MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance edgecross10-030
edge-crossing minimization in bipartite graphs modeled as a quadratic linear ordering problem This instance is for the edge crossing minimization problem in a bipartite graph G. G has to be drawn in the plane so that the nodes of its two shores are placed on two parallel horizontal lines. The task is to minimize the number of edge crossings by permuting the order of nodes on each layer, assuming that all edges are drawn as straight lines. The problem can be modeled as a quadratic objective over linear ordering variables.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 51.99999995 (ANTIGONE) 51.99999995 (BARON) 51.99999998 (COUENNE) 51.99999948 (CPLEX) 52.00000000 (GUROBI) 52.00000000 (LINDO) 52.00000000 (SCIP) 52.00000000 (SHOT) |
| Referencesⓘ | Buchheim, Christoph, Wiegele, Angelika, and Zheng, Lanbo, Exact Algorithms for the Quadratic Linear Ordering Problem, INFORMS Journal on Computing, 22:1, 2010, 168-177. |
| Sourceⓘ | POLIP instance quadratic_linear_ordering/bip_cross_min.10.10.30.1 |
| Applicationⓘ | Edge-crossing minimization in bipartite graphs |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 91 |
| #Binary Variablesⓘ | 90 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 88 |
| #Nonlinear Binary Variablesⓘ | 88 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 481 |
| #Linear Constraintsⓘ | 480 |
| #Quadratic Constraintsⓘ | 1 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 1529 |
| #Nonlinear Nonzeros in Jacobianⓘ | 88 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 634 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 88 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 88 |
| Average blocksize in Hessian of Lagrangianⓘ | 88.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.0000e+01 |
| Infeasibility of initial pointⓘ | 184 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 481 0 1 480 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 91 1 90 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1529 1441 88 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,objvar;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51
,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68
,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85
,b86,b87,b88,b89,b90;
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,e469,e470,e471,e472,e473,e474,e475,e476,e477,e478,e479,e480
,e481;
e1.. - b1 + b2 + b3 =L= 1;
e2.. b3 - b4 + b5 =L= 1;
e3.. b3 - b6 + b7 =L= 1;
e4.. b3 - b8 + b9 =L= 1;
e5.. b3 - b10 + b11 =L= 1;
e6.. b3 - b12 + b13 =L= 1;
e7.. b3 - b14 + b15 =L= 1;
e8.. b3 - b16 + b17 =L= 1;
e9.. b1 - b4 + b18 =L= 1;
e10.. b1 - b6 + b19 =L= 1;
e11.. b1 - b8 + b20 =L= 1;
e12.. b1 - b10 + b21 =L= 1;
e13.. b1 - b12 + b22 =L= 1;
e14.. b1 - b14 + b23 =L= 1;
e15.. b1 - b16 + b24 =L= 1;
e16.. b4 - b6 + b25 =L= 1;
e17.. b4 - b8 + b26 =L= 1;
e18.. b4 - b10 + b27 =L= 1;
e19.. b4 - b12 + b28 =L= 1;
e20.. b4 - b14 + b29 =L= 1;
e21.. b4 - b16 + b30 =L= 1;
e22.. b6 - b8 + b31 =L= 1;
e23.. b6 - b10 + b32 =L= 1;
e24.. b6 - b12 + b33 =L= 1;
e25.. b6 - b14 + b34 =L= 1;
e26.. b6 - b16 + b35 =L= 1;
e27.. b8 - b10 + b36 =L= 1;
e28.. b8 - b12 + b37 =L= 1;
e29.. b8 - b14 + b38 =L= 1;
e30.. b8 - b16 + b39 =L= 1;
e31.. b10 - b12 + b40 =L= 1;
e32.. b10 - b14 + b41 =L= 1;
e33.. b10 - b16 + b42 =L= 1;
e34.. b12 - b14 + b43 =L= 1;
e35.. b12 - b16 + b44 =L= 1;
e36.. b14 - b16 + b45 =L= 1;
e37.. b2 - b5 + b18 =L= 1;
e38.. b2 - b7 + b19 =L= 1;
e39.. b2 - b9 + b20 =L= 1;
e40.. b2 - b11 + b21 =L= 1;
e41.. b2 - b13 + b22 =L= 1;
e42.. b2 - b15 + b23 =L= 1;
e43.. b2 - b17 + b24 =L= 1;
e44.. b5 - b7 + b25 =L= 1;
e45.. b5 - b9 + b26 =L= 1;
e46.. b5 - b11 + b27 =L= 1;
e47.. b5 - b13 + b28 =L= 1;
e48.. b5 - b15 + b29 =L= 1;
e49.. b5 - b17 + b30 =L= 1;
e50.. b7 - b9 + b31 =L= 1;
e51.. b7 - b11 + b32 =L= 1;
e52.. b7 - b13 + b33 =L= 1;
e53.. b7 - b15 + b34 =L= 1;
e54.. b7 - b17 + b35 =L= 1;
e55.. b9 - b11 + b36 =L= 1;
e56.. b9 - b13 + b37 =L= 1;
e57.. b9 - b15 + b38 =L= 1;
e58.. b9 - b17 + b39 =L= 1;
e59.. b11 - b13 + b40 =L= 1;
e60.. b11 - b15 + b41 =L= 1;
e61.. b11 - b17 + b42 =L= 1;
e62.. b13 - b15 + b43 =L= 1;
e63.. b13 - b17 + b44 =L= 1;
e64.. b15 - b17 + b45 =L= 1;
e65.. b18 - b19 + b25 =L= 1;
e66.. b18 - b20 + b26 =L= 1;
e67.. b18 - b21 + b27 =L= 1;
e68.. b18 - b22 + b28 =L= 1;
e69.. b18 - b23 + b29 =L= 1;
e70.. b18 - b24 + b30 =L= 1;
e71.. b19 - b20 + b31 =L= 1;
e72.. b19 - b21 + b32 =L= 1;
e73.. b19 - b22 + b33 =L= 1;
e74.. b19 - b23 + b34 =L= 1;
e75.. b19 - b24 + b35 =L= 1;
e76.. b20 - b21 + b36 =L= 1;
e77.. b20 - b22 + b37 =L= 1;
e78.. b20 - b23 + b38 =L= 1;
e79.. b20 - b24 + b39 =L= 1;
e80.. b21 - b22 + b40 =L= 1;
e81.. b21 - b23 + b41 =L= 1;
e82.. b21 - b24 + b42 =L= 1;
e83.. b22 - b23 + b43 =L= 1;
e84.. b22 - b24 + b44 =L= 1;
e85.. b23 - b24 + b45 =L= 1;
e86.. b25 - b26 + b31 =L= 1;
e87.. b25 - b27 + b32 =L= 1;
e88.. b25 - b28 + b33 =L= 1;
e89.. b25 - b29 + b34 =L= 1;
e90.. b25 - b30 + b35 =L= 1;
e91.. b26 - b27 + b36 =L= 1;
e92.. b26 - b28 + b37 =L= 1;
e93.. b26 - b29 + b38 =L= 1;
e94.. b26 - b30 + b39 =L= 1;
e95.. b27 - b28 + b40 =L= 1;
e96.. b27 - b29 + b41 =L= 1;
e97.. b27 - b30 + b42 =L= 1;
e98.. b28 - b29 + b43 =L= 1;
e99.. b28 - b30 + b44 =L= 1;
e100.. b29 - b30 + b45 =L= 1;
e101.. b31 - b32 + b36 =L= 1;
e102.. b31 - b33 + b37 =L= 1;
e103.. b31 - b34 + b38 =L= 1;
e104.. b31 - b35 + b39 =L= 1;
e105.. b32 - b33 + b40 =L= 1;
e106.. b32 - b34 + b41 =L= 1;
e107.. b32 - b35 + b42 =L= 1;
e108.. b33 - b34 + b43 =L= 1;
e109.. b33 - b35 + b44 =L= 1;
e110.. b34 - b35 + b45 =L= 1;
e111.. b36 - b37 + b40 =L= 1;
e112.. b36 - b38 + b41 =L= 1;
e113.. b36 - b39 + b42 =L= 1;
e114.. b37 - b38 + b43 =L= 1;
e115.. b37 - b39 + b44 =L= 1;
e116.. b38 - b39 + b45 =L= 1;
e117.. b40 - b41 + b43 =L= 1;
e118.. b40 - b42 + b44 =L= 1;
e119.. b41 - b42 + b45 =L= 1;
e120.. b43 - b44 + b45 =L= 1;
e121.. b1 - b2 - b3 =L= 0;
e122.. - b3 + b4 - b5 =L= 0;
e123.. - b3 + b6 - b7 =L= 0;
e124.. - b3 + b8 - b9 =L= 0;
e125.. - b3 + b10 - b11 =L= 0;
e126.. - b3 + b12 - b13 =L= 0;
e127.. - b3 + b14 - b15 =L= 0;
e128.. - b3 + b16 - b17 =L= 0;
e129.. - b1 + b4 - b18 =L= 0;
e130.. - b1 + b6 - b19 =L= 0;
e131.. - b1 + b8 - b20 =L= 0;
e132.. - b1 + b10 - b21 =L= 0;
e133.. - b1 + b12 - b22 =L= 0;
e134.. - b1 + b14 - b23 =L= 0;
e135.. - b1 + b16 - b24 =L= 0;
e136.. - b4 + b6 - b25 =L= 0;
e137.. - b4 + b8 - b26 =L= 0;
e138.. - b4 + b10 - b27 =L= 0;
e139.. - b4 + b12 - b28 =L= 0;
e140.. - b4 + b14 - b29 =L= 0;
e141.. - b4 + b16 - b30 =L= 0;
e142.. - b6 + b8 - b31 =L= 0;
e143.. - b6 + b10 - b32 =L= 0;
e144.. - b6 + b12 - b33 =L= 0;
e145.. - b6 + b14 - b34 =L= 0;
e146.. - b6 + b16 - b35 =L= 0;
e147.. - b8 + b10 - b36 =L= 0;
e148.. - b8 + b12 - b37 =L= 0;
e149.. - b8 + b14 - b38 =L= 0;
e150.. - b8 + b16 - b39 =L= 0;
e151.. - b10 + b12 - b40 =L= 0;
e152.. - b10 + b14 - b41 =L= 0;
e153.. - b10 + b16 - b42 =L= 0;
e154.. - b12 + b14 - b43 =L= 0;
e155.. - b12 + b16 - b44 =L= 0;
e156.. - b14 + b16 - b45 =L= 0;
e157.. - b2 + b5 - b18 =L= 0;
e158.. - b2 + b7 - b19 =L= 0;
e159.. - b2 + b9 - b20 =L= 0;
e160.. - b2 + b11 - b21 =L= 0;
e161.. - b2 + b13 - b22 =L= 0;
e162.. - b2 + b15 - b23 =L= 0;
e163.. - b2 + b17 - b24 =L= 0;
e164.. - b5 + b7 - b25 =L= 0;
e165.. - b5 + b9 - b26 =L= 0;
e166.. - b5 + b11 - b27 =L= 0;
e167.. - b5 + b13 - b28 =L= 0;
e168.. - b5 + b15 - b29 =L= 0;
e169.. - b5 + b17 - b30 =L= 0;
e170.. - b7 + b9 - b31 =L= 0;
e171.. - b7 + b11 - b32 =L= 0;
e172.. - b7 + b13 - b33 =L= 0;
e173.. - b7 + b15 - b34 =L= 0;
e174.. - b7 + b17 - b35 =L= 0;
e175.. - b9 + b11 - b36 =L= 0;
e176.. - b9 + b13 - b37 =L= 0;
e177.. - b9 + b15 - b38 =L= 0;
e178.. - b9 + b17 - b39 =L= 0;
e179.. - b11 + b13 - b40 =L= 0;
e180.. - b11 + b15 - b41 =L= 0;
e181.. - b11 + b17 - b42 =L= 0;
e182.. - b13 + b15 - b43 =L= 0;
e183.. - b13 + b17 - b44 =L= 0;
e184.. - b15 + b17 - b45 =L= 0;
e185.. - b18 + b19 - b25 =L= 0;
e186.. - b18 + b20 - b26 =L= 0;
e187.. - b18 + b21 - b27 =L= 0;
e188.. - b18 + b22 - b28 =L= 0;
e189.. - b18 + b23 - b29 =L= 0;
e190.. - b18 + b24 - b30 =L= 0;
e191.. - b19 + b20 - b31 =L= 0;
e192.. - b19 + b21 - b32 =L= 0;
e193.. - b19 + b22 - b33 =L= 0;
e194.. - b19 + b23 - b34 =L= 0;
e195.. - b19 + b24 - b35 =L= 0;
e196.. - b20 + b21 - b36 =L= 0;
e197.. - b20 + b22 - b37 =L= 0;
e198.. - b20 + b23 - b38 =L= 0;
e199.. - b20 + b24 - b39 =L= 0;
e200.. - b21 + b22 - b40 =L= 0;
e201.. - b21 + b23 - b41 =L= 0;
e202.. - b21 + b24 - b42 =L= 0;
e203.. - b22 + b23 - b43 =L= 0;
e204.. - b22 + b24 - b44 =L= 0;
e205.. - b23 + b24 - b45 =L= 0;
e206.. - b25 + b26 - b31 =L= 0;
e207.. - b25 + b27 - b32 =L= 0;
e208.. - b25 + b28 - b33 =L= 0;
e209.. - b25 + b29 - b34 =L= 0;
e210.. - b25 + b30 - b35 =L= 0;
e211.. - b26 + b27 - b36 =L= 0;
e212.. - b26 + b28 - b37 =L= 0;
e213.. - b26 + b29 - b38 =L= 0;
e214.. - b26 + b30 - b39 =L= 0;
e215.. - b27 + b28 - b40 =L= 0;
e216.. - b27 + b29 - b41 =L= 0;
e217.. - b27 + b30 - b42 =L= 0;
e218.. - b28 + b29 - b43 =L= 0;
e219.. - b28 + b30 - b44 =L= 0;
e220.. - b29 + b30 - b45 =L= 0;
e221.. - b31 + b32 - b36 =L= 0;
e222.. - b31 + b33 - b37 =L= 0;
e223.. - b31 + b34 - b38 =L= 0;
e224.. - b31 + b35 - b39 =L= 0;
e225.. - b32 + b33 - b40 =L= 0;
e226.. - b32 + b34 - b41 =L= 0;
e227.. - b32 + b35 - b42 =L= 0;
e228.. - b33 + b34 - b43 =L= 0;
e229.. - b33 + b35 - b44 =L= 0;
e230.. - b34 + b35 - b45 =L= 0;
e231.. - b36 + b37 - b40 =L= 0;
e232.. - b36 + b38 - b41 =L= 0;
e233.. - b36 + b39 - b42 =L= 0;
e234.. - b37 + b38 - b43 =L= 0;
e235.. - b37 + b39 - b44 =L= 0;
e236.. - b38 + b39 - b45 =L= 0;
e237.. - b40 + b41 - b43 =L= 0;
e238.. - b40 + b42 - b44 =L= 0;
e239.. - b41 + b42 - b45 =L= 0;
e240.. - b43 + b44 - b45 =L= 0;
e241.. - b46 + b47 + b48 =L= 1;
e242.. b48 - b49 + b50 =L= 1;
e243.. b48 - b51 + b52 =L= 1;
e244.. b48 - b53 + b54 =L= 1;
e245.. b48 - b55 + b56 =L= 1;
e246.. b48 - b57 + b58 =L= 1;
e247.. b48 - b59 + b60 =L= 1;
e248.. b48 - b61 + b62 =L= 1;
e249.. b46 - b49 + b63 =L= 1;
e250.. b46 - b51 + b64 =L= 1;
e251.. b46 - b53 + b65 =L= 1;
e252.. b46 - b55 + b66 =L= 1;
e253.. b46 - b57 + b67 =L= 1;
e254.. b46 - b59 + b68 =L= 1;
e255.. b46 - b61 + b69 =L= 1;
e256.. b49 - b51 + b70 =L= 1;
e257.. b49 - b53 + b71 =L= 1;
e258.. b49 - b55 + b72 =L= 1;
e259.. b49 - b57 + b73 =L= 1;
e260.. b49 - b59 + b74 =L= 1;
e261.. b49 - b61 + b75 =L= 1;
e262.. b51 - b53 + b76 =L= 1;
e263.. b51 - b55 + b77 =L= 1;
e264.. b51 - b57 + b78 =L= 1;
e265.. b51 - b59 + b79 =L= 1;
e266.. b51 - b61 + b80 =L= 1;
e267.. b53 - b55 + b81 =L= 1;
e268.. b53 - b57 + b82 =L= 1;
e269.. b53 - b59 + b83 =L= 1;
e270.. b53 - b61 + b84 =L= 1;
e271.. b55 - b57 + b85 =L= 1;
e272.. b55 - b59 + b86 =L= 1;
e273.. b55 - b61 + b87 =L= 1;
e274.. b57 - b59 + b88 =L= 1;
e275.. b57 - b61 + b89 =L= 1;
e276.. b59 - b61 + b90 =L= 1;
e277.. b47 - b50 + b63 =L= 1;
e278.. b47 - b52 + b64 =L= 1;
e279.. b47 - b54 + b65 =L= 1;
e280.. b47 - b56 + b66 =L= 1;
e281.. b47 - b58 + b67 =L= 1;
e282.. b47 - b60 + b68 =L= 1;
e283.. b47 - b62 + b69 =L= 1;
e284.. b50 - b52 + b70 =L= 1;
e285.. b50 - b54 + b71 =L= 1;
e286.. b50 - b56 + b72 =L= 1;
e287.. b50 - b58 + b73 =L= 1;
e288.. b50 - b60 + b74 =L= 1;
e289.. b50 - b62 + b75 =L= 1;
e290.. b52 - b54 + b76 =L= 1;
e291.. b52 - b56 + b77 =L= 1;
e292.. b52 - b58 + b78 =L= 1;
e293.. b52 - b60 + b79 =L= 1;
e294.. b52 - b62 + b80 =L= 1;
e295.. b54 - b56 + b81 =L= 1;
e296.. b54 - b58 + b82 =L= 1;
e297.. b54 - b60 + b83 =L= 1;
e298.. b54 - b62 + b84 =L= 1;
e299.. b56 - b58 + b85 =L= 1;
e300.. b56 - b60 + b86 =L= 1;
e301.. b56 - b62 + b87 =L= 1;
e302.. b58 - b60 + b88 =L= 1;
e303.. b58 - b62 + b89 =L= 1;
e304.. b60 - b62 + b90 =L= 1;
e305.. b63 - b64 + b70 =L= 1;
e306.. b63 - b65 + b71 =L= 1;
e307.. b63 - b66 + b72 =L= 1;
e308.. b63 - b67 + b73 =L= 1;
e309.. b63 - b68 + b74 =L= 1;
e310.. b63 - b69 + b75 =L= 1;
e311.. b64 - b65 + b76 =L= 1;
e312.. b64 - b66 + b77 =L= 1;
e313.. b64 - b67 + b78 =L= 1;
e314.. b64 - b68 + b79 =L= 1;
e315.. b64 - b69 + b80 =L= 1;
e316.. b65 - b66 + b81 =L= 1;
e317.. b65 - b67 + b82 =L= 1;
e318.. b65 - b68 + b83 =L= 1;
e319.. b65 - b69 + b84 =L= 1;
e320.. b66 - b67 + b85 =L= 1;
e321.. b66 - b68 + b86 =L= 1;
e322.. b66 - b69 + b87 =L= 1;
e323.. b67 - b68 + b88 =L= 1;
e324.. b67 - b69 + b89 =L= 1;
e325.. b68 - b69 + b90 =L= 1;
e326.. b70 - b71 + b76 =L= 1;
e327.. b70 - b72 + b77 =L= 1;
e328.. b70 - b73 + b78 =L= 1;
e329.. b70 - b74 + b79 =L= 1;
e330.. b70 - b75 + b80 =L= 1;
e331.. b71 - b72 + b81 =L= 1;
e332.. b71 - b73 + b82 =L= 1;
e333.. b71 - b74 + b83 =L= 1;
e334.. b71 - b75 + b84 =L= 1;
e335.. b72 - b73 + b85 =L= 1;
e336.. b72 - b74 + b86 =L= 1;
e337.. b72 - b75 + b87 =L= 1;
e338.. b73 - b74 + b88 =L= 1;
e339.. b73 - b75 + b89 =L= 1;
e340.. b74 - b75 + b90 =L= 1;
e341.. b76 - b77 + b81 =L= 1;
e342.. b76 - b78 + b82 =L= 1;
e343.. b76 - b79 + b83 =L= 1;
e344.. b76 - b80 + b84 =L= 1;
e345.. b77 - b78 + b85 =L= 1;
e346.. b77 - b79 + b86 =L= 1;
e347.. b77 - b80 + b87 =L= 1;
e348.. b78 - b79 + b88 =L= 1;
e349.. b78 - b80 + b89 =L= 1;
e350.. b79 - b80 + b90 =L= 1;
e351.. b81 - b82 + b85 =L= 1;
e352.. b81 - b83 + b86 =L= 1;
e353.. b81 - b84 + b87 =L= 1;
e354.. b82 - b83 + b88 =L= 1;
e355.. b82 - b84 + b89 =L= 1;
e356.. b83 - b84 + b90 =L= 1;
e357.. b85 - b86 + b88 =L= 1;
e358.. b85 - b87 + b89 =L= 1;
e359.. b86 - b87 + b90 =L= 1;
e360.. b88 - b89 + b90 =L= 1;
e361.. b46 - b47 - b48 =L= 0;
e362.. - b48 + b49 - b50 =L= 0;
e363.. - b48 + b51 - b52 =L= 0;
e364.. - b48 + b53 - b54 =L= 0;
e365.. - b48 + b55 - b56 =L= 0;
e366.. - b48 + b57 - b58 =L= 0;
e367.. - b48 + b59 - b60 =L= 0;
e368.. - b48 + b61 - b62 =L= 0;
e369.. - b46 + b49 - b63 =L= 0;
e370.. - b46 + b51 - b64 =L= 0;
e371.. - b46 + b53 - b65 =L= 0;
e372.. - b46 + b55 - b66 =L= 0;
e373.. - b46 + b57 - b67 =L= 0;
e374.. - b46 + b59 - b68 =L= 0;
e375.. - b46 + b61 - b69 =L= 0;
e376.. - b49 + b51 - b70 =L= 0;
e377.. - b49 + b53 - b71 =L= 0;
e378.. - b49 + b55 - b72 =L= 0;
e379.. - b49 + b57 - b73 =L= 0;
e380.. - b49 + b59 - b74 =L= 0;
e381.. - b49 + b61 - b75 =L= 0;
e382.. - b51 + b53 - b76 =L= 0;
e383.. - b51 + b55 - b77 =L= 0;
e384.. - b51 + b57 - b78 =L= 0;
e385.. - b51 + b59 - b79 =L= 0;
e386.. - b51 + b61 - b80 =L= 0;
e387.. - b53 + b55 - b81 =L= 0;
e388.. - b53 + b57 - b82 =L= 0;
e389.. - b53 + b59 - b83 =L= 0;
e390.. - b53 + b61 - b84 =L= 0;
e391.. - b55 + b57 - b85 =L= 0;
e392.. - b55 + b59 - b86 =L= 0;
e393.. - b55 + b61 - b87 =L= 0;
e394.. - b57 + b59 - b88 =L= 0;
e395.. - b57 + b61 - b89 =L= 0;
e396.. - b59 + b61 - b90 =L= 0;
e397.. - b47 + b50 - b63 =L= 0;
e398.. - b47 + b52 - b64 =L= 0;
e399.. - b47 + b54 - b65 =L= 0;
e400.. - b47 + b56 - b66 =L= 0;
e401.. - b47 + b58 - b67 =L= 0;
e402.. - b47 + b60 - b68 =L= 0;
e403.. - b47 + b62 - b69 =L= 0;
e404.. - b50 + b52 - b70 =L= 0;
e405.. - b50 + b54 - b71 =L= 0;
e406.. - b50 + b56 - b72 =L= 0;
e407.. - b50 + b58 - b73 =L= 0;
e408.. - b50 + b60 - b74 =L= 0;
e409.. - b50 + b62 - b75 =L= 0;
e410.. - b52 + b54 - b76 =L= 0;
e411.. - b52 + b56 - b77 =L= 0;
e412.. - b52 + b58 - b78 =L= 0;
e413.. - b52 + b60 - b79 =L= 0;
e414.. - b52 + b62 - b80 =L= 0;
e415.. - b54 + b56 - b81 =L= 0;
e416.. - b54 + b58 - b82 =L= 0;
e417.. - b54 + b60 - b83 =L= 0;
e418.. - b54 + b62 - b84 =L= 0;
e419.. - b56 + b58 - b85 =L= 0;
e420.. - b56 + b60 - b86 =L= 0;
e421.. - b56 + b62 - b87 =L= 0;
e422.. - b58 + b60 - b88 =L= 0;
e423.. - b58 + b62 - b89 =L= 0;
e424.. - b60 + b62 - b90 =L= 0;
e425.. - b63 + b64 - b70 =L= 0;
e426.. - b63 + b65 - b71 =L= 0;
e427.. - b63 + b66 - b72 =L= 0;
e428.. - b63 + b67 - b73 =L= 0;
e429.. - b63 + b68 - b74 =L= 0;
e430.. - b63 + b69 - b75 =L= 0;
e431.. - b64 + b65 - b76 =L= 0;
e432.. - b64 + b66 - b77 =L= 0;
e433.. - b64 + b67 - b78 =L= 0;
e434.. - b64 + b68 - b79 =L= 0;
e435.. - b64 + b69 - b80 =L= 0;
e436.. - b65 + b66 - b81 =L= 0;
e437.. - b65 + b67 - b82 =L= 0;
e438.. - b65 + b68 - b83 =L= 0;
e439.. - b65 + b69 - b84 =L= 0;
e440.. - b66 + b67 - b85 =L= 0;
e441.. - b66 + b68 - b86 =L= 0;
e442.. - b66 + b69 - b87 =L= 0;
e443.. - b67 + b68 - b88 =L= 0;
e444.. - b67 + b69 - b89 =L= 0;
e445.. - b68 + b69 - b90 =L= 0;
e446.. - b70 + b71 - b76 =L= 0;
e447.. - b70 + b72 - b77 =L= 0;
e448.. - b70 + b73 - b78 =L= 0;
e449.. - b70 + b74 - b79 =L= 0;
e450.. - b70 + b75 - b80 =L= 0;
e451.. - b71 + b72 - b81 =L= 0;
e452.. - b71 + b73 - b82 =L= 0;
e453.. - b71 + b74 - b83 =L= 0;
e454.. - b71 + b75 - b84 =L= 0;
e455.. - b72 + b73 - b85 =L= 0;
e456.. - b72 + b74 - b86 =L= 0;
e457.. - b72 + b75 - b87 =L= 0;
e458.. - b73 + b74 - b88 =L= 0;
e459.. - b73 + b75 - b89 =L= 0;
e460.. - b74 + b75 - b90 =L= 0;
e461.. - b76 + b77 - b81 =L= 0;
e462.. - b76 + b78 - b82 =L= 0;
e463.. - b76 + b79 - b83 =L= 0;
e464.. - b76 + b80 - b84 =L= 0;
e465.. - b77 + b78 - b85 =L= 0;
e466.. - b77 + b79 - b86 =L= 0;
e467.. - b77 + b80 - b87 =L= 0;
e468.. - b78 + b79 - b88 =L= 0;
e469.. - b78 + b80 - b89 =L= 0;
e470.. - b79 + b80 - b90 =L= 0;
e471.. - b81 + b82 - b85 =L= 0;
e472.. - b81 + b83 - b86 =L= 0;
e473.. - b81 + b84 - b87 =L= 0;
e474.. - b82 + b83 - b88 =L= 0;
e475.. - b82 + b84 - b89 =L= 0;
e476.. - b83 + b84 - b90 =L= 0;
e477.. - b85 + b86 - b88 =L= 0;
e478.. - b85 + b87 - b89 =L= 0;
e479.. - b86 + b87 - b90 =L= 0;
e480.. - b88 + b89 - b90 =L= 0;
e481.. 2*b1 - 2*b1*b56 - b56 - 2*b1*b81 + 3*b81 - 2*b2*b56 + 2*b2 - 2*b2*b66 -
7*b66 - 2*b2*b77 + 2*b77 + 2*b2*b86 + 4*b86 - 2*b3*b47 - b3 + 7*b47 - 2*
b3*b52 - 2*b52 + 2*b3*b54 - 4*b54 + 2*b3*b56 - 2*b3*b60 + 3*b60 + 2*b3*
b65 - 5*b65 + 2*b3*b66 + 2*b3*b76 - b76 + 2*b3*b77 - 2*b3*b83 + 4*b83 -
2*b3*b86 - 2*b4*b47 - b4 - 2*b4*b50 + 9*b50 + 2*b4*b54 + 2*b4*b56 - 2*b4
*b62 + 9*b62 + 2*b4*b65 + 2*b4*b66 + 2*b4*b71 - 5*b71 + 2*b4*b72 - 10*
b72 - 2*b4*b84 + 3*b84 - 2*b4*b87 + 8*b87 - 2*b5*b50 + 2*b5*b52 + 2*b5*
b60 - 2*b5*b62 - 2*b5*b63 + 2*b63 + 2*b5*b64 - 4*b64 + 2*b5*b68 - 4*b68
- 2*b5*b69 + 7*b69 + 2*b5*b70 - 5*b70 + 2*b5*b74 - 5*b74 - 2*b5*b80 + 3
*b80 - 2*b5*b90 + 6*b90 - 2*b6*b50 + 4*b6 - 2*b6*b56 - 2*b6*b60 + 2*b6*
b71 + 2*b6*b72 - 2*b6*b81 - 2*b6*b83 - 2*b6*b86 - 2*b7*b50 + 5*b7 - 2*b7
*b56 - 2*b7*b60 - 2*b7*b63 - 2*b7*b66 - 2*b7*b68 + 2*b7*b70 + 2*b7*b74
- 2*b7*b77 - 2*b7*b79 + 3*b79 + 2*b7*b86 - 2*b8*b50 + 2*b8 - 2*b8*b60
+ 2*b8*b71 + 2*b8*b72 - 2*b8*b83 - 2*b8*b86 - 2*b9*b50 + 3*b9 - 2*b9*
b60 - 2*b9*b63 - 2*b9*b68 + 2*b9*b70 + 2*b9*b74 - 2*b9*b79 - 2*b10*b47
- 3*b10 + 2*b10*b54 + 2*b10*b56 + 2*b10*b65 + 2*b10*b66 + 2*b11*b52 - 4
*b11 + 2*b11*b60 + 2*b11*b64 + 2*b11*b68 - 2*b12*b47 + 3*b12 - 2*b12*b50
- 2*b12*b56 - 2*b12*b60 + 2*b12*b65 + 2*b12*b66 + 2*b12*b71 + 2*b12*b72
- 2*b12*b81 - 2*b12*b83 - 2*b12*b86 - 2*b13*b47 + 4*b13 - 2*b13*b50 - 2
*b13*b56 - 2*b13*b60 - 2*b13*b63 + 2*b13*b64 - 2*b13*b66 + 2*b13*b70 + 2
*b13*b74 - 2*b13*b77 - 2*b13*b79 + 2*b13*b86 - 2*b14*b47 - b14 - 2*b14*
b50 + 2*b14*b54 + 2*b14*b56 - 2*b14*b62 + 2*b14*b65 + 2*b14*b66 + 2*b14*
b71 + 2*b14*b72 - 2*b14*b84 - 2*b14*b87 - 2*b15*b50 + 2*b15*b52 + 2*b15*
b60 - 2*b15*b62 - 2*b15*b63 + 2*b15*b64 + 2*b15*b68 - 2*b15*b69 + 2*b15*
b70 + 2*b15*b74 - 2*b15*b80 - 2*b15*b90 + 2*b16*b48 + 3*b16 - 5*b48 + 2*
b16*b53 - b53 + 2*b16*b55 - 4*b55 - 2*b16*b58 + 5*b58 - 2*b16*b62 - 2*
b16*b82 + b82 - 2*b16*b84 - 2*b16*b85 + 4*b85 - 2*b16*b87 + 2*b17*b46 +
2*b17 - 5*b46 + 2*b17*b48 + 2*b17*b51 - b51 - 2*b17*b58 + 2*b17*b59 - 4*
b59 - 2*b17*b62 - 2*b17*b67 + 5*b67 - 2*b17*b69 - 2*b17*b78 + b78 - 2*
b17*b80 + 2*b17*b88 - 4*b88 - 2*b17*b90 + 2*b18*b56 - 2*b18 + 2*b18*b66
+ 2*b18*b72 - 2*b18*b87 + 2*b19*b72 - 2*b19*b86 + 2*b20*b72 - 2*b20*b86
+ 2*b21*b56 - 2*b21 + 2*b21*b66 + 2*b22*b66 - b22 + 2*b22*b72 - 2*b22*
b86 + 2*b23*b56 - 2*b23 + 2*b23*b66 + 2*b23*b72 - 2*b23*b87 + 2*b24*b55
+ b24 - 2*b24*b85 - 2*b24*b87 - 2*b25*b50 + 5*b25 - 2*b25*b56 - 2*b25*
b60 - 2*b25*b63 - 2*b25*b66 - 2*b25*b68 - 2*b25*b72 - 2*b25*b74 + 2*b25*
b75 + 5*b75 + 2*b25*b87 + 2*b25*b90 - 2*b26*b50 + 3*b26 - 2*b26*b60 - 2*
b26*b63 - 2*b26*b68 - 2*b26*b74 + 2*b26*b75 + 2*b26*b90 + 2*b27*b50 - 4*
b27 + 2*b27*b62 + 2*b27*b63 + 2*b27*b69 - 2*b28*b47 + 4*b28 - 2*b28*b50
- 2*b28*b56 - 2*b28*b60 - 2*b28*b66 - 2*b28*b68 + 2*b28*b69 - 2*b28*b72
- 2*b28*b74 + 2*b28*b75 + 2*b28*b87 + 2*b28*b90 + 2*b30*b46 + b30 + 2*
b30*b48 + 2*b30*b49 - 5*b49 - 2*b30*b58 + 2*b30*b61 - 2*b61 - 2*b30*b62
- 2*b30*b67 - 2*b30*b69 - 2*b30*b73 + 5*b73 - 2*b30*b75 + 2*b30*b89 - 2
*b89 + 2*b31*b72 - 2*b31*b86 + 2*b32*b50 - 6*b32 + 2*b32*b56 + 2*b32*b60
+ 2*b32*b63 + 2*b32*b66 + 2*b32*b68 + 2*b33*b63 - 3*b33 + 2*b33*b66 + 2
*b33*b68 + 2*b34*b50 - 5*b34 + 2*b34*b56 + 2*b34*b60 + 2*b34*b63 + 2*b34
*b66 + 2*b34*b68 + 2*b34*b72 + 2*b34*b74 - 2*b34*b75 - 2*b34*b87 - 2*b34
*b90 + 2*b35*b49 + b35 + 2*b35*b55 + 2*b35*b59 - 2*b35*b73 - 2*b35*b75
- 2*b35*b85 - 2*b35*b87 + 2*b35*b88 - 2*b35*b90 + 2*b36*b50 - 4*b36 + 2
*b36*b60 + 2*b36*b63 + 2*b36*b68 + 2*b37*b63 - 2*b37 + 2*b37*b68 - 2*b37
*b72 + 2*b37*b86 + 2*b38*b50 - 3*b38 + 2*b38*b60 + 2*b38*b63 + 2*b38*b68
+ 2*b38*b74 - 2*b38*b75 - 2*b38*b90 + 2*b39*b49 + 2*b39*b59 - 2*b39*b73
- 2*b39*b75 + 2*b39*b88 - 2*b39*b90 - 2*b40*b47 + 7*b40 - 2*b40*b50 - 2
*b40*b56 - 2*b40*b60 - 2*b40*b63 - 2*b40*b66 - 2*b40*b68 - 2*b41*b50 + 4
*b41 - 2*b41*b62 - 2*b41*b63 - 2*b41*b69 + 2*b42*b46 + 2*b42 + 2*b42*b48
- 2*b42*b58 - 2*b42*b62 - 2*b42*b67 - 2*b42*b69 + 2*b43*b47 - 4*b43 + 2
*b43*b50 + 2*b43*b56 + 2*b43*b60 + 2*b43*b66 + 2*b43*b68 - 2*b43*b69 + 2
*b43*b72 + 2*b43*b74 - 2*b43*b75 - 2*b43*b87 - 2*b43*b90 + 2*b44*b46 + 2
*b44 + 2*b44*b49 + 2*b44*b55 + 2*b44*b59 - 2*b44*b67 - 2*b44*b69 - 2*b44
*b73 - 2*b44*b75 - 2*b44*b85 - 2*b44*b87 + 2*b44*b88 - 2*b44*b90 + 2*b45
*b46 + b45 + 2*b45*b48 + 2*b45*b49 - 2*b45*b58 + 2*b45*b61 - 2*b45*b62
- 2*b45*b67 - 2*b45*b69 - 2*b45*b73 - 2*b45*b75 + 2*b45*b89 + objvar
=G= 184;
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: 2024-08-26 Git hash: 6cc1607f