0;
e252.. x143 - 27*b283 =L= 0;
e253.. x144 - 27*b284 =L= 0;
e254.. x145 - 27*b285 =L= 0;
e255.. x146 - 27*b286 =L= 0;
e256.. x147 - 27*b287 =L= 0;
e257.. x148 - 27*b298 =L= 0;
e258.. x149 - 27*b299 =L= 0;
e259.. x150 - 27*b300 =L= 0;
e260.. x151 - 27*b301 =L= 0;
e261.. x152 - 27*b302 =L= 0;
e262.. x153 - 27*b253 =L= 0;
e263.. x154 - 27.5*b258 =L= 0;
e264.. x155 - 27.5*b259 =L= 0;
e265.. x156 - 27.5*b260 =L= 0;
e266.. x157 - 27.5*b261 =L= 0;
e267.. x158 - 27*b268 =L= 0;
e268.. x159 - 27.5*b273 =L= 0;
e269.. x160 - 27.5*b274 =L= 0;
e270.. x161 - 27.5*b275 =L= 0;
e271.. x162 - 27.5*b276 =L= 0;
e272.. x163 - 27*b283 =L= 0;
e273.. x164 - 27.5*b288 =L= 0;
e274.. x165 - 27.5*b289 =L= 0;
e275.. x166 - 27.5*b290 =L= 0;
e276.. x167 - 27.5*b291 =L= 0;
e277.. x168 - 27*b298 =L= 0;
e278.. x169 - 27.5*b303 =L= 0;
e279.. x170 - 27.5*b304 =L= 0;
e280.. x171 - 27.5*b305 =L= 0;
e281.. x172 - 27.5*b306 =L= 0;
e282.. x173 - 27*b254 =L= 0;
e283.. x174 - 27.5*b258 =L= 0;
e284.. x175 - 28.5*b262 =L= 0;
e285.. x176 - 28.5*b263 =L= 0;
e286.. x177 - 28.5*b264 =L= 0;
e287.. x178 - 27*b269 =L= 0;
e288.. x179 - 27.5*b273 =L= 0;
e289.. x180 - 28.5*b277 =L= 0;
e290.. x181 - 28.5*b278 =L= 0;
e291.. x182 - 28.5*b279 =L= 0;
e292.. x183 - 27*b284 =L= 0;
e293.. x184 - 27.5*b288 =L= 0;
e294.. x185 - 28.5*b292 =L= 0;
e295.. x186 - 28.5*b293 =L= 0;
e296.. x187 - 28.5*b294 =L= 0;
e297.. x188 - 27*b299 =L= 0;
e298.. x189 - 27.5*b303 =L= 0;
e299.. x190 - 28.5*b307 =L= 0;
e300.. x191 - 28.5*b308 =L= 0;
e301.. x192 - 28.5*b309 =L= 0;
e302.. x193 - 27*b255 =L= 0;
e303.. x194 - 27.5*b259 =L= 0;
e304.. x195 - 28.5*b262 =L= 0;
e305.. x196 - 28.5*b265 =L= 0;
e306.. x197 - 28.5*b266 =L= 0;
e307.. x198 - 27*b270 =L= 0;
e308.. x199 - 27.5*b274 =L= 0;
e309.. x200 - 28.5*b277 =L= 0;
e310.. x201 - 28.5*b280 =L= 0;
e311.. x202 - 28.5*b281 =L= 0;
e312.. x203 - 27*b285 =L= 0;
e313.. x204 - 27.5*b289 =L= 0;
e314.. x205 - 28.5*b292 =L= 0;
e315.. x206 - 28.5*b295 =L= 0;
e316.. x207 - 28.5*b296 =L= 0;
e317.. x208 - 27*b300 =L= 0;
e318.. x209 - 27.5*b304 =L= 0;
e319.. x210 - 28.5*b307 =L= 0;
e320.. x211 - 28.5*b310 =L= 0;
e321.. x212 - 28.5*b311 =L= 0;
e322.. x213 - 27*b256 =L= 0;
e323.. x214 - 27.5*b260 =L= 0;
e324.. x215 - 28.5*b263 =L= 0;
e325.. x216 - 28.5*b265 =L= 0;
e326.. x217 - 28*b267 =L= 0;
e327.. x218 - 27*b271 =L= 0;
e328.. x219 - 27.5*b275 =L= 0;
e329.. x220 - 28.5*b278 =L= 0;
e330.. x221 - 28.5*b280 =L= 0;
e331.. x222 - 28*b282 =L= 0;
e332.. x223 - 27*b286 =L= 0;
e333.. x224 - 27.5*b290 =L= 0;
e334.. x225 - 28.5*b293 =L= 0;
e335.. x226 - 28.5*b295 =L= 0;
e336.. x227 - 28*b297 =L= 0;
e337.. x228 - 27*b301 =L= 0;
e338.. x229 - 27.5*b305 =L= 0;
e339.. x230 - 28.5*b308 =L= 0;
e340.. x231 - 28.5*b310 =L= 0;
e341.. x232 - 28*b312 =L= 0;
e342.. x233 - 27*b257 =L= 0;
e343.. x234 - 27.5*b261 =L= 0;
e344.. x235 - 28.5*b264 =L= 0;
e345.. x236 - 28.5*b266 =L= 0;
e346.. x237 - 28*b267 =L= 0;
e347.. x238 - 27*b272 =L= 0;
e348.. x239 - 27.5*b276 =L= 0;
e349.. x240 - 28.5*b279 =L= 0;
e350.. x241 - 28.5*b281 =L= 0;
e351.. x242 - 28*b282 =L= 0;
e352.. x243 - 27*b287 =L= 0;
e353.. x244 - 27.5*b291 =L= 0;
e354.. x245 - 28.5*b294 =L= 0;
e355.. x246 - 28.5*b296 =L= 0;
e356.. x247 - 28*b297 =L= 0;
e357.. x248 - 27*b302 =L= 0;
e358.. x249 - 27.5*b306 =L= 0;
e359.. x250 - 28.5*b309 =L= 0;
e360.. x251 - 28.5*b311 =L= 0;
e361.. x252 - 28*b312 =L= 0;
e362.. x13 - x33 + 6*b253 =L= 0;
e363.. x14 - x53 + 4*b254 =L= 0;
e364.. x15 - x73 + 3.5*b255 =L= 0;
e365.. x16 - x93 + 4.5*b256 =L= 0;
e366.. x17 - x113 + 5*b257 =L= 0;
e367.. x34 - x54 + 5*b258 =L= 0;
e368.. x35 - x74 + 4.5*b259 =L= 0;
e369.. x36 - x94 + 5.5*b260 =L= 0;
e370.. x37 - x114 + 6*b261 =L= 0;
e371.. x55 - x75 + 2.5*b262 =L= 0;
e372.. x56 - x95 + 3.5*b263 =L= 0;
e373.. x57 - x115 + 4*b264 =L= 0;
e374.. x76 - x96 + 3*b265 =L= 0;
e375.. x77 - x116 + 3.5*b266 =L= 0;
e376.. x97 - x117 + 4.5*b267 =L= 0;
e377.. - x18 + x38 + 6*b268 =L= 0;
e378.. - x19 + x58 + 4*b269 =L= 0;
e379.. - x20 + x78 + 3.5*b270 =L= 0;
e380.. - x21 + x98 + 4.5*b271 =L= 0;
e381.. - x22 + x118 + 5*b272 =L= 0;
e382.. - x39 + x59 + 5*b273 =L= 0;
e383.. - x40 + x79 + 4.5*b274 =L= 0;
e384.. - x41 + x99 + 5.5*b275 =L= 0;
e385.. - x42 + x119 + 6*b276 =L= 0;
e386.. - x60 + x80 + 2.5*b277 =L= 0;
e387.. - x61 + x100 + 3.5*b278 =L= 0;
e388.. - x62 + x120 + 4*b279 =L= 0;
e389.. - x81 + x101 + 3*b280 =L= 0;
e390.. - x82 + x121 + 3.5*b281 =L= 0;
e391.. - x102 + x122 + 4.5*b282 =L= 0;
e392.. x143 - x163 + 5.5*b283 =L= 0;
e393.. x144 - x183 + 4.5*b284 =L= 0;
e394.. x145 - x203 + 4.5*b285 =L= 0;
e395.. x146 - x223 + 5*b286 =L= 0;
e396.. x147 - x243 + 4*b287 =L= 0;
e397.. x164 - x184 + 4*b288 =L= 0;
e398.. x165 - x204 + 4*b289 =L= 0;
e399.. x166 - x224 + 4.5*b290 =L= 0;
e400.. x167 - x244 + 3.5*b291 =L= 0;
e401.. x185 - x205 + 3*b292 =L= 0;
e402.. x186 - x225 + 3.5*b293 =L= 0;
e403.. x187 - x245 + 2.5*b294 =L= 0;
e404.. x206 - x226 + 3.5*b295 =L= 0;
e405.. x207 - x246 + 2.5*b296 =L= 0;
e406.. x227 - x247 + 3*b297 =L= 0;
e407.. - x148 + x168 + 5.5*b298 =L= 0;
e408.. - x149 + x188 + 4.5*b299 =L= 0;
e409.. - x150 + x208 + 4.5*b300 =L= 0;
e410.. - x151 + x228 + 5*b301 =L= 0;
e411.. - x152 + x248 + 4*b302 =L= 0;
e412.. - x169 + x189 + 4*b303 =L= 0;
e413.. - x170 + x209 + 4*b304 =L= 0;
e414.. - x171 + x229 + 4.5*b305 =L= 0;
e415.. - x172 + x249 + 3.5*b306 =L= 0;
e416.. - x190 + x210 + 3*b307 =L= 0;
e417.. - x191 + x230 + 3.5*b308 =L= 0;
e418.. - x192 + x250 + 2.5*b309 =L= 0;
e419.. - x211 + x231 + 3.5*b310 =L= 0;
e420.. - x212 + x251 + 2.5*b311 =L= 0;
e421.. - x232 + x252 + 3*b312 =L= 0;
e422.. b253 + b268 + b283 + b298 =E= 1;
e423.. b254 + b269 + b284 + b299 =E= 1;
e424.. b255 + b270 + b285 + b300 =E= 1;
e425.. b256 + b271 + b286 + b301 =E= 1;
e426.. b257 + b272 + b287 + b302 =E= 1;
e427.. b258 + b273 + b288 + b303 =E= 1;
e428.. b259 + b274 + b289 + b304 =E= 1;
e429.. b260 + b275 + b290 + b305 =E= 1;
e430.. b261 + b276 + b291 + b306 =E= 1;
e431.. b262 + b277 + b292 + b307 =E= 1;
e432.. b263 + b278 + b293 + b308 =E= 1;
e433.. b264 + b279 + b294 + b309 =E= 1;
e434.. b265 + b280 + b295 + b310 =E= 1;
e435.. b266 + b281 + b296 + b311 =E= 1;
e436.. b267 + b282 + b297 + b312 =E= 1;
* set non-default bounds
x1.lo = 2.5; x1.up = 27.5;
x2.lo = 3.5; x2.up = 26.5;
x3.lo = 1.5; x3.up = 28.5;
x4.lo = 1; x4.up = 29;
x5.lo = 2; x5.up = 28;
x6.lo = 2.5; x6.up = 27.5;
x7.lo = 3; x7.up = 27;
x8.lo = 2.5; x8.up = 27.5;
x9.lo = 1.5; x9.up = 28.5;
x10.lo = 1.5; x10.up = 28.5;
x11.lo = 2; x11.up = 28;
x12.lo = 1; x12.up = 29;
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