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Instance gabriel01
The question to answer is to find the minimum value of k such that the k-Gabriel graph of any set of points in the plane is Hamiltonian. A known upper bound on k is 10. Infeasibility of this instance would give some indication for lower bounds on k.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 45.76046529 (ANTIGONE) 45.24444821 (BARON) 45.97971263 (COUENNE) 45.24444872 (GUROBI) 46.12113334 (LINDO) 45.24444885 (SCIP) 47.64330000 (SHOT) |
| Referencesⓘ | Kaiser, Tomáš, Saumell, Maria, and Cleemput, Nico Van, 10-Gabriel graphs are Hamiltonian, Information Processing Letters, 115:11, 2015, 877-881. |
| Sourceⓘ | QPLIB instance 0681, contributed by Maria Saumell |
| Applicationⓘ | Computational geometry |
| Added to libraryⓘ | 18 Aug 2018 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 215 |
| #Binary Variablesⓘ | 72 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 100 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 142 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 467 |
| #Linear Constraintsⓘ | 419 |
| #Quadratic Constraintsⓘ | 48 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 1647 |
| #Nonlinear Nonzeros in Jacobianⓘ | 512 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 416 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 12 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 5 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 10 |
| Average blocksize in Hessian of Lagrangianⓘ | 8.333333 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-02 |
| Maximal coefficientⓘ | 9.5200e+00 |
| Infeasibility of initial pointⓘ | 1.9 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 468 72 24 372 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 216 144 72 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1790 1278 512 0
*
* Solve m using MIQCP maximizing objvar;
Variables objvar,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,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102
,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115
,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128
,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141
,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154
,b155,b156,b157,b158,b159,x160,x161,x162,x163,x164,x165,x166,x167
,x168,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180
,x181,x182,b183,b184,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;
Positive Variables 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,x78,x79,x80,x81,x86,x87,x88,x89,x160,x161,x162
,x163,x164,x165,x166,x167,x168,x169,x170,x171,x172,x173,x174,x175
,x176,x177,x178,x179,x180,x181,x182,x193,x194,x195,x196,x197,x198
,x199,x200,x209,x210,x211,x212,x213,x214,x215,x216;
Binary Variables b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b183,b184;
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,e437,e438,e439,e440,e441
,e442,e443,e444,e445,e446,e447,e448,e449,e450,e451,e452,e453,e454
,e455,e456,e457,e458,e459,e460,e461,e462,e463,e464,e465,e466,e467
,e468;
e1.. - objvar - 0.45*x2 - 0.45*x3 - 0.45*x4 - 0.67*x5 - 0.67*x6 - 0.67*x7
- 1.03*x8 - 1.03*x9 - 1.03*x10 - 1.75*x11 - 1.75*x12 - 1.75*x13
- 1.57*x14 - 1.57*x15 - 1.57*x16 - 1.05*x17 - 1.05*x18 - 1.05*x19
- 0.13*x20 - 0.13*x21 - 0.13*x22 - 0.47*x23 - 0.47*x24 - 0.47*x25
- 0.34*x26 - 0.34*x27 - 0.34*x28 + 8.81*x29 + 8.81*x30 + 9.07*x31
+ 9.07*x32 - 0.6*x33 - 0.6*x34 - 0.6*x35 - 0.65*x36 - 0.65*x37 - 0.65*x38
- 0.75*x39 - 0.75*x40 - 0.75*x41 + 9.52*x42 + 9.52*x43 + 9.52*x44
+ 8.69*x45 + 8.69*x46 - 0.83*x47 - 0.83*x48 - 0.83*x49 - x50 - x51 - x52
- 0.44*x53 - 0.44*x54 - 0.44*x55 + 8.64*x56 + 8.64*x57 + 8.64*x58
+ 8.83*x59 + 8.83*x60 - 0.87*x61 - 0.87*x62 - 0.87*x63 - 0.4*x64
- 0.4*x65 - 0.4*x66 - 0.8*x67 - 0.8*x68 - 0.8*x69 + 8.69*x70 + 8.69*x71
+ 9.34*x72 + 9.34*x73 - 0.2*b90 - 0.2*b91 - 0.2*b92 - 0.62*b93 - 0.62*b94
- 0.62*b95 - 0.35*b96 - 0.35*b97 - 0.35*b98 - 0.76*b99 - 0.76*b100
- 0.76*b101 - 0.38*b102 - 0.38*b103 - 0.38*b104 - 0.08*b105 - 0.08*b106
- 0.08*b107 - 0.93*b108 - 0.93*b109 - 0.93*b110 - 0.57*b111 - 0.57*b112
- 0.57*b113 - 0.01*b114 - 0.01*b115 - 0.01*b116 - 0.16*b117 - 0.16*b118
- 0.31*b119 - 0.31*b120 - 0.17*b121 - 0.17*b122 - 0.17*b123 - 0.26*b124
- 0.26*b125 - 0.26*b126 - 0.69*b127 - 0.69*b128 - 0.69*b129 - 0.45*b130
- 0.45*b131 - 0.45*b132 - 0.23*b133 - 0.23*b134 - 0.15*b135 - 0.15*b136
- 0.15*b137 - 0.54*b138 - 0.54*b139 - 0.54*b140 - 0.08*b141 - 0.08*b142
- 0.08*b143 - 0.11*b144 - 0.11*b145 - 0.11*b146 - 0.82*b147 - 0.82*b148
- 0.82*b149 - 0.08*b150 - 0.08*b151 - 0.08*b152 - 0.26*b153 - 0.26*b154
- 0.26*b155 - 0.43*b156 - 0.43*b157 - 0.18*b158 - 0.18*b159 =E= 0;
e2.. x2 + x5 + x8 + x160 =E= 1.9;
e3.. x11 + x14 + x17 + x161 =E= 1.8;
e4.. - x11 + x20 + x23 + x26 - x33 - x47 - x61 + x162 =E= 0.3;
e5.. - x2 - x14 - x20 + x33 + x36 + x39 + x42 - x50 - x64 + x163 =E= 1.8;
e6.. - x5 - x17 - x23 - x36 + x47 + x50 + x53 + x56 - x67 + x164 =E= 1.3;
e7.. - x8 - x26 - x39 - x53 + x61 + x64 + x67 + x165 =E= 0.2;
e8.. - x42 - x56 + x166 =E= -0.35;
e9.. x3 + x6 + x9 - x160 + x167 =E= 0.1;
e10.. x4 + x7 + x10 - x167 + x168 =E= 0.7;
e11.. x12 + x15 + x18 - x161 + x169 =E= 0.8;
e12.. x13 + x16 + x19 - x169 + x170 =E= 0.3;
e13.. - x12 + x21 + x24 + x27 + x29 + x31 - x34 - x48 - x62 - x162 + x171
=E= 0;
e14.. - x13 + x22 + x25 + x28 + x30 + x32 - x35 - x49 - x63 - x171 + x172
=E= 0;
e15.. - x3 - x15 - x21 + x34 + x37 + x40 + x43 + x45 - x51 - x65 - x163 + x173
=E= 0;
e16.. - x4 - x16 - x22 + x35 + x38 + x41 + x44 + x46 - x52 - x66 - x173 + x174
=E= 0;
e17.. - x6 - x18 - x24 - x37 + x48 + x51 + x54 + x57 + x59 - x68 - x164 + x175
=E= 0;
e18.. - x7 - x19 - x25 - x38 + x49 + x52 + x55 + x58 + x60 - x69 - x175 + x176
=E= 0;
e19.. - x9 - x27 - x40 - x54 + x62 + x65 + x68 + x70 + x72 - x165 + x177 =E= 0
;
e20.. - x10 - x28 - x41 - x55 + x63 + x66 + x69 + x71 + x73 - x177 + x178
=E= 0;
e21.. - x29 - x43 - x57 - x70 - x166 + x179 =E= -0.44;
e22.. - x30 - x44 - x58 - x71 - x179 + x180 =E= -0.77;
e23.. - x31 - x45 - x59 - x72 + x181 =E= 0.69;
e24.. - x32 - x46 - x60 - x73 - x181 + x182 =E= -0.8;
e25.. x2 - b90 =L= 0;
e26.. x3 - b91 =L= 0;
e27.. x4 - b92 =L= 0;
e28.. x5 - b93 =L= 0;
e29.. x6 - b94 =L= 0;
e30.. x7 - b95 =L= 0;
e31.. x8 - b96 =L= 0;
e32.. x9 - b97 =L= 0;
e33.. x10 - b98 =L= 0;
e34.. x11 - b99 =L= 0;
e35.. x12 - b100 =L= 0;
e36.. x13 - b101 =L= 0;
e37.. x14 - b102 =L= 0;
e38.. x15 - b103 =L= 0;
e39.. x16 - b104 =L= 0;
e40.. x17 - b105 =L= 0;
e41.. x18 - b106 =L= 0;
e42.. x19 - b107 =L= 0;
e43.. x20 - b108 =L= 0;
e44.. x21 - b109 =L= 0;
e45.. x22 - b110 =L= 0;
e46.. x23 - b111 =L= 0;
e47.. x24 - b112 =L= 0;
e48.. x25 - b113 =L= 0;
e49.. x26 - b114 =L= 0;
e50.. x27 - b115 =L= 0;
e51.. x28 - b116 =L= 0;
e52.. x29 - b117 =L= 0;
e53.. x30 - b118 =L= 0;
e54.. x31 - b119 =L= 0;
e55.. x32 - b120 =L= 0;
e56.. x33 - b121 =L= 0;
e57.. x34 - b122 =L= 0;
e58.. x35 - b123 =L= 0;
e59.. x36 - b124 =L= 0;
e60.. x37 - b125 =L= 0;
e61.. x38 - b126 =L= 0;
e62.. x39 - b127 =L= 0;
e63.. x40 - b128 =L= 0;
e64.. x41 - b129 =L= 0;
e65.. x42 - b130 =L= 0;
e66.. x43 - b131 =L= 0;
e67.. x44 - b132 =L= 0;
e68.. x45 - b133 =L= 0;
e69.. x46 - b134 =L= 0;
e70.. x47 - b135 =L= 0;
e71.. x48 - b136 =L= 0;
e72.. x49 - b137 =L= 0;
e73.. x50 - b138 =L= 0;
e74.. x51 - b139 =L= 0;
e75.. x52 - b140 =L= 0;
e76.. x53 - b141 =L= 0;
e77.. x54 - b142 =L= 0;
e78.. x55 - b143 =L= 0;
e79.. x56 - b144 =L= 0;
e80.. x57 - b145 =L= 0;
e81.. x58 - b146 =L= 0;
e82.. x59 - b183 =L= 0;
e83.. x60 - b184 =L= 0;
e84.. x61 - b147 =L= 0;
e85.. x62 - b148 =L= 0;
e86.. x63 - b149 =L= 0;
e87.. x64 - b150 =L= 0;
e88.. x65 - b151 =L= 0;
e89.. x66 - b152 =L= 0;
e90.. x67 - b153 =L= 0;
e91.. x68 - b154 =L= 0;
e92.. x69 - b155 =L= 0;
e93.. x70 - b156 =L= 0;
e94.. x71 - b157 =L= 0;
e95.. x72 - b158 =L= 0;
e96.. x73 - b159 =L= 0;
e97.. 0.1*b119 - x185 =L= -0.7;
e98.. 0.1*b120 - x186 =L= -0.7;
e99.. 0.1*b133 - x187 =L= -0.7;
e100.. 0.1*b134 - x188 =L= -0.7;
e101.. 0.1*b183 - x189 =L= -0.7;
e102.. 0.1*b184 - x190 =L= -0.7;
e103.. 0.1*b158 - x191 =L= -0.7;
e104.. 0.1*b159 - x192 =L= -0.7;
e105.. 0.5*b117 - x193 =L= 0;
e106.. 0.5*b118 - x194 =L= 0;
e107.. 0.1*b119 - x193 =L= 0;
e108.. 0.1*b120 - x194 =L= 0;
e109.. 0.5*b131 - x195 =L= 0;
e110.. 0.5*b132 - x196 =L= 0;
e111.. 0.1*b133 - x195 =L= 0;
e112.. 0.1*b134 - x196 =L= 0;
e113.. 0.5*b145 - x197 =L= 0;
e114.. 0.5*b146 - x198 =L= 0;
e115.. 0.1*b183 - x197 =L= 0;
e116.. 0.1*b184 - x198 =L= 0;
e117.. 0.5*b156 - x199 =L= 0;
e118.. 0.5*b157 - x200 =L= 0;
e119.. 0.1*b158 - x199 =L= 0;
e120.. 0.1*b159 - x200 =L= 0;
e121.. 0.05*b117 - x201 =L= -0.66;
e122.. 0.05*b118 - x202 =L= -0.66;
e123.. 0.13*b119 - x201 =L= -0.66;
e124.. 0.13*b120 - x202 =L= -0.66;
e125.. 0.05*b131 - x203 =L= -0.66;
e126.. 0.05*b132 - x204 =L= -0.66;
e127.. 0.13*b133 - x203 =L= -0.66;
e128.. 0.13*b134 - x204 =L= -0.66;
e129.. 0.05*b145 - x205 =L= -0.66;
e130.. 0.05*b146 - x206 =L= -0.66;
e131.. 0.13*b183 - x205 =L= -0.66;
e132.. 0.13*b184 - x206 =L= -0.66;
e133.. 0.05*b156 - x207 =L= -0.66;
e134.. 0.05*b157 - x208 =L= -0.66;
e135.. 0.13*b158 - x207 =L= -0.66;
e136.. 0.13*b159 - x208 =L= -0.66;
e137.. 0.48*b117 - x209 =L= 0;
e138.. 0.48*b118 - x210 =L= 0;
e139.. 0.09*b119 - x209 =L= 0;
e140.. 0.09*b120 - x210 =L= 0;
e141.. 0.48*b131 - x211 =L= 0;
e142.. 0.48*b132 - x212 =L= 0;
e143.. 0.09*b133 - x211 =L= 0;
e144.. 0.09*b134 - x212 =L= 0;
e145.. 0.48*b145 - x213 =L= 0;
e146.. 0.48*b146 - x214 =L= 0;
e147.. 0.09*b183 - x213 =L= 0;
e148.. 0.09*b184 - x214 =L= 0;
e149.. 0.48*b156 - x215 =L= 0;
e150.. 0.48*b157 - x216 =L= 0;
e151.. 0.09*b158 - x215 =L= 0;
e152.. 0.09*b159 - x216 =L= 0;
e153.. - 0.2*b119 - x193 =G= -0.9;
e154.. - 0.2*b120 - x194 =G= -0.9;
e155.. - 0.2*b133 - x195 =G= -0.9;
e156.. - 0.2*b134 - x196 =G= -0.9;
e157.. - 0.2*b183 - x197 =G= -0.9;
e158.. - 0.2*b184 - x198 =G= -0.9;
e159.. - 0.2*b158 - x199 =G= -0.9;
e160.. - 0.2*b159 - x200 =G= -0.9;
e161.. - 0.05*b117 - x201 =G= -1;
e162.. - 0.05*b118 - x202 =G= -1;
e163.. - 0.05*b131 - x203 =G= -1;
e164.. - 0.05*b132 - x204 =G= -1;
e165.. - 0.05*b145 - x205 =G= -1;
e166.. - 0.05*b146 - x206 =G= -1;
e167.. - 0.05*b156 - x207 =G= -1;
e168.. - 0.05*b157 - x208 =G= -1;
e169.. - 0.12*b119 - x209 =G= -0.92;
e170.. - 0.12*b120 - x210 =G= -0.92;
e171.. - 0.12*b133 - x211 =G= -0.92;
e172.. - 0.12*b134 - x212 =G= -0.92;
e173.. - 0.12*b183 - x213 =G= -0.92;
e174.. - 0.12*b184 - x214 =G= -0.92;
e175.. - 0.12*b158 - x215 =G= -0.92;
e176.. - 0.12*b159 - x216 =G= -0.92;
e177.. b99 + b108 =L= 1;
e178.. b100 + b109 =L= 1;
e179.. b101 + b110 =L= 1;
e180.. b99 + b111 =L= 1;
e181.. b100 + b112 =L= 1;
e182.. b101 + b113 =L= 1;
e183.. b99 + b114 =L= 1;
e184.. b100 + b115 =L= 1;
e185.. b101 + b116 =L= 1;
e186.. b100 + b117 =L= 1;
e187.. b101 + b118 =L= 1;
e188.. b100 + b119 =L= 1;
e189.. b101 + b120 =L= 1;
e190.. b108 + b121 =L= 1;
e191.. b109 + b122 =L= 1;
e192.. b110 + b123 =L= 1;
e193.. b111 + b121 =L= 1;
e194.. b112 + b122 =L= 1;
e195.. b113 + b123 =L= 1;
e196.. b114 + b121 =L= 1;
e197.. b115 + b122 =L= 1;
e198.. b116 + b123 =L= 1;
e199.. b117 + b122 =L= 1;
e200.. b118 + b123 =L= 1;
e201.. b119 + b122 =L= 1;
e202.. b120 + b123 =L= 1;
e203.. b108 + b135 =L= 1;
e204.. b109 + b136 =L= 1;
e205.. b110 + b137 =L= 1;
e206.. b111 + b135 =L= 1;
e207.. b112 + b136 =L= 1;
e208.. b113 + b137 =L= 1;
e209.. b114 + b135 =L= 1;
e210.. b115 + b136 =L= 1;
e211.. b116 + b137 =L= 1;
e212.. b117 + b136 =L= 1;
e213.. b118 + b137 =L= 1;
e214.. b119 + b136 =L= 1;
e215.. b120 + b137 =L= 1;
e216.. b108 + b147 =L= 1;
e217.. b109 + b148 =L= 1;
e218.. b110 + b149 =L= 1;
e219.. b111 + b147 =L= 1;
e220.. b112 + b148 =L= 1;
e221.. b113 + b149 =L= 1;
e222.. b114 + b147 =L= 1;
e223.. b115 + b148 =L= 1;
e224.. b116 + b149 =L= 1;
e225.. b117 + b148 =L= 1;
e226.. b118 + b149 =L= 1;
e227.. b119 + b148 =L= 1;
e228.. b120 + b149 =L= 1;
e229.. b90 + b121 =L= 1;
e230.. b91 + b122 =L= 1;
e231.. b92 + b123 =L= 1;
e232.. b90 + b124 =L= 1;
e233.. b91 + b125 =L= 1;
e234.. b92 + b126 =L= 1;
e235.. b90 + b127 =L= 1;
e236.. b91 + b128 =L= 1;
e237.. b92 + b129 =L= 1;
e238.. b90 + b130 =L= 1;
e239.. b91 + b131 =L= 1;
e240.. b92 + b132 =L= 1;
e241.. b91 + b133 =L= 1;
e242.. b92 + b134 =L= 1;
e243.. b102 + b121 =L= 1;
e244.. b103 + b122 =L= 1;
e245.. b104 + b123 =L= 1;
e246.. b102 + b124 =L= 1;
e247.. b103 + b125 =L= 1;
e248.. b104 + b126 =L= 1;
e249.. b102 + b127 =L= 1;
e250.. b103 + b128 =L= 1;
e251.. b104 + b129 =L= 1;
e252.. b102 + b130 =L= 1;
e253.. b103 + b131 =L= 1;
e254.. b104 + b132 =L= 1;
e255.. b103 + b133 =L= 1;
e256.. b104 + b134 =L= 1;
e257.. b108 + b121 =L= 1;
e258.. b109 + b122 =L= 1;
e259.. b110 + b123 =L= 1;
e260.. b108 + b124 =L= 1;
e261.. b109 + b125 =L= 1;
e262.. b110 + b126 =L= 1;
e263.. b108 + b127 =L= 1;
e264.. b109 + b128 =L= 1;
e265.. b110 + b129 =L= 1;
e266.. b108 + b130 =L= 1;
e267.. b109 + b131 =L= 1;
e268.. b110 + b132 =L= 1;
e269.. b109 + b133 =L= 1;
e270.. b110 + b134 =L= 1;
e271.. b121 + b138 =L= 1;
e272.. b122 + b139 =L= 1;
e273.. b123 + b140 =L= 1;
e274.. b124 + b138 =L= 1;
e275.. b125 + b139 =L= 1;
e276.. b126 + b140 =L= 1;
e277.. b127 + b138 =L= 1;
e278.. b128 + b139 =L= 1;
e279.. b129 + b140 =L= 1;
e280.. b130 + b138 =L= 1;
e281.. b131 + b139 =L= 1;
e282.. b132 + b140 =L= 1;
e283.. b133 + b139 =L= 1;
e284.. b134 + b140 =L= 1;
e285.. b121 + b150 =L= 1;
e286.. b122 + b151 =L= 1;
e287.. b123 + b152 =L= 1;
e288.. b124 + b150 =L= 1;
e289.. b125 + b151 =L= 1;
e290.. b126 + b152 =L= 1;
e291.. b127 + b150 =L= 1;
e292.. b128 + b151 =L= 1;
e293.. b129 + b152 =L= 1;
e294.. b130 + b150 =L= 1;
e295.. b131 + b151 =L= 1;
e296.. b132 + b152 =L= 1;
e297.. b133 + b151 =L= 1;
e298.. b134 + b152 =L= 1;
e299.. b93 + b135 =L= 1;
e300.. b94 + b136 =L= 1;
e301.. b95 + b137 =L= 1;
e302.. b93 + b138 =L= 1;
e303.. b94 + b139 =L= 1;
e304.. b95 + b140 =L= 1;
e305.. b93 + b141 =L= 1;
e306.. b94 + b142 =L= 1;
e307.. b95 + b143 =L= 1;
e308.. b93 + b144 =L= 1;
e309.. b94 + b145 =L= 1;
e310.. b95 + b146 =L= 1;
e311.. b94 + b183 =L= 1;
e312.. b95 + b184 =L= 1;
e313.. b105 + b135 =L= 1;
e314.. b106 + b136 =L= 1;
e315.. b107 + b137 =L= 1;
e316.. b105 + b138 =L= 1;
e317.. b106 + b139 =L= 1;
e318.. b107 + b140 =L= 1;
e319.. b105 + b141 =L= 1;
e320.. b106 + b142 =L= 1;
e321.. b107 + b143 =L= 1;
e322.. b105 + b144 =L= 1;
e323.. b106 + b145 =L= 1;
e324.. b107 + b146 =L= 1;
e325.. b106 + b183 =L= 1;
e326.. b107 + b184 =L= 1;
e327.. b111 + b135 =L= 1;
e328.. b112 + b136 =L= 1;
e329.. b113 + b137 =L= 1;
e330.. b111 + b138 =L= 1;
e331.. b112 + b139 =L= 1;
e332.. b113 + b140 =L= 1;
e333.. b111 + b141 =L= 1;
e334.. b112 + b142 =L= 1;
e335.. b113 + b143 =L= 1;
e336.. b111 + b144 =L= 1;
e337.. b112 + b145 =L= 1;
e338.. b113 + b146 =L= 1;
e339.. b112 + b183 =L= 1;
e340.. b113 + b184 =L= 1;
e341.. b124 + b135 =L= 1;
e342.. b125 + b136 =L= 1;
e343.. b126 + b137 =L= 1;
e344.. b124 + b138 =L= 1;
e345.. b125 + b139 =L= 1;
e346.. b126 + b140 =L= 1;
e347.. b124 + b141 =L= 1;
e348.. b125 + b142 =L= 1;
e349.. b126 + b143 =L= 1;
e350.. b124 + b144 =L= 1;
e351.. b125 + b145 =L= 1;
e352.. b126 + b146 =L= 1;
e353.. b125 + b183 =L= 1;
e354.. b126 + b184 =L= 1;
e355.. b135 + b153 =L= 1;
e356.. b136 + b154 =L= 1;
e357.. b137 + b155 =L= 1;
e358.. b138 + b153 =L= 1;
e359.. b139 + b154 =L= 1;
e360.. b140 + b155 =L= 1;
e361.. b141 + b153 =L= 1;
e362.. b142 + b154 =L= 1;
e363.. b143 + b155 =L= 1;
e364.. b144 + b153 =L= 1;
e365.. b145 + b154 =L= 1;
e366.. b146 + b155 =L= 1;
e367.. b154 + b183 =L= 1;
e368.. b155 + b184 =L= 1;
e369.. b96 + b147 =L= 1;
e370.. b97 + b148 =L= 1;
e371.. b98 + b149 =L= 1;
e372.. b96 + b150 =L= 1;
e373.. b97 + b151 =L= 1;
e374.. b98 + b152 =L= 1;
e375.. b96 + b153 =L= 1;
e376.. b97 + b154 =L= 1;
e377.. b98 + b155 =L= 1;
e378.. b97 + b156 =L= 1;
e379.. b98 + b157 =L= 1;
e380.. b97 + b158 =L= 1;
e381.. b98 + b159 =L= 1;
e382.. b114 + b147 =L= 1;
e383.. b115 + b148 =L= 1;
e384.. b116 + b149 =L= 1;
e385.. b114 + b150 =L= 1;
e386.. b115 + b151 =L= 1;
e387.. b116 + b152 =L= 1;
e388.. b114 + b153 =L= 1;
e389.. b115 + b154 =L= 1;
e390.. b116 + b155 =L= 1;
e391.. b115 + b156 =L= 1;
e392.. b116 + b157 =L= 1;
e393.. b115 + b158 =L= 1;
e394.. b116 + b159 =L= 1;
e395.. b127 + b147 =L= 1;
e396.. b128 + b148 =L= 1;
e397.. b129 + b149 =L= 1;
e398.. b127 + b150 =L= 1;
e399.. b128 + b151 =L= 1;
e400.. b129 + b152 =L= 1;
e401.. b127 + b153 =L= 1;
e402.. b128 + b154 =L= 1;
e403.. b129 + b155 =L= 1;
e404.. b128 + b156 =L= 1;
e405.. b129 + b157 =L= 1;
e406.. b128 + b158 =L= 1;
e407.. b129 + b159 =L= 1;
e408.. b141 + b147 =L= 1;
e409.. b142 + b148 =L= 1;
e410.. b143 + b149 =L= 1;
e411.. b141 + b150 =L= 1;
e412.. b142 + b151 =L= 1;
e413.. b143 + b152 =L= 1;
e414.. b141 + b153 =L= 1;
e415.. b142 + b154 =L= 1;
e416.. b143 + b155 =L= 1;
e417.. b142 + b156 =L= 1;
e418.. b143 + b157 =L= 1;
e419.. b142 + b158 =L= 1;
e420.. b143 + b159 =L= 1;
e421.. x185*x162 - 0.9*x11 + 0.7*x20 + 0.7*x23 + 0.7*x26 - 0.8*x33 - 0.7*x47
- 0.7*x61 =E= 0.21;
e422.. x187*x163 - 0.7*x2 - 0.9*x14 - 0.7*x20 + 0.8*x33 + 0.8*x36 + 0.8*x39
+ 0.8*x42 - 0.7*x50 - 0.7*x64 =E= 1.44;
e423.. x189*x164 - 0.7*x5 - 0.9*x17 - 0.7*x23 - 0.8*x36 + 0.7*x47 + 0.7*x50
+ 0.7*x53 + 0.7*x56 - 0.7*x67 =E= 0.91;
e424.. x191*x165 - 0.7*x8 - 0.7*x26 - 0.8*x39 - 0.7*x53 + 0.7*x61 + 0.7*x64
+ 0.7*x67 =E= 0.14;
e425.. x193*x162 - 0.01*x11 - 0.9*x33 - 0.8*x47 - 0.3*x61 =E= 0;
e426.. x195*x163 - 0.2*x2 - 0.01*x14 + 0.9*x33 + 0.9*x36 + 0.9*x39 + 0.9*x42
- 0.8*x50 - 0.3*x64 =E= 1.62;
e427.. x197*x164 - 0.2*x5 - 0.01*x17 - 0.9*x36 + 0.8*x47 + 0.8*x50 + 0.8*x53
+ 0.8*x56 - 0.3*x67 =E= 1.04;
e428.. x199*x165 - 0.2*x8 - 0.9*x39 - 0.8*x53 + 0.3*x61 + 0.3*x64 + 0.3*x67
=E= 0.06;
e429.. x201*x162 - 0.88*x11 + 0.68*x20 + 0.68*x23 + 0.68*x26 - 0.81*x33
- 0.71*x47 - 0.66*x61 =E= 0.204;
e430.. x203*x163 - 0.69*x2 - 0.88*x14 - 0.68*x20 + 0.81*x33 + 0.81*x36
+ 0.81*x39 + 0.81*x42 - 0.71*x50 - 0.66*x64 =E= 1.458;
e431.. x205*x164 - 0.69*x5 - 0.88*x17 - 0.68*x23 - 0.81*x36 + 0.71*x47
+ 0.71*x50 + 0.71*x53 + 0.71*x56 - 0.66*x67 =E= 0.923;
e432.. x207*x165 - 0.69*x8 - 0.68*x26 - 0.81*x39 - 0.71*x53 + 0.66*x61
+ 0.66*x64 + 0.66*x67 =E= 0.132;
e433.. x209*x162 + 0.01*x20 + 0.01*x23 + 0.01*x26 - 0.9*x33 - 0.8*x47 - 0.4*x61
=E= 0.003;
e434.. x211*x163 - 0.18*x2 - 0.01*x20 + 0.9*x33 + 0.9*x36 + 0.9*x39 + 0.9*x42
- 0.8*x50 - 0.4*x64 =E= 1.62;
e435.. x213*x164 - 0.18*x5 - 0.01*x23 - 0.9*x36 + 0.8*x47 + 0.8*x50 + 0.8*x53
+ 0.8*x56 - 0.4*x67 =E= 1.04;
e436.. x215*x165 - 0.18*x8 - 0.01*x26 - 0.9*x39 - 0.8*x53 + 0.4*x61 + 0.4*x64
+ 0.4*x67 =E= 0.08;
e437.. x185*x21 + x185*x24 + x185*x27 + x185*x29 + x185*x31 - x187*x34 - x189*
x48 - x191*x62 - x185*x162 + x186*x171 - 0.9*x12 =E= 0;
e438.. x186*x22 + x186*x25 + x186*x28 + x186*x30 + x186*x32 - x188*x35 - x190*
x49 - x192*x63 + x172*x74 - x186*x171 - 0.9*x13 =E= 0;
e439.. x187*x34 - x185*x21 + x187*x37 + x187*x40 + x187*x43 + x187*x45 - x189*
x51 - x191*x65 - x187*x163 + x188*x173 - 0.7*x3 - 0.9*x15 =E= 0;
e440.. x188*x35 - x186*x22 + x188*x38 + x188*x41 + x188*x44 + x188*x46 - x190*
x52 - x192*x66 + x174*x75 - x188*x173 - 0.7*x4 - 0.9*x16 =E= 0;
e441.. (-x185*x24) - x187*x37 + x189*x48 + x189*x51 + x189*x54 + x189*x57 +
x189*x59 - x191*x68 - x189*x164 + x190*x175 - 0.7*x6 - 0.9*x18 =E= 0;
e442.. (-x186*x25) - x188*x38 + x190*x49 + x190*x52 + x190*x55 + x190*x58 +
x190*x60 - x192*x69 + x176*x76 - x190*x175 - 0.7*x7 - 0.9*x19 =E= 0;
e443.. (-x185*x27) - x187*x40 - x189*x54 + x191*x62 + x191*x65 + x191*x68 +
x191*x70 + x191*x72 - x191*x165 + x192*x177 - 0.7*x9 =E= 0;
e444.. (-x186*x28) - x188*x41 - x190*x55 + x192*x63 + x192*x66 + x192*x69 +
x192*x71 + x192*x73 + x178*x77 - x192*x177 - 0.7*x10 =E= 0;
e445.. x193*x21 + x193*x24 + x193*x27 + x193*x29 + x193*x31 - x195*x34 - x197*
x48 - x199*x62 - x193*x162 + x194*x171 - 0.01*x12 =E= 0;
e446.. x194*x22 + x194*x25 + x194*x28 + x194*x30 + x194*x32 - x196*x35 - x198*
x49 - x200*x63 + x172*x78 - x194*x171 - 0.01*x13 =E= 0;
e447.. x195*x34 - x193*x21 + x195*x37 + x195*x40 + x195*x43 + x195*x45 - x197*
x51 - x199*x65 - x195*x163 + x196*x173 - 0.2*x3 - 0.01*x15 =E= 0;
e448.. x196*x35 - x194*x22 + x196*x38 + x196*x41 + x196*x44 + x196*x46 - x198*
x52 - x200*x66 + x174*x79 - x196*x173 - 0.2*x4 - 0.01*x16 =E= 0;
e449.. (-x193*x24) - x195*x37 + x197*x48 + x197*x51 + x197*x54 + x197*x57 +
x197*x59 - x199*x68 - x197*x164 + x198*x175 - 0.2*x6 - 0.01*x18 =E= 0;
e450.. (-x194*x25) - x196*x38 + x198*x49 + x198*x52 + x198*x55 + x198*x58 +
x198*x60 - x200*x69 + x176*x80 - x198*x175 - 0.2*x7 - 0.01*x19 =E= 0;
e451.. (-x193*x27) - x195*x40 - x197*x54 + x199*x62 + x199*x65 + x199*x68 +
x199*x70 + x199*x72 - x199*x165 + x200*x177 - 0.2*x9 =E= 0;
e452.. (-x194*x28) - x196*x41 - x198*x55 + x200*x63 + x200*x66 + x200*x69 +
x200*x71 + x200*x73 + x178*x81 - x200*x177 - 0.2*x10 =E= 0;
e453.. x201*x21 + x201*x24 + x201*x27 + x201*x29 + x201*x31 - x203*x34 - x205*
x48 - x207*x62 - x201*x162 + x202*x171 - 0.88*x12 =E= 0;
e454.. x202*x22 + x202*x25 + x202*x28 + x202*x30 + x202*x32 - x204*x35 - x206*
x49 - x208*x63 + x172*x82 - x202*x171 - 0.88*x13 =E= 0;
e455.. x203*x34 - x201*x21 + x203*x37 + x203*x40 + x203*x43 + x203*x45 - x205*
x51 - x207*x65 - x203*x163 + x204*x173 - 0.69*x3 - 0.88*x15 =E= 0;
e456.. x204*x35 - x202*x22 + x204*x38 + x204*x41 + x204*x44 + x204*x46 - x206*
x52 - x208*x66 + x174*x83 - x204*x173 - 0.69*x4 - 0.88*x16 =E= 0;
e457.. (-x201*x24) - x203*x37 + x205*x48 + x205*x51 + x205*x54 + x205*x57 +
x205*x59 - x207*x68 - x205*x164 + x206*x175 - 0.69*x6 - 0.88*x18 =E= 0;
e458.. (-x202*x25) - x204*x38 + x206*x49 + x206*x52 + x206*x55 + x206*x58 +
x206*x60 - x208*x69 + x176*x84 - x206*x175 - 0.69*x7 - 0.88*x19 =E= 0;
e459.. (-x201*x27) - x203*x40 - x205*x54 + x207*x62 + x207*x65 + x207*x68 +
x207*x70 + x207*x72 - x207*x165 + x208*x177 - 0.69*x9 =E= 0;
e460.. (-x202*x28) - x204*x41 - x206*x55 + x208*x63 + x208*x66 + x208*x69 +
x208*x71 + x208*x73 + x178*x85 - x208*x177 - 0.69*x10 =E= 0;
e461.. x211*x34 - x209*x21 + x211*x37 + x211*x40 + x211*x43 + x211*x45 - x213*
x51 - x215*x65 - x211*x163 + x212*x173 - 0.18*x3 =E= 0;
e462.. x212*x35 - x210*x22 + x212*x38 + x212*x41 + x212*x44 + x212*x46 - x214*
x52 - x216*x66 + x174*x87 - x212*x173 - 0.18*x4 =E= 0;
e463.. (-x209*x24) - x211*x37 + x213*x48 + x213*x51 + x213*x54 + x213*x57 +
x213*x59 - x215*x68 - x213*x164 + x214*x175 - 0.18*x6 =E= 0;
e464.. (-x210*x25) - x212*x38 + x214*x49 + x214*x52 + x214*x55 + x214*x58 +
x214*x60 - x216*x69 + x176*x88 - x214*x175 - 0.18*x7 =E= 0;
e465.. (-x209*x27) - x211*x40 - x213*x54 + x215*x62 + x215*x65 + x215*x68 +
x215*x70 + x215*x72 - x215*x165 + x216*x177 - 0.18*x9 =E= 0;
e466.. (-x210*x28) - x212*x41 - x214*x55 + x216*x63 + x216*x66 + x216*x69 +
x216*x71 + x216*x73 + x178*x89 - x216*x177 - 0.18*x10 =E= 0;
e467.. x209*x21 + x209*x24 + x209*x27 + x209*x29 + x209*x31 - x211*x34 - x213*
x48 - x215*x62 - x209*x162 + x210*x171 =E= 0;
e468.. x210*x22 + x210*x25 + x210*x28 + x210*x30 + x210*x32 - x212*x35 - x214*
x49 - x216*x63 + x172*x86 - x210*x171 =E= 0;
* set non-default bounds
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x10.up = 1;
x11.up = 1;
x12.up = 1;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 1;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.up = 1;
x29.up = 1;
x30.up = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1;
x38.up = 1;
x39.up = 1;
x40.up = 1;
x41.up = 1;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 1;
x51.up = 1;
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 1;
x63.up = 1;
x64.up = 1;
x65.up = 1;
x66.up = 1;
x67.up = 1;
x68.up = 1;
x69.up = 1;
x70.up = 1;
x71.up = 1;
x72.up = 1;
x73.up = 1;
x74.lo = 0.7; x74.up = 1;
x75.lo = 0.7; x75.up = 1;
x76.lo = 0.7; x76.up = 1;
x77.lo = 0.7; x77.up = 1;
x78.up = 0.9;
x79.up = 0.9;
x80.up = 0.9;
x81.up = 0.9;
x82.lo = 0.66; x82.up = 1;
x83.lo = 0.66; x83.up = 1;
x84.lo = 0.66; x84.up = 1;
x85.lo = 0.66; x85.up = 1;
x86.up = 0.92;
x87.up = 0.92;
x88.up = 0.92;
x89.up = 0.92;
x160.up = 2;
x161.up = 2;
x162.up = 2;
x163.up = 2;
x164.up = 2;
x165.up = 2;
x166.up = 2;
x167.up = 2;
x168.up = 2;
x169.up = 2;
x170.up = 2;
x171.up = 2;
x172.up = 2;
x173.up = 2;
x174.up = 2;
x175.up = 2;
x176.up = 2;
x177.up = 2;
x178.up = 2;
x179.up = 2;
x180.up = 2;
x181.up = 2;
x182.up = 2;
x185.lo = 0.7; x185.up = 1;
x186.lo = 0.7; x186.up = 1;
x187.lo = 0.7; x187.up = 1;
x188.lo = 0.7; x188.up = 1;
x189.lo = 0.7; x189.up = 1;
x190.lo = 0.7; x190.up = 1;
x191.lo = 0.7; x191.up = 1;
x192.lo = 0.7; x192.up = 1;
x193.up = 0.9;
x194.up = 0.9;
x195.up = 0.9;
x196.up = 0.9;
x197.up = 0.9;
x198.up = 0.9;
x199.up = 0.9;
x200.up = 0.9;
x201.lo = 0.66; x201.up = 1;
x202.lo = 0.66; x202.up = 1;
x203.lo = 0.66; x203.up = 1;
x204.lo = 0.66; x204.up = 1;
x205.lo = 0.66; x205.up = 1;
x206.lo = 0.66; x206.up = 1;
x207.lo = 0.66; x207.up = 1;
x208.lo = 0.66; x208.up = 1;
x209.up = 0.92;
x210.up = 0.92;
x211.up = 0.92;
x212.up = 0.92;
x213.up = 0.92;
x214.up = 0.92;
x215.up = 0.92;
x216.up = 0.92;
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% maximizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc