MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance transswitch0039p

Optimal Transmission Switching problem modeled using trigonometric functions (polar coordinates)
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
41866.12319000 p1 ( gdx sol )
(infeas: 6e-10)
Other points (infeas > 1e-08)  
Dual Bounds
2.00000000 (COUENNE)
2.00000000 (LINDO)
2.00000000 (SCIP)
2.00000002 (SHOT)
References Hijazi, H L, Coffrin, C, and Van Hentenryck, P, Convex Quadratic Relaxations of Nonlinear Programs in Power Systems, Tech. Rep. 2013-09, Optimization Online, 2013.
Application Electricity Networks
Added to library 14 Mar 2014
Problem type MBNLP
#Variables 328
#Binary Variables 46
#Integer Variables 0
#Nonlinear Variables 318
#Nonlinear Binary Variables 46
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 10
#Nonlinear Nonzeros in Objective 10
#Constraints 657
#Linear Constraints 381
#Quadratic Constraints 92
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 184
Operands in Gen. Nonlin. Functions cos mul sin sqr
Constraints curvature indefinite
#Nonzeros in Jacobian 1979
#Nonlinear Nonzeros in Jacobian 1104
#Nonzeros in (Upper-Left) Hessian of Lagrangian 1086
#Nonzeros in Diagonal of Hessian of Lagrangian 272
#Blocks in Hessian of Lagrangian 195
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 124
Average blocksize in Hessian of Lagrangian 1.630769
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 6.7559e-01
Maximal coefficient 3.8235e+02
Infeasibility of initial point 11.04
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
*        658      264      151      243        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        329      283       46        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*       1990      876     1114        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,x253,x254,x255,x256,x257,x258,x259
          ,x260,x261,x262,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,x309,x310,x311
          ,x312,x313,x314,x315,x316,x317,x318,x319,x320,x321,x322,x323,x324
          ,x325,x326,x327,x328,objvar;

Binary Variables  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;

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,e482,e483,e484,e485,e486,e487,e488,e489,e490,e491,e492,e493
          ,e494,e495,e496,e497,e498,e499,e500,e501,e502,e503,e504,e505,e506
          ,e507,e508,e509,e510,e511,e512,e513,e514,e515,e516,e517,e518,e519
          ,e520,e521,e522,e523,e524,e525,e526,e527,e528,e529,e530,e531,e532
          ,e533,e534,e535,e536,e537,e538,e539,e540,e541,e542,e543,e544,e545
          ,e546,e547,e548,e549,e550,e551,e552,e553,e554,e555,e556,e557,e558
          ,e559,e560,e561,e562,e563,e564,e565,e566,e567,e568,e569,e570,e571
          ,e572,e573,e574,e575,e576,e577,e578,e579,e580,e581,e582,e583,e584
          ,e585,e586,e587,e588,e589,e590,e591,e592,e593,e594,e595,e596,e597
          ,e598,e599,e600,e601,e602,e603,e604,e605,e606,e607,e608,e609,e610
          ,e611,e612,e613,e614,e615,e616,e617,e618,e619,e620,e621,e622,e623
          ,e624,e625,e626,e627,e628,e629,e630,e631,e632,e633,e634,e635,e636
          ,e637,e638,e639,e640,e641,e642,e643,e644,e645,e646,e647,e648,e649
          ,e650,e651,e652,e653,e654,e655,e656,e657,e658;


e1.. 100*sqr(x309) + 30*x309 + 100*sqr(x310) + 30*x310 + 100*sqr(x311) + 30*
     x311 + 100*sqr(x312) + 30*x312 + 100*sqr(x313) + 30*x313 + 100*sqr(x314)
      + 30*x314 + 100*sqr(x315) + 30*x315 + 100*sqr(x316) + 30*x316 + 100*sqr(
     x317) + 30*x317 + 100*sqr(x318) + 30*x318 - objvar =E= -2;

e2.. -(0.844411840765037*sqr(x12) - 0.844411840765037*x12*x13*cos(x235 - x236)
      + 22.9574469207994*x12*x13*sin(x235 - x236))*b263 + x40 =E= 0;

e3.. -(0.844411840765037*sqr(x13) - 0.844411840765037*x13*x12*cos(x236 - x235)
      + 22.9574469207994*x13*x12*sin(x236 - x235))*b263 + x41 =E= 0;

e4.. -(6.34517766497462*sqr(x5) - 6.34517766497462*x5*x8*cos(x228 - x231) + 
     88.8324873096447*x5*x8*sin(x228 - x231))*b264 + x42 =E= 0;

e5.. -(6.34517766497462*sqr(x8) - 6.34517766497462*x8*x5*cos(x231 - x228) + 
     88.8324873096447*x8*x5*sin(x231 - x228))*b264 + x43 =E= 0;

e6.. -(8.78293601003764*sqr(x16) - 8.78293601003764*x16*x17*cos(x239 - x240) + 
     111.668757841907*x16*x17*sin(x239 - x240))*b265 + x44 =E= 0;

e7.. -(8.78293601003764*sqr(x17) - 8.78293601003764*x17*x16*cos(x240 - x239) + 
     111.668757841907*x17*x16*sin(x240 - x239))*b265 + x45 =E= 0;

e8.. -40*x6*x31*sin(x229 - x254)*b266 + x46 =E= 0;

e9.. -40*x31*x6*sin(x254 - x229)*b266 + x47 =E= 0;

e10.. -(7.05882352941176*sqr(x6) - 7.05882352941176*x6*x7*cos(x229 - x230) + 
      108.235294117647*x6*x7*sin(x229 - x230))*b267 + x48 =E= 0;

e11.. -(7.05882352941176*sqr(x7) - 7.05882352941176*x7*x6*cos(x230 - x229) + 
      108.235294117647*x7*x6*sin(x230 - x229))*b267 + x49 =E= 0;

e12.. -(1.59744408945687*sqr(x1) - 1.59744408945687*x1*x39*cos(x224 - x262) + 
      39.9361022364217*x1*x39*sin(x224 - x262))*b268 + x50 =E= 0;

e13.. -(1.59744408945687*sqr(x39) - 1.59744408945687*x39*x1*cos(x262 - x224) + 
      39.9361022364217*x39*x1*sin(x262 - x224))*b268 + x51 =E= 0;

e14.. -(6.42054574638844*sqr(x26) - 6.42054574638844*x26*x27*cos(x249 - x250)
       + 67.4157303370787*x26*x27*sin(x249 - x250))*b269 + x52 =E= 0;

e15.. -(6.42054574638844*sqr(x27) - 6.42054574638844*x27*x26*cos(x250 - x249)
       + 67.4157303370787*x27*x26*sin(x250 - x249))*b269 + x53 =E= 0;

e16.. -50*x10*x32*sin(x233 - x255)*b270 + x54 =E= 0;

e17.. -50*x32*x10*sin(x255 - x233)*b270 + x55 =E= 0;

e18.. -(2.0570568805614*sqr(x1) - 2.0570568805614*x1*x2*cos(x224 - x225) + 
      24.1557250831639*x1*x2*sin(x224 - x225))*b271 + x56 =E= 0;

e19.. -(2.0570568805614*sqr(x2) - 2.0570568805614*x2*x1*cos(x225 - x224) + 
      24.1557250831639*x2*x1*sin(x225 - x224))*b271 + x57 =E= 0;

e20.. -(2.85475866309456*sqr(x3) - 2.85475866309456*x3*x4*cos(x226 - x227) + 
      46.7741227107032*x3*x4*sin(x226 - x227))*b272 + x58 =E= 0;

e21.. -(2.85475866309456*sqr(x4) - 2.85475866309456*x4*x3*cos(x227 - x226) + 
      46.7741227107032*x4*x3*sin(x227 - x226))*b272 + x59 =E= 0;

e22.. -69.9300699300699*x22*x35*sin(x245 - x258)*b273 + x60 =E= 0;

e23.. -69.9300699300699*x35*x22*sin(x258 - x245)*b273 + x61 =E= 0;

e24.. -(5.65955594253374*sqr(x2) - 5.65955594253374*x2*x3*cos(x225 - x226) + 
      65.737919024815*x2*x3*sin(x225 - x226))*b274 + x62 =E= 0;

e25.. -(5.65955594253374*sqr(x3) - 5.65955594253374*x3*x2*cos(x226 - x225) + 
      65.737919024815*x3*x2*sin(x226 - x225))*b274 + x63 =E= 0;

e26.. -(1.78885058218955*sqr(x23) - 1.78885058218955*x23*x24*cos(x246 - x247)
       + 28.4589865348338*x23*x24*sin(x246 - x247))*b275 + x64 =E= 0;

e27.. -(1.78885058218955*sqr(x24) - 1.78885058218955*x24*x23*cos(x247 - x246)
       + 28.4589865348338*x24*x23*sin(x247 - x246))*b275 + x65 =E= 0;

e28.. -(6.08775057616211*sqr(x28) - 6.08775057616211*x28*x29*cos(x251 - x252)
       + 65.660738357177*x28*x29*sin(x251 - x252))*b276 + x66 =E= 0;

e29.. -(6.08775057616211*sqr(x29) - 6.08775057616211*x29*x28*cos(x252 - x251)
       + 65.660738357177*x29*x28*sin(x252 - x251))*b276 + x67 =E= 0;

e30.. -(2.7708506511499*sqr(x20) - 2.7708506511499*x20*x34*cos(x243 - x257) + 
      55.4170130229981*x20*x34*sin(x243 - x257))*b277 + x68 =E= 0;

e31.. -(2.7708506511499*sqr(x34) - 2.7708506511499*x34*x20*cos(x257 - x243) + 
      55.4170130229981*x34*x20*sin(x257 - x243))*b277 + x69 =E= 0;

e32.. -(1.73849944821539*sqr(x8) - 1.73849944821539*x8*x9*cos(x231 - x232) + 
      27.4380565087908*x8*x9*sin(x231 - x232))*b278 + x70 =E= 0;

e33.. -(1.73849944821539*sqr(x9) - 1.73849944821539*x9*x8*cos(x232 - x231) + 
      27.4380565087908*x9*x8*sin(x232 - x231))*b278 + x71 =E= 0;

e34.. -(4.31922386869559*sqr(x17) - 4.31922386869559*x17*x27*cos(x240 - x250)
       + 57.4789022526414*x17*x27*sin(x240 - x250))*b279 + x72 =E= 0;

e35.. -(4.31922386869559*sqr(x27) - 4.31922386869559*x27*x17*cos(x250 - x240)
       + 57.4789022526414*x27*x17*sin(x250 - x240))*b279 + x73 =E= 0;

e36.. -(4.06834825061025*sqr(x21) - 4.06834825061025*x21*x22*cos(x244 - x245)
       + 71.1960943856794*x21*x22*sin(x244 - x245))*b280 + x74 =E= 0;

e37.. -(4.06834825061025*sqr(x22) - 4.06834825061025*x22*x21*cos(x245 - x244)
       + 71.1960943856794*x22*x21*sin(x245 - x244))*b280 + x75 =E= 0;

e38.. -(10.335154289089*sqr(x6) - 10.335154289089*x6*x11*cos(x229 - x234) + 
      121.068950243614*x6*x11*sin(x229 - x234))*b281 + x76 =E= 0;

e39.. -(10.335154289089*sqr(x11) - 10.335154289089*x11*x6*cos(x234 - x229) + 
      121.068950243614*x11*x6*sin(x234 - x229))*b281 + x77 =E= 0;

e40.. -(6.17630544637844*sqr(x3) - 6.17630544637844*x3*x18*cos(x226 - x241) + 
      74.6771476698484*x3*x18*sin(x226 - x241))*b282 + x78 =E= 0;

e41.. -(6.17630544637844*sqr(x18) - 6.17630544637844*x18*x3*cos(x241 - x226) + 
      74.6771476698484*x18*x3*sin(x241 - x226))*b282 + x79 =E= 0;

e42.. -(4.17961913220658*sqr(x16) - 4.17961913220658*x16*x19*cos(x239 - x242)
       + 50.9391081737677*x16*x19*sin(x239 - x242))*b283 + x80 =E= 0;

e43.. -(4.17961913220658*sqr(x19) - 4.17961913220658*x19*x16*cos(x242 - x239)
       + 50.9391081737677*x19*x16*sin(x242 - x239))*b283 + x81 =E= 0;

e44.. -(3.66626512334363*sqr(x19) - 3.66626512334363*x19*x20*cos(x242 - x243)
       + 72.2777981459174*x19*x20*sin(x242 - x243))*b284 + x82 =E= 0;

e45.. -(3.66626512334363*sqr(x20) - 3.66626512334363*x20*x19*cos(x243 - x242)
       + 72.2777981459174*x20*x19*sin(x243 - x242))*b284 + x83 =E= 0;

e46.. -(3.03740757263675*sqr(x25) - 3.03740757263675*x25*x26*cos(x248 - x249)
       + 30.6588326863022*x25*x26*sin(x248 - x249))*b285 + x84 =E= 0;

e47.. -(3.03740757263675*sqr(x26) - 3.03740757263675*x26*x25*cos(x249 - x248)
       + 30.6588326863022*x26*x25*sin(x249 - x248))*b285 + x85 =E= 0;

e48.. -(10.0930806324997*sqr(x15) - 10.0930806324997*x15*x16*cos(x238 - x239)
       + 105.416619939442*x15*x16*sin(x238 - x239))*b286 + x86 =E= 0;

e49.. -(10.0930806324997*sqr(x16) - 10.0930806324997*x16*x15*cos(x239 - x238)
       + 105.416619939442*x16*x15*sin(x239 - x238))*b286 + x87 =E= 0;

e50.. -(0.844411840765037*sqr(x12) - 0.844411840765037*x12*x11*cos(x235 - x234)
       + 22.9574469207994*x12*x11*sin(x235 - x234))*b287 + x88 =E= 0;

e51.. -(0.844411840765037*sqr(x11) - 0.844411840765037*x11*x12*cos(x234 - x235)
       + 22.9574469207994*x11*x12*sin(x234 - x235))*b287 + x89 =E= 0;

e52.. -(10.335154289089*sqr(x17) - 10.335154289089*x17*x18*cos(x240 - x241) + 
      121.068950243614*x17*x18*sin(x240 - x241))*b288 + x90 =E= 0;

e53.. -(10.335154289089*sqr(x18) - 10.335154289089*x18*x17*cos(x241 - x240) + 
      121.068950243614*x18*x17*sin(x241 - x240))*b288 + x91 =E= 0;

e54.. -(4.86381322957198*sqr(x4) - 4.86381322957198*x4*x5*cos(x227 - x228) + 
      77.8210116731518*x4*x5*sin(x227 - x228))*b289 + x92 =E= 0;

e55.. -(4.86381322957198*sqr(x5) - 4.86381322957198*x5*x4*cos(x228 - x227) + 
      77.8210116731518*x5*x4*sin(x228 - x227))*b289 + x93 =E= 0;

e56.. -(4.37421400842036*sqr(x16) - 4.37421400842036*x16*x21*cos(x239 - x244)
       + 73.8148613920936*x16*x21*sin(x239 - x244))*b290 + x94 =E= 0;

e57.. -(4.37421400842036*sqr(x21) - 4.37421400842036*x21*x16*cos(x244 - x239)
       + 73.8148613920936*x21*x16*sin(x244 - x239))*b290 + x95 =E= 0;

e58.. -(1.59744408945687*sqr(x9) - 1.59744408945687*x9*x39*cos(x232 - x262) + 
      39.9361022364217*x9*x39*sin(x232 - x262))*b291 + x96 =E= 0;

e59.. -(1.59744408945687*sqr(x39) - 1.59744408945687*x39*x9*cos(x262 - x232) + 
      39.9361022364217*x39*x9*sin(x262 - x232))*b291 + x97 =E= 0;

e60.. -(6.48508430609598*sqr(x22) - 6.48508430609598*x22*x23*cos(x245 - x246)
       + 103.761348897536*x22*x23*sin(x245 - x246))*b292 + x98 =E= 0;

e61.. -(6.48508430609598*sqr(x23) - 6.48508430609598*x23*x22*cos(x246 - x245)
       + 103.761348897536*x23*x22*sin(x246 - x245))*b292 + x99 =E= 0;

e62.. -(8.75316086364521*sqr(x13) - 8.75316086364521*x13*x14*cos(x236 - x237)
       + 98.2299163586851*x13*x14*sin(x236 - x237))*b293 + x100 =E= 0;

e63.. -(8.75316086364521*sqr(x14) - 8.75316086364521*x14*x13*cos(x237 - x236)
       + 98.2299163586851*x14*x13*sin(x237 - x236))*b293 + x101 =E= 0;

e64.. -55.2486187845304*x2*x30*sin(x225 - x253)*b294 + x102 =E= 0;

e65.. -55.2486187845304*x30*x2*sin(x253 - x225)*b294 + x103 =E= 0;

e66.. -(21.4477211796247*sqr(x10) - 21.4477211796247*x10*x13*cos(x233 - x236)
       + 230.563002680965*x10*x13*sin(x233 - x236))*b295 + x104 =E= 0;

e67.. -(21.4477211796247*sqr(x13) - 21.4477211796247*x13*x10*cos(x236 - x233)
       + 230.563002680965*x13*x10*sin(x236 - x233))*b295 + x105 =E= 0;

e68.. -(29.4117647058824*sqr(x5) - 29.4117647058824*x5*x6*cos(x228 - x229) + 
      382.352941176471*x5*x6*sin(x228 - x229))*b296 + x106 =E= 0;

e69.. -(29.4117647058824*sqr(x6) - 29.4117647058824*x6*x5*cos(x229 - x228) + 
      382.352941176471*x6*x5*sin(x229 - x228))*b296 + x107 =E= 0;

e70.. -(8.59598853868195*sqr(x16) - 8.59598853868195*x16*x24*cos(x239 - x247)
       + 169.054441260745*x16*x24*sin(x239 - x247))*b297 + x108 =E= 0;

e71.. -(8.59598853868195*sqr(x24) - 8.59598853868195*x24*x16*cos(x247 - x239)
       + 169.054441260745*x24*x16*sin(x247 - x239))*b297 + x109 =E= 0;

e72.. -(1.11399925733383*sqr(x25) - 1.11399925733383*x25*x37*cos(x248 - x260)
       + 43.0746379502414*x25*x37*sin(x248 - x260))*b298 + x110 =E= 0;

e73.. -(1.11399925733383*sqr(x37) - 1.11399925733383*x37*x25*cos(x260 - x248)
       + 43.0746379502414*x37*x25*sin(x260 - x248))*b298 + x111 =E= 0;

e74.. -(3.27868852459016*sqr(x29) - 3.27868852459016*x29*x38*cos(x252 - x261)
       + 63.9344262295082*x29*x38*sin(x252 - x261))*b299 + x112 =E= 0;

e75.. -(3.27868852459016*sqr(x38) - 3.27868852459016*x38*x29*cos(x261 - x252)
       + 63.9344262295082*x38*x29*sin(x261 - x252))*b299 + x113 =E= 0;

e76.. -(3.7964271402358*sqr(x14) - 3.7964271402358*x14*x15*cos(x237 - x238) + 
      45.7680383017316*x14*x15*sin(x237 - x238))*b300 + x114 =E= 0;

e77.. -(3.7964271402358*sqr(x15) - 3.7964271402358*x15*x14*cos(x238 - x237) + 
      45.7680383017316*x15*x14*sin(x238 - x237))*b300 + x115 =E= 0;

e78.. -(0.675593508897567*sqr(x23) - 0.675593508897567*x23*x36*cos(x246 - x259)
       + 36.7522868840276*x23*x36*sin(x246 - x259))*b301 + x116 =E= 0;

e79.. -(0.675593508897567*sqr(x36) - 0.675593508897567*x36*x23*cos(x259 - x246)
       + 36.7522868840276*x36*x23*sin(x259 - x246))*b301 + x117 =E= 0;

e80.. -(1.44716330603188*sqr(x26) - 1.44716330603188*x26*x29*cos(x249 - x252)
       + 15.8680187064899*x26*x29*sin(x249 - x252))*b302 + x118 =E= 0;

e81.. -(1.44716330603188*sqr(x29) - 1.44716330603188*x29*x26*cos(x252 - x249)
       + 15.8680187064899*x29*x26*sin(x252 - x249))*b302 + x119 =E= 0;

e82.. -(3.46311779547816*sqr(x19) - 3.46311779547816*x19*x33*cos(x242 - x256)
       + 70.2518181368426*x19*x33*sin(x242 - x256))*b303 + x120 =E= 0;

e83.. -(3.46311779547816*sqr(x33) - 3.46311779547816*x33*x19*cos(x256 - x242)
       + 70.2518181368426*x33*x19*sin(x256 - x242))*b303 + x121 =E= 0;

e84.. -(4.78898533373242*sqr(x4) - 4.78898533373242*x4*x14*cos(x227 - x237) + 
      77.2223885064352*x4*x14*sin(x227 - x237))*b304 + x122 =E= 0;

e85.. -(4.78898533373242*sqr(x14) - 4.78898533373242*x14*x4*cos(x237 - x227) + 
      77.2223885064352*x14*x4*sin(x237 - x227))*b304 + x123 =E= 0;

e86.. -(21.4477211796247*sqr(x10) - 21.4477211796247*x10*x11*cos(x233 - x234)
       + 230.563002680965*x10*x11*sin(x233 - x234))*b305 + x124 =E= 0;

e87.. -(21.4477211796247*sqr(x11) - 21.4477211796247*x11*x10*cos(x234 - x233)
       + 230.563002680965*x11*x10*sin(x234 - x233))*b305 + x125 =E= 0;

e88.. -(56.9290826284971*sqr(x2) - 56.9290826284971*x2*x25*cos(x225 - x248) + 
      69.9414443721535*x2*x25*sin(x225 - x248))*b306 + x126 =E= 0;

e89.. -(56.9290826284971*sqr(x25) - 56.9290826284971*x25*x2*cos(x248 - x225) + 
      69.9414443721535*x25*x2*sin(x248 - x225))*b306 + x127 =E= 0;

e90.. -(18.7617260787993*sqr(x7) - 18.7617260787993*x7*x8*cos(x230 - x231) + 
      215.759849906191*x7*x8*sin(x230 - x231))*b307 + x128 =E= 0;

e91.. -(18.7617260787993*sqr(x8) - 18.7617260787993*x8*x7*cos(x231 - x230) + 
      215.759849906191*x8*x7*sin(x231 - x230))*b307 + x129 =E= 0;

e92.. -(1.89824522679616*sqr(x26) - 1.89824522679616*x26*x28*cos(x249 - x251)
       + 20.9248427325902*x26*x28*sin(x249 - x251))*b308 + x130 =E= 0;

e93.. -(1.89824522679616*sqr(x28) - 1.89824522679616*x28*x26*cos(x251 - x249)
       + 20.9248427325902*x28*x26*sin(x251 - x249))*b308 + x131 =E= 0;

e94.. -(22.9574469207994*sqr(x12) - 22.9574469207994*x12*x13*cos(x235 - x236)
       - 0.844411840765037*x12*x13*sin(x235 - x236))*b263 + x132 =E= 0;

e95.. -(22.9574469207994*sqr(x13) - 22.9574469207994*x13*x12*cos(x236 - x235)
       - 0.844411840765037*x13*x12*sin(x236 - x235))*b263 + x133 =E= 0;

e96.. -(88.7586873096447*sqr(x5) - 88.8324873096447*x5*x8*cos(x228 - x231) - 
      6.34517766497462*x5*x8*sin(x228 - x231))*b264 + x134 =E= 0;

e97.. -(88.7586873096447*sqr(x8) - 88.8324873096447*x8*x5*cos(x231 - x228) - 
      6.34517766497462*x8*x5*sin(x231 - x228))*b264 + x135 =E= 0;

e98.. -(111.601657841907*sqr(x16) - 111.668757841907*x16*x17*cos(x239 - x240)
       - 8.78293601003764*x16*x17*sin(x239 - x240))*b265 + x136 =E= 0;

e99.. -(111.601657841907*sqr(x17) - 111.668757841907*x17*x16*cos(x240 - x239)
       - 8.78293601003764*x17*x16*sin(x240 - x239))*b265 + x137 =E= 0;

e100.. -(40*sqr(x6) - 40*x6*x31*cos(x229 - x254))*b266 + x138 =E= 0;

e101.. -(40*sqr(x31) - 40*x31*x6*cos(x254 - x229))*b266 + x139 =E= 0;

e102.. -(108.178794117647*sqr(x6) - 108.235294117647*x6*x7*cos(x229 - x230) - 
       7.05882352941176*x6*x7*sin(x229 - x230))*b267 + x140 =E= 0;

e103.. -(108.178794117647*sqr(x7) - 108.235294117647*x7*x6*cos(x230 - x229) - 
       7.05882352941176*x7*x6*sin(x230 - x229))*b267 + x141 =E= 0;

e104.. -(39.5611022364217*sqr(x1) - 39.9361022364217*x1*x39*cos(x224 - x262) - 
       1.59744408945687*x1*x39*sin(x224 - x262))*b268 + x142 =E= 0;

e105.. -(39.5611022364217*sqr(x39) - 39.9361022364217*x39*x1*cos(x262 - x224)
        - 1.59744408945687*x39*x1*sin(x262 - x224))*b268 + x143 =E= 0;

e106.. -(67.2959303370787*sqr(x26) - 67.4157303370787*x26*x27*cos(x249 - x250)
        - 6.42054574638844*x26*x27*sin(x249 - x250))*b269 + x144 =E= 0;

e107.. -(67.2959303370787*sqr(x27) - 67.4157303370787*x27*x26*cos(x250 - x249)
        - 6.42054574638844*x27*x26*sin(x250 - x249))*b269 + x145 =E= 0;

e108.. -(50*sqr(x10) - 50*x10*x32*cos(x233 - x255))*b270 + x146 =E= 0;

e109.. -(50*sqr(x32) - 50*x32*x10*cos(x255 - x233))*b270 + x147 =E= 0;

e110.. -(23.8063750831639*sqr(x1) - 24.1557250831639*x1*x2*cos(x224 - x225) - 
       2.0570568805614*x1*x2*sin(x224 - x225))*b271 + x148 =E= 0;

e111.. -(23.8063750831639*sqr(x2) - 24.1557250831639*x2*x1*cos(x225 - x224) - 
       2.0570568805614*x2*x1*sin(x225 - x224))*b271 + x149 =E= 0;

e112.. -(46.6634227107032*sqr(x3) - 46.7741227107032*x3*x4*cos(x226 - x227) - 
       2.85475866309456*x3*x4*sin(x226 - x227))*b272 + x150 =E= 0;

e113.. -(46.6634227107032*sqr(x4) - 46.7741227107032*x4*x3*cos(x227 - x226) - 
       2.85475866309456*x4*x3*sin(x227 - x226))*b272 + x151 =E= 0;

e114.. -(69.9300699300699*sqr(x22) - 69.9300699300699*x22*x35*cos(x245 - x258))
       *b273 + x152 =E= 0;

e115.. -(69.9300699300699*sqr(x35) - 69.9300699300699*x35*x22*cos(x258 - x245))
       *b273 + x153 =E= 0;

e116.. -(65.609319024815*sqr(x2) - 65.737919024815*x2*x3*cos(x225 - x226) - 
       5.65955594253374*x2*x3*sin(x225 - x226))*b274 + x154 =E= 0;

e117.. -(65.609319024815*sqr(x3) - 65.737919024815*x3*x2*cos(x226 - x225) - 
       5.65955594253374*x3*x2*sin(x226 - x225))*b274 + x155 =E= 0;

e118.. -(28.2784865348338*sqr(x23) - 28.4589865348338*x23*x24*cos(x246 - x247)
        - 1.78885058218955*x23*x24*sin(x246 - x247))*b275 + x156 =E= 0;

e119.. -(28.2784865348338*sqr(x24) - 28.4589865348338*x24*x23*cos(x247 - x246)
        - 1.78885058218955*x24*x23*sin(x247 - x246))*b275 + x157 =E= 0;

e120.. -(65.536238357177*sqr(x28) - 65.660738357177*x28*x29*cos(x251 - x252) - 
       6.08775057616211*x28*x29*sin(x251 - x252))*b276 + x158 =E= 0;

e121.. -(65.536238357177*sqr(x29) - 65.660738357177*x29*x28*cos(x252 - x251) - 
       6.08775057616211*x29*x28*sin(x252 - x251))*b276 + x159 =E= 0;

e122.. -(55.4170130229981*sqr(x20) - 55.4170130229981*x20*x34*cos(x243 - x257)
        - 2.7708506511499*x20*x34*sin(x243 - x257))*b277 + x160 =E= 0;

e123.. -(55.4170130229981*sqr(x34) - 55.4170130229981*x34*x20*cos(x257 - x243)
        - 2.7708506511499*x34*x20*sin(x257 - x243))*b277 + x161 =E= 0;

e124.. -(27.2478565087908*sqr(x8) - 27.4380565087908*x8*x9*cos(x231 - x232) - 
       1.73849944821539*x8*x9*sin(x231 - x232))*b278 + x162 =E= 0;

e125.. -(27.2478565087908*sqr(x9) - 27.4380565087908*x9*x8*cos(x232 - x231) - 
       1.73849944821539*x9*x8*sin(x232 - x231))*b278 + x163 =E= 0;

e126.. -(57.3181022526414*sqr(x17) - 57.4789022526414*x17*x27*cos(x240 - x250)
        - 4.31922386869559*x17*x27*sin(x240 - x250))*b279 + x164 =E= 0;

e127.. -(57.3181022526414*sqr(x27) - 57.4789022526414*x27*x17*cos(x250 - x240)
        - 4.31922386869559*x27*x17*sin(x250 - x240))*b279 + x165 =E= 0;

e128.. -(71.0678443856794*sqr(x21) - 71.1960943856794*x21*x22*cos(x244 - x245)
        - 4.06834825061025*x21*x22*sin(x244 - x245))*b280 + x166 =E= 0;

e129.. -(71.0678443856794*sqr(x22) - 71.1960943856794*x22*x21*cos(x245 - x244)
        - 4.06834825061025*x22*x21*sin(x245 - x244))*b280 + x167 =E= 0;

e130.. -(120.999500243614*sqr(x6) - 121.068950243614*x6*x11*cos(x229 - x234) - 
       10.335154289089*x6*x11*sin(x229 - x234))*b281 + x168 =E= 0;

e131.. -(120.999500243614*sqr(x11) - 121.068950243614*x11*x6*cos(x234 - x229)
        - 10.335154289089*x11*x6*sin(x234 - x229))*b281 + x169 =E= 0;

e132.. -(74.5702476698484*sqr(x3) - 74.6771476698484*x3*x18*cos(x226 - x241) - 
       6.17630544637844*x3*x18*sin(x226 - x241))*b282 + x170 =E= 0;

e133.. -(74.5702476698484*sqr(x18) - 74.6771476698484*x18*x3*cos(x241 - x226)
        - 6.17630544637844*x18*x3*sin(x241 - x226))*b282 + x171 =E= 0;

e134.. -(50.7871081737677*sqr(x16) - 50.9391081737677*x16*x19*cos(x239 - x242)
        - 4.17961913220658*x16*x19*sin(x239 - x242))*b283 + x172 =E= 0;

e135.. -(50.7871081737677*sqr(x19) - 50.9391081737677*x19*x16*cos(x242 - x239)
        - 4.17961913220658*x19*x16*sin(x242 - x239))*b283 + x173 =E= 0;

e136.. -(72.2777981459174*sqr(x19) - 72.2777981459174*x19*x20*cos(x242 - x243)
        - 3.66626512334363*x19*x20*sin(x242 - x243))*b284 + x174 =E= 0;

e137.. -(72.2777981459174*sqr(x20) - 72.2777981459174*x20*x19*cos(x243 - x242)
        - 3.66626512334363*x20*x19*sin(x243 - x242))*b284 + x175 =E= 0;

e138.. -(30.3933326863022*sqr(x25) - 30.6588326863022*x25*x26*cos(x248 - x249)
        - 3.03740757263675*x25*x26*sin(x248 - x249))*b285 + x176 =E= 0;

e139.. -(30.3933326863022*sqr(x26) - 30.6588326863022*x26*x25*cos(x249 - x248)
        - 3.03740757263675*x26*x25*sin(x249 - x248))*b285 + x177 =E= 0;

e140.. -(105.331119939442*sqr(x15) - 105.416619939442*x15*x16*cos(x238 - x239)
        - 10.0930806324997*x15*x16*sin(x238 - x239))*b286 + x178 =E= 0;

e141.. -(105.331119939442*sqr(x16) - 105.416619939442*x16*x15*cos(x239 - x238)
        - 10.0930806324997*x16*x15*sin(x239 - x238))*b286 + x179 =E= 0;

e142.. -(22.9574469207994*sqr(x12) - 22.9574469207994*x12*x11*cos(x235 - x234)
        - 0.844411840765037*x12*x11*sin(x235 - x234))*b287 + x180 =E= 0;

e143.. -(22.9574469207994*sqr(x11) - 22.9574469207994*x11*x12*cos(x234 - x235)
        - 0.844411840765037*x11*x12*sin(x234 - x235))*b287 + x181 =E= 0;

e144.. -(121.003000243614*sqr(x17) - 121.068950243614*x17*x18*cos(x240 - x241)
        - 10.335154289089*x17*x18*sin(x240 - x241))*b288 + x182 =E= 0;

e145.. -(121.003000243614*sqr(x18) - 121.068950243614*x18*x17*cos(x241 - x240)
        - 10.335154289089*x18*x17*sin(x241 - x240))*b288 + x183 =E= 0;

e146.. -(77.7539116731518*sqr(x4) - 77.8210116731518*x4*x5*cos(x227 - x228) - 
       4.86381322957198*x4*x5*sin(x227 - x228))*b289 + x184 =E= 0;

e147.. -(77.7539116731518*sqr(x5) - 77.8210116731518*x5*x4*cos(x228 - x227) - 
       4.86381322957198*x5*x4*sin(x228 - x227))*b289 + x185 =E= 0;

e148.. -(73.6874613920936*sqr(x16) - 73.8148613920936*x16*x21*cos(x239 - x244)
        - 4.37421400842036*x16*x21*sin(x239 - x244))*b290 + x186 =E= 0;

e149.. -(73.6874613920936*sqr(x21) - 73.8148613920936*x21*x16*cos(x244 - x239)
        - 4.37421400842036*x21*x16*sin(x244 - x239))*b290 + x187 =E= 0;

e150.. -(39.3361022364217*sqr(x9) - 39.9361022364217*x9*x39*cos(x232 - x262) - 
       1.59744408945687*x9*x39*sin(x232 - x262))*b291 + x188 =E= 0;

e151.. -(39.3361022364217*sqr(x39) - 39.9361022364217*x39*x9*cos(x262 - x232)
        - 1.59744408945687*x39*x9*sin(x262 - x232))*b291 + x189 =E= 0;

e152.. -(103.669048897536*sqr(x22) - 103.761348897536*x22*x23*cos(x245 - x246)
        - 6.48508430609598*x22*x23*sin(x245 - x246))*b292 + x190 =E= 0;

e153.. -(103.669048897536*sqr(x23) - 103.761348897536*x23*x22*cos(x246 - x245)
        - 6.48508430609598*x23*x22*sin(x246 - x245))*b292 + x191 =E= 0;

e154.. -(98.1437663586851*sqr(x13) - 98.2299163586851*x13*x14*cos(x236 - x237)
        - 8.75316086364521*x13*x14*sin(x236 - x237))*b293 + x192 =E= 0;

e155.. -(98.1437663586851*sqr(x14) - 98.2299163586851*x14*x13*cos(x237 - x236)
        - 8.75316086364521*x14*x13*sin(x237 - x236))*b293 + x193 =E= 0;

e156.. -(55.2486187845304*sqr(x2) - 55.2486187845304*x2*x30*cos(x225 - x253))*
       b294 + x194 =E= 0;

e157.. -(55.2486187845304*sqr(x30) - 55.2486187845304*x30*x2*cos(x253 - x225))*
       b294 + x195 =E= 0;

e158.. -(230.526552680965*sqr(x10) - 230.563002680965*x10*x13*cos(x233 - x236)
        - 21.4477211796247*x10*x13*sin(x233 - x236))*b295 + x196 =E= 0;

e159.. -(230.526552680965*sqr(x13) - 230.563002680965*x13*x10*cos(x236 - x233)
        - 21.4477211796247*x13*x10*sin(x236 - x233))*b295 + x197 =E= 0;

e160.. -(382.331241176471*sqr(x5) - 382.352941176471*x5*x6*cos(x228 - x229) - 
       29.4117647058824*x5*x6*sin(x228 - x229))*b296 + x198 =E= 0;

e161.. -(382.331241176471*sqr(x6) - 382.352941176471*x6*x5*cos(x229 - x228) - 
       29.4117647058824*x6*x5*sin(x229 - x228))*b296 + x199 =E= 0;

e162.. -(169.020441260745*sqr(x16) - 169.054441260745*x16*x24*cos(x239 - x247)
        - 8.59598853868195*x16*x24*sin(x239 - x247))*b297 + x200 =E= 0;

e163.. -(169.020441260745*sqr(x24) - 169.054441260745*x24*x16*cos(x247 - x239)
        - 8.59598853868195*x24*x16*sin(x247 - x239))*b297 + x201 =E= 0;

e164.. -(43.0746379502414*sqr(x25) - 43.0746379502414*x25*x37*cos(x248 - x260)
        - 1.11399925733383*x25*x37*sin(x248 - x260))*b298 + x202 =E= 0;

e165.. -(43.0746379502414*sqr(x37) - 43.0746379502414*x37*x25*cos(x260 - x248)
        - 1.11399925733383*x37*x25*sin(x260 - x248))*b298 + x203 =E= 0;

e166.. -(63.9344262295082*sqr(x29) - 63.9344262295082*x29*x38*cos(x252 - x261)
        - 3.27868852459016*x29*x38*sin(x252 - x261))*b299 + x204 =E= 0;

e167.. -(63.9344262295082*sqr(x38) - 63.9344262295082*x38*x29*cos(x261 - x252)
        - 3.27868852459016*x38*x29*sin(x261 - x252))*b299 + x205 =E= 0;

e168.. -(45.5850383017316*sqr(x14) - 45.7680383017316*x14*x15*cos(x237 - x238)
        - 3.7964271402358*x14*x15*sin(x237 - x238))*b300 + x206 =E= 0;

e169.. -(45.5850383017316*sqr(x15) - 45.7680383017316*x15*x14*cos(x238 - x237)
        - 3.7964271402358*x15*x14*sin(x238 - x237))*b300 + x207 =E= 0;

e170.. -(36.7522868840276*sqr(x23) - 36.7522868840276*x23*x36*cos(x246 - x259)
        - 0.675593508897567*x23*x36*sin(x246 - x259))*b301 + x208 =E= 0;

e171.. -(36.7522868840276*sqr(x36) - 36.7522868840276*x36*x23*cos(x259 - x246)
        - 0.675593508897567*x36*x23*sin(x259 - x246))*b301 + x209 =E= 0;

e172.. -(15.3535187064899*sqr(x26) - 15.8680187064899*x26*x29*cos(x249 - x252)
        - 1.44716330603188*x26*x29*sin(x249 - x252))*b302 + x210 =E= 0;

e173.. -(15.3535187064899*sqr(x29) - 15.8680187064899*x29*x26*cos(x252 - x249)
        - 1.44716330603188*x29*x26*sin(x252 - x249))*b302 + x211 =E= 0;

e174.. -(70.2518181368426*sqr(x19) - 70.2518181368426*x19*x33*cos(x242 - x256)
        - 3.46311779547816*x19*x33*sin(x242 - x256))*b303 + x212 =E= 0;

e175.. -(70.2518181368426*sqr(x33) - 70.2518181368426*x33*x19*cos(x256 - x242)
        - 3.46311779547816*x33*x19*sin(x256 - x242))*b303 + x213 =E= 0;

e176.. -(77.1532885064352*sqr(x4) - 77.2223885064352*x4*x14*cos(x227 - x237) - 
       4.78898533373242*x4*x14*sin(x227 - x237))*b304 + x214 =E= 0;

e177.. -(77.1532885064352*sqr(x14) - 77.2223885064352*x14*x4*cos(x237 - x227)
        - 4.78898533373242*x14*x4*sin(x237 - x227))*b304 + x215 =E= 0;

e178.. -(230.526552680965*sqr(x10) - 230.563002680965*x10*x11*cos(x233 - x234)
        - 21.4477211796247*x10*x11*sin(x233 - x234))*b305 + x216 =E= 0;

e179.. -(230.526552680965*sqr(x11) - 230.563002680965*x11*x10*cos(x234 - x233)
        - 21.4477211796247*x11*x10*sin(x234 - x233))*b305 + x217 =E= 0;

e180.. -(69.8684443721535*sqr(x2) - 69.9414443721535*x2*x25*cos(x225 - x248) - 
       56.9290826284971*x2*x25*sin(x225 - x248))*b306 + x218 =E= 0;

e181.. -(69.8684443721535*sqr(x25) - 69.9414443721535*x25*x2*cos(x248 - x225)
        - 56.9290826284971*x25*x2*sin(x248 - x225))*b306 + x219 =E= 0;

e182.. -(215.720849906191*sqr(x7) - 215.759849906191*x7*x8*cos(x230 - x231) - 
       18.7617260787993*x7*x8*sin(x230 - x231))*b307 + x220 =E= 0;

e183.. -(215.720849906191*sqr(x8) - 215.759849906191*x8*x7*cos(x231 - x230) - 
       18.7617260787993*x8*x7*sin(x231 - x230))*b307 + x221 =E= 0;

e184.. -(20.5347427325902*sqr(x26) - 20.9248427325902*x26*x28*cos(x249 - x251)
        - 1.89824522679616*x26*x28*sin(x249 - x251))*b308 + x222 =E= 0;

e185.. -(20.5347427325902*sqr(x28) - 20.9248427325902*x28*x26*cos(x251 - x249)
        - 1.89824522679616*x28*x26*sin(x251 - x249))*b308 + x223 =E= 0;

e186.. sqr(x40) + sqr(x132) =L= 25;

e187.. sqr(x41) + sqr(x133) =L= 25;

e188.. sqr(x42) + sqr(x134) =L= 81;

e189.. sqr(x43) + sqr(x135) =L= 81;

e190.. sqr(x44) + sqr(x136) =L= 36;

e191.. sqr(x45) + sqr(x137) =L= 36;

e192.. sqr(x46) + sqr(x138) =L= 324;

e193.. sqr(x47) + sqr(x139) =L= 324;

e194.. sqr(x48) + sqr(x140) =L= 81;

e195.. sqr(x49) + sqr(x141) =L= 81;

e196.. sqr(x50) + sqr(x142) =L= 100;

e197.. sqr(x51) + sqr(x143) =L= 100;

e198.. sqr(x52) + sqr(x144) =L= 36;

e199.. sqr(x53) + sqr(x145) =L= 36;

e200.. sqr(x54) + sqr(x146) =L= 81;

e201.. sqr(x55) + sqr(x147) =L= 81;

e202.. sqr(x56) + sqr(x148) =L= 36;

e203.. sqr(x57) + sqr(x149) =L= 36;

e204.. sqr(x58) + sqr(x150) =L= 25;

e205.. sqr(x59) + sqr(x151) =L= 25;

e206.. sqr(x60) + sqr(x152) =L= 81;

e207.. sqr(x61) + sqr(x153) =L= 81;

e208.. sqr(x62) + sqr(x154) =L= 25;

e209.. sqr(x63) + sqr(x155) =L= 25;

e210.. sqr(x64) + sqr(x156) =L= 36;

e211.. sqr(x65) + sqr(x157) =L= 36;

e212.. sqr(x66) + sqr(x158) =L= 36;

e213.. sqr(x67) + sqr(x159) =L= 36;

e214.. sqr(x68) + sqr(x160) =L= 81;

e215.. sqr(x69) + sqr(x161) =L= 81;

e216.. sqr(x70) + sqr(x162) =L= 81;

e217.. sqr(x71) + sqr(x163) =L= 81;

e218.. sqr(x72) + sqr(x164) =L= 36;

e219.. sqr(x73) + sqr(x165) =L= 36;

e220.. sqr(x74) + sqr(x166) =L= 81;

e221.. sqr(x75) + sqr(x167) =L= 81;

e222.. sqr(x76) + sqr(x168) =L= 23.04;

e223.. sqr(x77) + sqr(x169) =L= 23.04;

e224.. sqr(x78) + sqr(x170) =L= 25;

e225.. sqr(x79) + sqr(x171) =L= 25;

e226.. sqr(x80) + sqr(x172) =L= 36;

e227.. sqr(x81) + sqr(x173) =L= 36;

e228.. sqr(x82) + sqr(x174) =L= 81;

e229.. sqr(x83) + sqr(x175) =L= 81;

e230.. sqr(x84) + sqr(x176) =L= 36;

e231.. sqr(x85) + sqr(x177) =L= 36;

e232.. sqr(x86) + sqr(x178) =L= 36;

e233.. sqr(x87) + sqr(x179) =L= 36;

e234.. sqr(x88) + sqr(x180) =L= 25;

e235.. sqr(x89) + sqr(x181) =L= 25;

e236.. sqr(x90) + sqr(x182) =L= 36;

e237.. sqr(x91) + sqr(x183) =L= 36;

e238.. sqr(x92) + sqr(x184) =L= 36;

e239.. sqr(x93) + sqr(x185) =L= 36;

e240.. sqr(x94) + sqr(x186) =L= 36;

e241.. sqr(x95) + sqr(x187) =L= 36;

e242.. sqr(x96) + sqr(x188) =L= 81;

e243.. sqr(x97) + sqr(x189) =L= 81;

e244.. sqr(x98) + sqr(x190) =L= 36;

e245.. sqr(x99) + sqr(x191) =L= 36;

e246.. sqr(x100) + sqr(x192) =L= 36;

e247.. sqr(x101) + sqr(x193) =L= 36;

e248.. sqr(x102) + sqr(x194) =L= 81;

e249.. sqr(x103) + sqr(x195) =L= 81;

e250.. sqr(x104) + sqr(x196) =L= 36;

e251.. sqr(x105) + sqr(x197) =L= 36;

e252.. sqr(x106) + sqr(x198) =L= 144;

e253.. sqr(x107) + sqr(x199) =L= 144;

e254.. sqr(x108) + sqr(x200) =L= 36;

e255.. sqr(x109) + sqr(x201) =L= 36;

e256.. sqr(x110) + sqr(x202) =L= 81;

e257.. sqr(x111) + sqr(x203) =L= 81;

e258.. sqr(x112) + sqr(x204) =L= 144;

e259.. sqr(x113) + sqr(x205) =L= 144;

e260.. sqr(x114) + sqr(x206) =L= 36;

e261.. sqr(x115) + sqr(x207) =L= 36;

e262.. sqr(x116) + sqr(x208) =L= 81;

e263.. sqr(x117) + sqr(x209) =L= 81;

e264.. sqr(x118) + sqr(x210) =L= 36;

e265.. sqr(x119) + sqr(x211) =L= 36;

e266.. sqr(x120) + sqr(x212) =L= 81;

e267.. sqr(x121) + sqr(x213) =L= 81;

e268.. sqr(x122) + sqr(x214) =L= 25;

e269.. sqr(x123) + sqr(x215) =L= 25;

e270.. sqr(x124) + sqr(x216) =L= 36;

e271.. sqr(x125) + sqr(x217) =L= 36;

e272.. sqr(x126) + sqr(x218) =L= 25;

e273.. sqr(x127) + sqr(x219) =L= 25;

e274.. sqr(x128) + sqr(x220) =L= 81;

e275.. sqr(x129) + sqr(x221) =L= 81;

e276.. sqr(x130) + sqr(x222) =L= 36;

e277.. sqr(x131) + sqr(x223) =L= 36;

e278..    x309 =L= 10.4;

e279..    x310 =L= 6.46;

e280..    x311 =L= 7.25;

e281..    x312 =L= 6.52;

e282..    x313 =L= 5.08;

e283..    x314 =L= 6.87;

e284..    x315 =L= 5.8;

e285..    x316 =L= 5.64;

e286..    x317 =L= 8.65;

e287..    x318 =L= 11;

e288..    x309 =G= 0;

e289..    x310 =G= 0;

e290..    x311 =G= 0;

e291..    x312 =G= 0;

e292..    x313 =G= 0;

e293..    x314 =G= 0;

e294..    x315 =G= 0;

e295..    x316 =G= 0;

e296..    x317 =G= 0;

e297..    x318 =G= 0;

e298..    x319 =L= 4;

e299..    x320 =L= 3;

e300..    x321 =L= 3;

e301..    x322 =L= 2.5;

e302..    x323 =L= 1.67;

e303..    x324 =L= 3;

e304..    x325 =L= 2.4;

e305..    x326 =L= 2.5;

e306..    x327 =L= 3;

e307..    x328 =L= 3;

e308..    x319 =G= 1.4;

e309..    x320 =G= -1;

e310..    x321 =G= 1.5;

e311..    x322 =G= 0;

e312..    x323 =G= 0;

e313..    x324 =G= -1;

e314..    x325 =G= 0;

e315..    x326 =G= 0;

e316..    x327 =G= -1.5;

e317..    x328 =G= -1;

e318..    x1 =L= 1.06;

e319..    x2 =L= 1.06;

e320..    x3 =L= 1.06;

e321..    x4 =L= 1.06;

e322..    x5 =L= 1.06;

e323..    x6 =L= 1.06;

e324..    x7 =L= 1.06;

e325..    x8 =L= 1.06;

e326..    x9 =L= 1.06;

e327..    x10 =L= 1.06;

e328..    x11 =L= 1.06;

e329..    x12 =L= 1.06;

e330..    x13 =L= 1.06;

e331..    x14 =L= 1.06;

e332..    x15 =L= 1.06;

e333..    x16 =L= 1.06;

e334..    x17 =L= 1.06;

e335..    x18 =L= 1.06;

e336..    x19 =L= 1.06;

e337..    x20 =L= 1.06;

e338..    x21 =L= 1.06;

e339..    x22 =L= 1.06;

e340..    x23 =L= 1.06;

e341..    x24 =L= 1.06;

e342..    x25 =L= 1.06;

e343..    x26 =L= 1.06;

e344..    x27 =L= 1.06;

e345..    x28 =L= 1.06;

e346..    x29 =L= 1.06;

e347..    x30 =L= 1.06;

e348..    x31 =L= 1.06;

e349..    x32 =L= 1.06;

e350..    x33 =L= 1.06;

e351..    x34 =L= 1.06;

e352..    x35 =L= 1.06;

e353..    x36 =L= 1.06;

e354..    x37 =L= 1.06;

e355..    x38 =L= 1.06;

e356..    x39 =L= 1.06;

e357..    x1 =G= 0.94;

e358..    x2 =G= 0.94;

e359..    x3 =G= 0.94;

e360..    x4 =G= 0.94;

e361..    x5 =G= 0.94;

e362..    x6 =G= 0.94;

e363..    x7 =G= 0.94;

e364..    x8 =G= 0.94;

e365..    x9 =G= 0.94;

e366..    x10 =G= 0.94;

e367..    x11 =G= 0.94;

e368..    x12 =G= 0.94;

e369..    x13 =G= 0.94;

e370..    x14 =G= 0.94;

e371..    x15 =G= 0.94;

e372..    x16 =G= 0.94;

e373..    x17 =G= 0.94;

e374..    x18 =G= 0.94;

e375..    x19 =G= 0.94;

e376..    x20 =G= 0.94;

e377..    x21 =G= 0.94;

e378..    x22 =G= 0.94;

e379..    x23 =G= 0.94;

e380..    x24 =G= 0.94;

e381..    x25 =G= 0.94;

e382..    x26 =G= 0.94;

e383..    x27 =G= 0.94;

e384..    x28 =G= 0.94;

e385..    x29 =G= 0.94;

e386..    x30 =G= 0.94;

e387..    x31 =G= 0.94;

e388..    x32 =G= 0.94;

e389..    x33 =G= 0.94;

e390..    x34 =G= 0.94;

e391..    x35 =G= 0.94;

e392..    x36 =G= 0.94;

e393..    x37 =G= 0.94;

e394..    x38 =G= 0.94;

e395..    x39 =G= 0.94;

e396..    x235 - x236 =G= -0.26;

e397..  - x235 + x236 =G= -0.26;

e398..    x228 - x231 =G= -0.26;

e399..  - x228 + x231 =G= -0.26;

e400..    x239 - x240 =G= -0.26;

e401..  - x239 + x240 =G= -0.26;

e402..    x229 - x254 =G= -0.26;

e403..  - x229 + x254 =G= -0.26;

e404..    x229 - x230 =G= -0.26;

e405..  - x229 + x230 =G= -0.26;

e406..    x224 - x262 =G= -0.26;

e407..  - x224 + x262 =G= -0.26;

e408..    x249 - x250 =G= -0.26;

e409..  - x249 + x250 =G= -0.26;

e410..    x233 - x255 =G= -0.26;

e411..  - x233 + x255 =G= -0.26;

e412..    x224 - x225 =G= -0.26;

e413..  - x224 + x225 =G= -0.26;

e414..    x226 - x227 =G= -0.26;

e415..  - x226 + x227 =G= -0.26;

e416..    x245 - x258 =G= -0.26;

e417..  - x245 + x258 =G= -0.26;

e418..    x225 - x226 =G= -0.26;

e419..  - x225 + x226 =G= -0.26;

e420..    x246 - x247 =G= -0.26;

e421..  - x246 + x247 =G= -0.26;

e422..    x251 - x252 =G= -0.26;

e423..  - x251 + x252 =G= -0.26;

e424..    x243 - x257 =G= -0.26;

e425..  - x243 + x257 =G= -0.26;

e426..    x231 - x232 =G= -0.26;

e427..  - x231 + x232 =G= -0.26;

e428..    x240 - x250 =G= -0.26;

e429..  - x240 + x250 =G= -0.26;

e430..    x244 - x245 =G= -0.26;

e431..  - x244 + x245 =G= -0.26;

e432..    x229 - x234 =G= -0.26;

e433..  - x229 + x234 =G= -0.26;

e434..    x226 - x241 =G= -0.26;

e435..  - x226 + x241 =G= -0.26;

e436..    x239 - x242 =G= -0.26;

e437..  - x239 + x242 =G= -0.26;

e438..    x242 - x243 =G= -0.26;

e439..  - x242 + x243 =G= -0.26;

e440..    x248 - x249 =G= -0.26;

e441..  - x248 + x249 =G= -0.26;

e442..    x238 - x239 =G= -0.26;

e443..  - x238 + x239 =G= -0.26;

e444..  - x234 + x235 =G= -0.26;

e445..    x234 - x235 =G= -0.26;

e446..    x240 - x241 =G= -0.26;

e447..  - x240 + x241 =G= -0.26;

e448..    x227 - x228 =G= -0.26;

e449..  - x227 + x228 =G= -0.26;

e450..    x239 - x244 =G= -0.26;

e451..  - x239 + x244 =G= -0.26;

e452..    x232 - x262 =G= -0.26;

e453..  - x232 + x262 =G= -0.26;

e454..    x245 - x246 =G= -0.26;

e455..  - x245 + x246 =G= -0.26;

e456..    x236 - x237 =G= -0.26;

e457..  - x236 + x237 =G= -0.26;

e458..    x225 - x253 =G= -0.26;

e459..  - x225 + x253 =G= -0.26;

e460..    x233 - x236 =G= -0.26;

e461..  - x233 + x236 =G= -0.26;

e462..    x228 - x229 =G= -0.26;

e463..  - x228 + x229 =G= -0.26;

e464..    x239 - x247 =G= -0.26;

e465..  - x239 + x247 =G= -0.26;

e466..    x248 - x260 =G= -0.26;

e467..  - x248 + x260 =G= -0.26;

e468..    x252 - x261 =G= -0.26;

e469..  - x252 + x261 =G= -0.26;

e470..    x237 - x238 =G= -0.26;

e471..  - x237 + x238 =G= -0.26;

e472..    x246 - x259 =G= -0.26;

e473..  - x246 + x259 =G= -0.26;

e474..    x249 - x252 =G= -0.26;

e475..  - x249 + x252 =G= -0.26;

e476..    x242 - x256 =G= -0.26;

e477..  - x242 + x256 =G= -0.26;

e478..    x227 - x237 =G= -0.26;

e479..  - x227 + x237 =G= -0.26;

e480..    x233 - x234 =G= -0.26;

e481..  - x233 + x234 =G= -0.26;

e482..    x225 - x248 =G= -0.26;

e483..  - x225 + x248 =G= -0.26;

e484..    x230 - x231 =G= -0.26;

e485..  - x230 + x231 =G= -0.26;

e486..    x249 - x251 =G= -0.26;

e487..  - x249 + x251 =G= -0.26;

e488..    x235 - x236 =L= 0.26;

e489..  - x235 + x236 =L= 0.26;

e490..    x228 - x231 =L= 0.26;

e491..  - x228 + x231 =L= 0.26;

e492..    x239 - x240 =L= 0.26;

e493..  - x239 + x240 =L= 0.26;

e494..    x229 - x254 =L= 0.26;

e495..  - x229 + x254 =L= 0.26;

e496..    x229 - x230 =L= 0.26;

e497..  - x229 + x230 =L= 0.26;

e498..    x224 - x262 =L= 0.26;

e499..  - x224 + x262 =L= 0.26;

e500..    x249 - x250 =L= 0.26;

e501..  - x249 + x250 =L= 0.26;

e502..    x233 - x255 =L= 0.26;

e503..  - x233 + x255 =L= 0.26;

e504..    x224 - x225 =L= 0.26;

e505..  - x224 + x225 =L= 0.26;

e506..    x226 - x227 =L= 0.26;

e507..  - x226 + x227 =L= 0.26;

e508..    x245 - x258 =L= 0.26;

e509..  - x245 + x258 =L= 0.26;

e510..    x225 - x226 =L= 0.26;

e511..  - x225 + x226 =L= 0.26;

e512..    x246 - x247 =L= 0.26;

e513..  - x246 + x247 =L= 0.26;

e514..    x251 - x252 =L= 0.26;

e515..  - x251 + x252 =L= 0.26;

e516..    x243 - x257 =L= 0.26;

e517..  - x243 + x257 =L= 0.26;

e518..    x231 - x232 =L= 0.26;

e519..  - x231 + x232 =L= 0.26;

e520..    x240 - x250 =L= 0.26;

e521..  - x240 + x250 =L= 0.26;

e522..    x244 - x245 =L= 0.26;

e523..  - x244 + x245 =L= 0.26;

e524..    x229 - x234 =L= 0.26;

e525..  - x229 + x234 =L= 0.26;

e526..    x226 - x241 =L= 0.26;

e527..  - x226 + x241 =L= 0.26;

e528..    x239 - x242 =L= 0.26;

e529..  - x239 + x242 =L= 0.26;

e530..    x242 - x243 =L= 0.26;

e531..  - x242 + x243 =L= 0.26;

e532..    x248 - x249 =L= 0.26;

e533..  - x248 + x249 =L= 0.26;

e534..    x238 - x239 =L= 0.26;

e535..  - x238 + x239 =L= 0.26;

e536..  - x234 + x235 =L= 0.26;

e537..    x234 - x235 =L= 0.26;

e538..    x240 - x241 =L= 0.26;

e539..  - x240 + x241 =L= 0.26;

e540..    x227 - x228 =L= 0.26;

e541..  - x227 + x228 =L= 0.26;

e542..    x239 - x244 =L= 0.26;

e543..  - x239 + x244 =L= 0.26;

e544..    x232 - x262 =L= 0.26;

e545..  - x232 + x262 =L= 0.26;

e546..    x245 - x246 =L= 0.26;

e547..  - x245 + x246 =L= 0.26;

e548..    x236 - x237 =L= 0.26;

e549..  - x236 + x237 =L= 0.26;

e550..    x225 - x253 =L= 0.26;

e551..  - x225 + x253 =L= 0.26;

e552..    x233 - x236 =L= 0.26;

e553..  - x233 + x236 =L= 0.26;

e554..    x228 - x229 =L= 0.26;

e555..  - x228 + x229 =L= 0.26;

e556..    x239 - x247 =L= 0.26;

e557..  - x239 + x247 =L= 0.26;

e558..    x248 - x260 =L= 0.26;

e559..  - x248 + x260 =L= 0.26;

e560..    x252 - x261 =L= 0.26;

e561..  - x252 + x261 =L= 0.26;

e562..    x237 - x238 =L= 0.26;

e563..  - x237 + x238 =L= 0.26;

e564..    x246 - x259 =L= 0.26;

e565..  - x246 + x259 =L= 0.26;

e566..    x249 - x252 =L= 0.26;

e567..  - x249 + x252 =L= 0.26;

e568..    x242 - x256 =L= 0.26;

e569..  - x242 + x256 =L= 0.26;

e570..    x227 - x237 =L= 0.26;

e571..  - x227 + x237 =L= 0.26;

e572..    x233 - x234 =L= 0.26;

e573..  - x233 + x234 =L= 0.26;

e574..    x225 - x248 =L= 0.26;

e575..  - x225 + x248 =L= 0.26;

e576..    x230 - x231 =L= 0.26;

e577..  - x230 + x231 =L= 0.26;

e578..    x249 - x251 =L= 0.26;

e579..  - x249 + x251 =L= 0.26;

e580..    x254 =E= 0;

e581..    x103 - x309 =E= 0;

e582..    x47 - x310 =E= -0.092;

e583..    x55 - x311 =E= 0;

e584..    x121 - x312 =E= 0;

e585..    x69 - x313 =E= 0;

e586..    x61 - x314 =E= 0;

e587..    x117 - x315 =E= 0;

e588..    x111 - x316 =E= 0;

e589..    x113 - x317 =E= 0;

e590..    x51 + x97 - x318 =E= -11.04;

e591..    x195 - x319 =E= 0;

e592..    x139 - x320 =E= -0.046;

e593..    x147 - x321 =E= 0;

e594..    x213 - x322 =E= 0;

e595..    x161 - x323 =E= 0;

e596..    x153 - x324 =E= 0;

e597..    x209 - x325 =E= 0;

e598..    x203 - x326 =E= 0;

e599..    x205 - x327 =E= 0;

e600..    x143 + x189 - x328 =E= -2.5;

e601..    x50 + x56 =E= -0.976;

e602..    x57 + x62 + x102 + x126 =E= 0;

e603..    x58 + x63 + x78 =E= -3.22;

e604..    x59 + x92 + x122 =E= -5;

e605..    x42 + x93 + x106 =E= 0;

e606..    x46 + x48 + x76 + x107 =E= 0;

e607..    x49 + x128 =E= -2.338;

e608..    x43 + x70 + x129 =E= -5.22;

e609..    x71 + x96 =E= -0.065;

e610..    x54 + x104 + x124 =E= 0;

e611..    x77 + x89 + x125 =E= 0;

e612..    x40 + x88 =E= -0.0853;

e613..    x41 + x100 + x105 =E= 0;

e614..    x101 + x114 + x123 =E= 0;

e615..    x86 + x115 =E= -3.2;

e616..    x44 + x80 + x87 + x94 + x108 =E= -3.29;

e617..    x45 + x72 + x90 =E= 0;

e618..    x79 + x91 =E= -1.58;

e619..    x81 + x82 + x120 =E= 0;

e620..    x68 + x83 =E= -6.8;

e621..    x74 + x95 =E= -2.74;

e622..    x60 + x75 + x98 =E= 0;

e623..    x64 + x99 + x116 =E= -2.475;

e624..    x65 + x109 =E= -3.086;

e625..    x84 + x110 + x127 =E= -2.24;

e626..    x52 + x85 + x118 + x130 =E= -1.39;

e627..    x53 + x73 =E= -2.81;

e628..    x66 + x131 =E= -2.06;

e629..    x67 + x112 + x119 =E= -2.835;

e630..    x142 + x148 =E= -0.442;

e631..    x149 + x154 + x194 + x218 =E= 0;

e632..    x150 + x155 + x170 =E= -0.024;

e633..    x151 + x184 + x214 =E= -1.84;

e634..    x134 + x185 + x198 =E= 0;

e635..    x138 + x140 + x168 + x199 =E= 0;

e636..    x141 + x220 =E= -0.84;

e637..    x135 + x162 + x221 =E= -1.766;

e638..    x163 + x188 =E= 0.666;

e639..    x146 + x196 + x216 =E= 0;

e640..    x169 + x181 + x217 =E= 0;

e641..    x132 + x180 =E= -0.88;

e642..    x133 + x192 + x197 =E= 0;

e643..    x193 + x206 + x215 =E= 0;

e644..    x178 + x207 =E= -1.53;

e645..    x136 + x172 + x179 + x186 + x200 =E= -0.323;

e646..    x137 + x164 + x182 =E= 0;

e647..    x171 + x183 =E= -0.3;

e648..    x173 + x174 + x212 =E= 0;

e649..    x160 + x175 =E= -1.03;

e650..    x166 + x187 =E= -1.15;

e651..    x152 + x167 + x190 =E= 0;

e652..    x156 + x191 + x208 =E= -0.846;

e653..    x157 + x201 =E= 0.922;

e654..    x176 + x202 + x219 =E= -0.472;

e655..    x144 + x177 + x210 + x222 =E= -0.17;

e656..    x145 + x165 =E= -0.755;

e657..    x158 + x223 =E= -0.276;

e658..    x159 + x204 + x211 =E= -0.269;

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: 2022-08-11 Git hash: f176bd52
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