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Instance p_ball_15b_5p_2d_h
Select 5-points in 2-dimensional balls, such that the l1-distance between all points is minimized. Only one point can be assigned to each ball, and in total there are 15 balls with radius one. This is a convex-hull formulation.
Formatsⓘ | ams gms mod nl osil py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | 6.59545931 (ALPHAECP) 6.59986769 (ANTIGONE) 6.59984278 (BARON) 6.59986767 (BONMIN) 6.59982425 (COUENNE) 6.59986769 (LINDO) 6.59986136 (SCIP) 0.00000000 (SHOT) |
Referencesⓘ | Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020. |
Sourceⓘ | p_ball_15b_5p_2d_H.gms with the epsilon in the perspective formulation changed to 1e-4, contributed by Jan Kronqvist and Ruth Misener |
Applicationⓘ | Geometry |
Added to libraryⓘ | 26 Aug 2020 |
Problem typeⓘ | MBNLP |
#Variablesⓘ | 255 |
#Binary Variablesⓘ | 75 |
#Integer Variablesⓘ | 0 |
#Nonlinear Variablesⓘ | 225 |
#Nonlinear Binary Variablesⓘ | 75 |
#Nonlinear Integer Variablesⓘ | 0 |
Objective Senseⓘ | min |
Objective typeⓘ | linear |
Objective curvatureⓘ | linear |
#Nonzeros in Objectiveⓘ | 20 |
#Nonlinear Nonzeros in Objectiveⓘ | 0 |
#Constraintsⓘ | 299 |
#Linear Constraintsⓘ | 224 |
#Quadratic Constraintsⓘ | 0 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 0 |
#General Nonlinear Constraintsⓘ | 75 |
Operands in Gen. Nonlin. Functionsⓘ | div mul sqr |
Constraints curvatureⓘ | convex |
#Nonzeros in Jacobianⓘ | 963 |
#Nonlinear Nonzeros in Jacobianⓘ | 225 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 525 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 225 |
#Blocks in Hessian of Lagrangianⓘ | 75 |
Minimal blocksize in Hessian of Lagrangianⓘ | 3 |
Maximal blocksize in Hessian of Lagrangianⓘ | 3 |
Average blocksize in Hessian of Lagrangianⓘ | 3.0 |
#Semicontinuitiesⓘ | 0 |
#Nonlinear Semicontinuitiesⓘ | 0 |
#SOS type 1ⓘ | 0 |
#SOS type 2ⓘ | 0 |
Minimal coefficientⓘ | 1.0000e-04 |
Maximal coefficientⓘ | 1.0000e+01 |
Infeasibility of initial pointⓘ | 1 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 300 16 0 284 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 256 181 75 0 0 0 0 0 * FX 0 * * Nonzero counts * Total const NL DLL * 984 759 225 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,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,objvar; Positive Variables 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; 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; 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; e1.. x76 - x77 - x78 =L= 0; e2.. - x76 + x77 - x78 =L= 0; e3.. x79 - x80 - x81 =L= 0; e4.. - x79 + x80 - x81 =L= 0; e5.. x76 - x82 - x83 =L= 0; e6.. - x76 + x82 - x83 =L= 0; e7.. x79 - x84 - x85 =L= 0; e8.. - x79 + x84 - x85 =L= 0; e9.. x76 - x86 - x87 =L= 0; e10.. - x76 + x86 - x87 =L= 0; e11.. x79 - x88 - x89 =L= 0; e12.. - x79 + x88 - x89 =L= 0; e13.. x76 - x90 - x91 =L= 0; e14.. - x76 + x90 - x91 =L= 0; e15.. x79 - x92 - x93 =L= 0; e16.. - x79 + x92 - x93 =L= 0; e17.. x77 - x82 - x94 =L= 0; e18.. - x77 + x82 - x94 =L= 0; e19.. x80 - x84 - x95 =L= 0; e20.. - x80 + x84 - x95 =L= 0; e21.. x77 - x86 - x96 =L= 0; e22.. - x77 + x86 - x96 =L= 0; e23.. x80 - x88 - x97 =L= 0; e24.. - x80 + x88 - x97 =L= 0; e25.. x77 - x90 - x98 =L= 0; e26.. - x77 + x90 - x98 =L= 0; e27.. x80 - x92 - x99 =L= 0; e28.. - x80 + x92 - x99 =L= 0; e29.. x82 - x86 - x100 =L= 0; e30.. - x82 + x86 - x100 =L= 0; e31.. x84 - x88 - x101 =L= 0; e32.. - x84 + x88 - x101 =L= 0; e33.. x82 - x90 - x102 =L= 0; e34.. - x82 + x90 - x102 =L= 0; e35.. x84 - x92 - x103 =L= 0; e36.. - x84 + x92 - x103 =L= 0; e37.. x86 - x90 - x104 =L= 0; e38.. - x86 + x90 - x104 =L= 0; e39.. x88 - x92 - x105 =L= 0; e40.. - x88 + x92 - x105 =L= 0; e41.. (-1 + sqr(8.68340342427357 - x106/(0.0001 + 0.9999*b1)) + sqr( 8.57974596088368 - x107/(0.0001 + 0.9999*b1)))*(0.0001 + 0.9999*b1) + 0.0148013535781986*b1 =L= 0.0148013535781986; e42.. (-1 + sqr(9.63614333912176 - x108/(0.0001 + 0.9999*b2)) + sqr( 8.80176337918095 - x109/(0.0001 + 0.9999*b2)))*(0.0001 + 0.9999*b2) + 0.0169326297035192*b2 =L= 0.0169326297035192; e43.. (-1 + sqr(3.68142205418198 - x110/(0.0001 + 0.9999*b3)) + sqr( 1.1692321814062 - x111/(0.0001 + 0.9999*b3)))*(0.0001 + 0.9999*b3) + 0.00139199722350534*b3 =L= 0.00139199722350534; e44.. (-1 + sqr(9.7121756733827 - x112/(0.0001 + 0.9999*b4)) + sqr( 7.68772804421774 - x113/(0.0001 + 0.9999*b4)))*(0.0001 + 0.9999*b4) + 0.0152427518792499*b4 =L= 0.0152427518792499; e45.. (-1 + sqr(3.2772228491781 - x114/(0.0001 + 0.9999*b5)) + sqr( 8.20105404549271 - x115/(0.0001 + 0.9999*b5)))*(0.0001 + 0.9999*b5) + 0.00769974770602674*b5 =L= 0.00769974770602674; e46.. (-1 + sqr(8.95169370625893 - x116/(0.0001 + 0.9999*b6)) + sqr( 5.71833771240185 - x117/(0.0001 + 0.9999*b6)))*(0.0001 + 0.9999*b6) + 0.0111832206403753*b6 =L= 0.0111832206403753; e47.. (-1 + sqr(6.39713701672676 - x118/(0.0001 + 0.9999*b7)) + sqr( 2.19374777991393 - x119/(0.0001 + 0.9999*b7)))*(0.0001 + 0.9999*b7) + 0.00447358913326531*b7 =L= 0.00447358913326531; e48.. (-1 + sqr(8.63324272987351 - x120/(0.0001 + 0.9999*b8)) + sqr( 2.92174290170279 - x121/(0.0001 + 0.9999*b8)))*(0.0001 + 0.9999*b8) + 0.00820694616165644*b8 =L= 0.00820694616165644; e49.. (-1 + sqr(3.63244627881363 - x122/(0.0001 + 0.9999*b9)) + sqr( 1.91739848753332 - x123/(0.0001 + 0.9999*b9)))*(0.0001 + 0.9999*b9) + 0.00158710829284621*b9 =L= 0.00158710829284621; e50.. (-1 + sqr(0.303084489788861 - x124/(0.0001 + 0.9999*b10)) + sqr( 2.88588654972735 - x125/(0.0001 + 0.9999*b10)))*(0.0001 + 0.9999*b10) + 0.00074202013858478*b10 =L= 0.00074202013858478; e51.. (-1 + sqr(9.32557624217471 - x126/(0.0001 + 0.9999*b11)) + sqr( 5.59175556022082 - x127/(0.0001 + 0.9999*b11)))*(0.0001 + 0.9999*b11) + 0.0117234102493874*b11 =L= 0.0117234102493874; e52.. (-1 + sqr(8.52118108549064 - x128/(0.0001 + 0.9999*b12)) + sqr( 5.32332318998315 - x129/(0.0001 + 0.9999*b12)))*(0.0001 + 0.9999*b12) + 0.00999482968767358*b12 =L= 0.00999482968767358; e53.. (-1 + sqr(4.01861330995576 - x130/(0.0001 + 0.9999*b13)) + sqr( 9.65380890252737 - x131/(0.0001 + 0.9999*b13)))*(0.0001 + 0.9999*b13) + 0.010834527926147*b13 =L= 0.010834527926147; e54.. (-1 + sqr(2.49020328922613 - x132/(0.0001 + 0.9999*b14)) + sqr( 0.874596139412213 - x133/(0.0001 + 0.9999*b14)))*(0.0001 + 0.9999*b14) + 0.000596603082874738*b14 =L= 0.000596603082874738; e55.. (-1 + sqr(0.545671492825244 - x134/(0.0001 + 0.9999*b15)) + sqr( 3.81401698819633 - x135/(0.0001 + 0.9999*b15)))*(0.0001 + 0.9999*b15) + 0.00138444829643323*b15 =L= 0.00138444829643323; e56.. b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 + b11 + b12 + b13 + b14 + b15 =E= 1; e57.. (-1 + sqr(8.68340342427357 - x136/(0.0001 + 0.9999*b16)) + sqr( 8.57974596088368 - x137/(0.0001 + 0.9999*b16)))*(0.0001 + 0.9999*b16) + 0.0148013535781986*b16 =L= 0.0148013535781986; e58.. (-1 + sqr(9.63614333912176 - x138/(0.0001 + 0.9999*b17)) + sqr( 8.80176337918095 - x139/(0.0001 + 0.9999*b17)))*(0.0001 + 0.9999*b17) + 0.0169326297035192*b17 =L= 0.0169326297035192; e59.. (-1 + sqr(3.68142205418198 - x140/(0.0001 + 0.9999*b18)) + sqr( 1.1692321814062 - x141/(0.0001 + 0.9999*b18)))*(0.0001 + 0.9999*b18) + 0.00139199722350534*b18 =L= 0.00139199722350534; e60.. (-1 + sqr(9.7121756733827 - x142/(0.0001 + 0.9999*b19)) + sqr( 7.68772804421774 - x143/(0.0001 + 0.9999*b19)))*(0.0001 + 0.9999*b19) + 0.0152427518792499*b19 =L= 0.0152427518792499; e61.. (-1 + sqr(3.2772228491781 - x144/(0.0001 + 0.9999*b20)) + sqr( 8.20105404549271 - x145/(0.0001 + 0.9999*b20)))*(0.0001 + 0.9999*b20) + 0.00769974770602674*b20 =L= 0.00769974770602674; e62.. (-1 + sqr(8.95169370625893 - x146/(0.0001 + 0.9999*b21)) + sqr( 5.71833771240185 - x147/(0.0001 + 0.9999*b21)))*(0.0001 + 0.9999*b21) + 0.0111832206403753*b21 =L= 0.0111832206403753; e63.. (-1 + sqr(6.39713701672676 - x148/(0.0001 + 0.9999*b22)) + sqr( 2.19374777991393 - x149/(0.0001 + 0.9999*b22)))*(0.0001 + 0.9999*b22) + 0.00447358913326531*b22 =L= 0.00447358913326531; e64.. (-1 + sqr(8.63324272987351 - x150/(0.0001 + 0.9999*b23)) + sqr( 2.92174290170279 - x151/(0.0001 + 0.9999*b23)))*(0.0001 + 0.9999*b23) + 0.00820694616165644*b23 =L= 0.00820694616165644; e65.. (-1 + sqr(3.63244627881363 - x152/(0.0001 + 0.9999*b24)) + sqr( 1.91739848753332 - x153/(0.0001 + 0.9999*b24)))*(0.0001 + 0.9999*b24) + 0.00158710829284621*b24 =L= 0.00158710829284621; e66.. (-1 + sqr(0.303084489788861 - x154/(0.0001 + 0.9999*b25)) + sqr( 2.88588654972735 - x155/(0.0001 + 0.9999*b25)))*(0.0001 + 0.9999*b25) + 0.00074202013858478*b25 =L= 0.00074202013858478; e67.. (-1 + sqr(9.32557624217471 - x156/(0.0001 + 0.9999*b26)) + sqr( 5.59175556022082 - x157/(0.0001 + 0.9999*b26)))*(0.0001 + 0.9999*b26) + 0.0117234102493874*b26 =L= 0.0117234102493874; e68.. (-1 + sqr(8.52118108549064 - x158/(0.0001 + 0.9999*b27)) + sqr( 5.32332318998315 - x159/(0.0001 + 0.9999*b27)))*(0.0001 + 0.9999*b27) + 0.00999482968767358*b27 =L= 0.00999482968767358; e69.. (-1 + sqr(4.01861330995576 - x160/(0.0001 + 0.9999*b28)) + sqr( 9.65380890252737 - x161/(0.0001 + 0.9999*b28)))*(0.0001 + 0.9999*b28) + 0.010834527926147*b28 =L= 0.010834527926147; e70.. (-1 + sqr(2.49020328922613 - x162/(0.0001 + 0.9999*b29)) + sqr( 0.874596139412213 - x163/(0.0001 + 0.9999*b29)))*(0.0001 + 0.9999*b29) + 0.000596603082874738*b29 =L= 0.000596603082874738; e71.. (-1 + sqr(0.545671492825244 - x164/(0.0001 + 0.9999*b30)) + sqr( 3.81401698819633 - x165/(0.0001 + 0.9999*b30)))*(0.0001 + 0.9999*b30) + 0.00138444829643323*b30 =L= 0.00138444829643323; e72.. b16 + b17 + b18 + b19 + b20 + b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 =E= 1; e73.. (-1 + sqr(8.68340342427357 - x166/(0.0001 + 0.9999*b31)) + sqr( 8.57974596088368 - x167/(0.0001 + 0.9999*b31)))*(0.0001 + 0.9999*b31) + 0.0148013535781986*b31 =L= 0.0148013535781986; e74.. (-1 + sqr(9.63614333912176 - x168/(0.0001 + 0.9999*b32)) + sqr( 8.80176337918095 - x169/(0.0001 + 0.9999*b32)))*(0.0001 + 0.9999*b32) + 0.0169326297035192*b32 =L= 0.0169326297035192; e75.. (-1 + sqr(3.68142205418198 - x170/(0.0001 + 0.9999*b33)) + sqr( 1.1692321814062 - x171/(0.0001 + 0.9999*b33)))*(0.0001 + 0.9999*b33) + 0.00139199722350534*b33 =L= 0.00139199722350534; e76.. (-1 + sqr(9.7121756733827 - x172/(0.0001 + 0.9999*b34)) + sqr( 7.68772804421774 - x173/(0.0001 + 0.9999*b34)))*(0.0001 + 0.9999*b34) + 0.0152427518792499*b34 =L= 0.0152427518792499; e77.. (-1 + sqr(3.2772228491781 - x174/(0.0001 + 0.9999*b35)) + sqr( 8.20105404549271 - x175/(0.0001 + 0.9999*b35)))*(0.0001 + 0.9999*b35) + 0.00769974770602674*b35 =L= 0.00769974770602674; e78.. (-1 + sqr(8.95169370625893 - x176/(0.0001 + 0.9999*b36)) + sqr( 5.71833771240185 - x177/(0.0001 + 0.9999*b36)))*(0.0001 + 0.9999*b36) + 0.0111832206403753*b36 =L= 0.0111832206403753; e79.. (-1 + sqr(6.39713701672676 - x178/(0.0001 + 0.9999*b37)) + sqr( 2.19374777991393 - x179/(0.0001 + 0.9999*b37)))*(0.0001 + 0.9999*b37) + 0.00447358913326531*b37 =L= 0.00447358913326531; e80.. (-1 + sqr(8.63324272987351 - x180/(0.0001 + 0.9999*b38)) + sqr( 2.92174290170279 - x181/(0.0001 + 0.9999*b38)))*(0.0001 + 0.9999*b38) + 0.00820694616165644*b38 =L= 0.00820694616165644; e81.. (-1 + sqr(3.63244627881363 - x182/(0.0001 + 0.9999*b39)) + sqr( 1.91739848753332 - x183/(0.0001 + 0.9999*b39)))*(0.0001 + 0.9999*b39) + 0.00158710829284621*b39 =L= 0.00158710829284621; e82.. (-1 + sqr(0.303084489788861 - x184/(0.0001 + 0.9999*b40)) + sqr( 2.88588654972735 - x185/(0.0001 + 0.9999*b40)))*(0.0001 + 0.9999*b40) + 0.00074202013858478*b40 =L= 0.00074202013858478; e83.. (-1 + sqr(9.32557624217471 - x186/(0.0001 + 0.9999*b41)) + sqr( 5.59175556022082 - x187/(0.0001 + 0.9999*b41)))*(0.0001 + 0.9999*b41) + 0.0117234102493874*b41 =L= 0.0117234102493874; e84.. (-1 + sqr(8.52118108549064 - x188/(0.0001 + 0.9999*b42)) + sqr( 5.32332318998315 - x189/(0.0001 + 0.9999*b42)))*(0.0001 + 0.9999*b42) + 0.00999482968767358*b42 =L= 0.00999482968767358; e85.. (-1 + sqr(4.01861330995576 - x190/(0.0001 + 0.9999*b43)) + sqr( 9.65380890252737 - x191/(0.0001 + 0.9999*b43)))*(0.0001 + 0.9999*b43) + 0.010834527926147*b43 =L= 0.010834527926147; e86.. (-1 + sqr(2.49020328922613 - x192/(0.0001 + 0.9999*b44)) + sqr( 0.874596139412213 - x193/(0.0001 + 0.9999*b44)))*(0.0001 + 0.9999*b44) + 0.000596603082874738*b44 =L= 0.000596603082874738; e87.. (-1 + sqr(0.545671492825244 - x194/(0.0001 + 0.9999*b45)) + sqr( 3.81401698819633 - x195/(0.0001 + 0.9999*b45)))*(0.0001 + 0.9999*b45) + 0.00138444829643323*b45 =L= 0.00138444829643323; e88.. b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 + b41 + b42 + b43 + b44 + b45 =E= 1; e89.. (-1 + sqr(8.68340342427357 - x196/(0.0001 + 0.9999*b46)) + sqr( 8.57974596088368 - x197/(0.0001 + 0.9999*b46)))*(0.0001 + 0.9999*b46) + 0.0148013535781986*b46 =L= 0.0148013535781986; e90.. (-1 + sqr(9.63614333912176 - x198/(0.0001 + 0.9999*b47)) + sqr( 8.80176337918095 - x199/(0.0001 + 0.9999*b47)))*(0.0001 + 0.9999*b47) + 0.0169326297035192*b47 =L= 0.0169326297035192; e91.. (-1 + sqr(3.68142205418198 - x200/(0.0001 + 0.9999*b48)) + sqr( 1.1692321814062 - x201/(0.0001 + 0.9999*b48)))*(0.0001 + 0.9999*b48) + 0.00139199722350534*b48 =L= 0.00139199722350534; e92.. (-1 + sqr(9.7121756733827 - x202/(0.0001 + 0.9999*b49)) + sqr( 7.68772804421774 - x203/(0.0001 + 0.9999*b49)))*(0.0001 + 0.9999*b49) + 0.0152427518792499*b49 =L= 0.0152427518792499; e93.. (-1 + sqr(3.2772228491781 - x204/(0.0001 + 0.9999*b50)) + sqr( 8.20105404549271 - x205/(0.0001 + 0.9999*b50)))*(0.0001 + 0.9999*b50) + 0.00769974770602674*b50 =L= 0.00769974770602674; e94.. (-1 + sqr(8.95169370625893 - x206/(0.0001 + 0.9999*b51)) + sqr( 5.71833771240185 - x207/(0.0001 + 0.9999*b51)))*(0.0001 + 0.9999*b51) + 0.0111832206403753*b51 =L= 0.0111832206403753; e95.. (-1 + sqr(6.39713701672676 - x208/(0.0001 + 0.9999*b52)) + sqr( 2.19374777991393 - x209/(0.0001 + 0.9999*b52)))*(0.0001 + 0.9999*b52) + 0.00447358913326531*b52 =L= 0.00447358913326531; e96.. (-1 + sqr(8.63324272987351 - x210/(0.0001 + 0.9999*b53)) + sqr( 2.92174290170279 - x211/(0.0001 + 0.9999*b53)))*(0.0001 + 0.9999*b53) + 0.00820694616165644*b53 =L= 0.00820694616165644; e97.. (-1 + sqr(3.63244627881363 - x212/(0.0001 + 0.9999*b54)) + sqr( 1.91739848753332 - x213/(0.0001 + 0.9999*b54)))*(0.0001 + 0.9999*b54) + 0.00158710829284621*b54 =L= 0.00158710829284621; e98.. (-1 + sqr(0.303084489788861 - x214/(0.0001 + 0.9999*b55)) + sqr( 2.88588654972735 - x215/(0.0001 + 0.9999*b55)))*(0.0001 + 0.9999*b55) + 0.00074202013858478*b55 =L= 0.00074202013858478; e99.. (-1 + sqr(9.32557624217471 - x216/(0.0001 + 0.9999*b56)) + sqr( 5.59175556022082 - x217/(0.0001 + 0.9999*b56)))*(0.0001 + 0.9999*b56) + 0.0117234102493874*b56 =L= 0.0117234102493874; e100.. (-1 + sqr(8.52118108549064 - x218/(0.0001 + 0.9999*b57)) + sqr( 5.32332318998315 - x219/(0.0001 + 0.9999*b57)))*(0.0001 + 0.9999*b57) + 0.00999482968767358*b57 =L= 0.00999482968767358; e101.. (-1 + sqr(4.01861330995576 - x220/(0.0001 + 0.9999*b58)) + sqr( 9.65380890252737 - x221/(0.0001 + 0.9999*b58)))*(0.0001 + 0.9999*b58) + 0.010834527926147*b58 =L= 0.010834527926147; e102.. (-1 + sqr(2.49020328922613 - x222/(0.0001 + 0.9999*b59)) + sqr( 0.874596139412213 - x223/(0.0001 + 0.9999*b59)))*(0.0001 + 0.9999*b59) + 0.000596603082874738*b59 =L= 0.000596603082874738; e103.. (-1 + sqr(0.545671492825244 - x224/(0.0001 + 0.9999*b60)) + sqr( 3.81401698819633 - x225/(0.0001 + 0.9999*b60)))*(0.0001 + 0.9999*b60) + 0.00138444829643323*b60 =L= 0.00138444829643323; e104.. b46 + b47 + b48 + b49 + b50 + b51 + b52 + b53 + b54 + b55 + b56 + b57 + b58 + b59 + b60 =E= 1; e105.. (-1 + sqr(8.68340342427357 - x226/(0.0001 + 0.9999*b61)) + sqr( 8.57974596088368 - x227/(0.0001 + 0.9999*b61)))*(0.0001 + 0.9999*b61) + 0.0148013535781986*b61 =L= 0.0148013535781986; e106.. (-1 + sqr(9.63614333912176 - x228/(0.0001 + 0.9999*b62)) + sqr( 8.80176337918095 - x229/(0.0001 + 0.9999*b62)))*(0.0001 + 0.9999*b62) + 0.0169326297035192*b62 =L= 0.0169326297035192; e107.. (-1 + sqr(3.68142205418198 - x230/(0.0001 + 0.9999*b63)) + sqr( 1.1692321814062 - x231/(0.0001 + 0.9999*b63)))*(0.0001 + 0.9999*b63) + 0.00139199722350534*b63 =L= 0.00139199722350534; e108.. (-1 + sqr(9.7121756733827 - x232/(0.0001 + 0.9999*b64)) + sqr( 7.68772804421774 - x233/(0.0001 + 0.9999*b64)))*(0.0001 + 0.9999*b64) + 0.0152427518792499*b64 =L= 0.0152427518792499; e109.. (-1 + sqr(3.2772228491781 - x234/(0.0001 + 0.9999*b65)) + sqr( 8.20105404549271 - x235/(0.0001 + 0.9999*b65)))*(0.0001 + 0.9999*b65) + 0.00769974770602674*b65 =L= 0.00769974770602674; e110.. (-1 + sqr(8.95169370625893 - x236/(0.0001 + 0.9999*b66)) + sqr( 5.71833771240185 - x237/(0.0001 + 0.9999*b66)))*(0.0001 + 0.9999*b66) + 0.0111832206403753*b66 =L= 0.0111832206403753; e111.. (-1 + sqr(6.39713701672676 - x238/(0.0001 + 0.9999*b67)) + sqr( 2.19374777991393 - x239/(0.0001 + 0.9999*b67)))*(0.0001 + 0.9999*b67) + 0.00447358913326531*b67 =L= 0.00447358913326531; e112.. (-1 + sqr(8.63324272987351 - x240/(0.0001 + 0.9999*b68)) + sqr( 2.92174290170279 - x241/(0.0001 + 0.9999*b68)))*(0.0001 + 0.9999*b68) + 0.00820694616165644*b68 =L= 0.00820694616165644; e113.. (-1 + sqr(3.63244627881363 - x242/(0.0001 + 0.9999*b69)) + sqr( 1.91739848753332 - x243/(0.0001 + 0.9999*b69)))*(0.0001 + 0.9999*b69) + 0.00158710829284621*b69 =L= 0.00158710829284621; e114.. (-1 + sqr(0.303084489788861 - x244/(0.0001 + 0.9999*b70)) + sqr( 2.88588654972735 - x245/(0.0001 + 0.9999*b70)))*(0.0001 + 0.9999*b70) + 0.00074202013858478*b70 =L= 0.00074202013858478; e115.. (-1 + sqr(9.32557624217471 - x246/(0.0001 + 0.9999*b71)) + sqr( 5.59175556022082 - x247/(0.0001 + 0.9999*b71)))*(0.0001 + 0.9999*b71) + 0.0117234102493874*b71 =L= 0.0117234102493874; e116.. (-1 + sqr(8.52118108549064 - x248/(0.0001 + 0.9999*b72)) + sqr( 5.32332318998315 - x249/(0.0001 + 0.9999*b72)))*(0.0001 + 0.9999*b72) + 0.00999482968767358*b72 =L= 0.00999482968767358; e117.. (-1 + sqr(4.01861330995576 - x250/(0.0001 + 0.9999*b73)) + sqr( 9.65380890252737 - x251/(0.0001 + 0.9999*b73)))*(0.0001 + 0.9999*b73) + 0.010834527926147*b73 =L= 0.010834527926147; e118.. (-1 + sqr(2.49020328922613 - x252/(0.0001 + 0.9999*b74)) + sqr( 0.874596139412213 - x253/(0.0001 + 0.9999*b74)))*(0.0001 + 0.9999*b74) + 0.000596603082874738*b74 =L= 0.000596603082874738; e119.. (-1 + sqr(0.545671492825244 - x254/(0.0001 + 0.9999*b75)) + sqr( 3.81401698819633 - x255/(0.0001 + 0.9999*b75)))*(0.0001 + 0.9999*b75) + 0.00138444829643323*b75 =L= 0.00138444829643323; e120.. b61 + b62 + b63 + b64 + b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72 + b73 + b74 + b75 =E= 1; e121.. b1 + b16 + b31 + b46 + b61 =L= 1; e122.. b2 + b17 + b32 + b47 + b62 =L= 1; e123.. b3 + b18 + b33 + b48 + b63 =L= 1; e124.. b4 + b19 + b34 + b49 + b64 =L= 1; e125.. b5 + b20 + b35 + b50 + b65 =L= 1; e126.. b6 + b21 + b36 + b51 + b66 =L= 1; e127.. b7 + b22 + b37 + b52 + b67 =L= 1; e128.. b8 + b23 + b38 + b53 + b68 =L= 1; e129.. b9 + b24 + b39 + b54 + b69 =L= 1; e130.. b10 + b25 + b40 + b55 + b70 =L= 1; e131.. b11 + b26 + b41 + b56 + b71 =L= 1; e132.. b12 + b27 + b42 + b57 + b72 =L= 1; e133.. b13 + b28 + b43 + b58 + b73 =L= 1; e134.. b14 + b29 + b44 + b59 + b74 =L= 1; e135.. b15 + b30 + b45 + b60 + b75 =L= 1; e136.. - x76 + x106 + x108 + x110 + x112 + x114 + x116 + x118 + x120 + x122 + x124 + x126 + x128 + x130 + x132 + x134 =E= 0; e137.. - x79 + x107 + x109 + x111 + x113 + x115 + x117 + x119 + x121 + x123 + x125 + x127 + x129 + x131 + x133 + x135 =E= 0; e138.. - x77 + x136 + x138 + x140 + x142 + x144 + x146 + x148 + x150 + x152 + x154 + x156 + x158 + x160 + x162 + x164 =E= 0; e139.. - x80 + x137 + x139 + x141 + x143 + x145 + x147 + x149 + x151 + x153 + x155 + x157 + x159 + x161 + x163 + x165 =E= 0; e140.. - x82 + x166 + x168 + x170 + x172 + x174 + x176 + x178 + x180 + x182 + x184 + x186 + x188 + x190 + x192 + x194 =E= 0; e141.. - x84 + x167 + x169 + x171 + x173 + x175 + x177 + x179 + x181 + x183 + x185 + x187 + x189 + x191 + x193 + x195 =E= 0; e142.. - x86 + x196 + x198 + x200 + x202 + x204 + x206 + x208 + x210 + x212 + x214 + x216 + x218 + x220 + x222 + x224 =E= 0; e143.. - x88 + x197 + x199 + x201 + x203 + x205 + x207 + x209 + x211 + x213 + x215 + x217 + x219 + x221 + x223 + x225 =E= 0; e144.. - x90 + x226 + x228 + x230 + x232 + x234 + x236 + x238 + x240 + x242 + x244 + x246 + x248 + x250 + x252 + x254 =E= 0; e145.. - x92 + x227 + x229 + x231 + x233 + x235 + x237 + x239 + x241 + x243 + x245 + x247 + x249 + x251 + x253 + x255 =E= 0; e146.. - 10*b1 + x106 =L= 0; e147.. - 10*b2 + x108 =L= 0; e148.. - 10*b3 + x110 =L= 0; e149.. - 10*b4 + x112 =L= 0; e150.. - 10*b5 + x114 =L= 0; e151.. - 10*b6 + x116 =L= 0; e152.. - 10*b7 + x118 =L= 0; e153.. - 10*b8 + x120 =L= 0; e154.. - 10*b9 + x122 =L= 0; e155.. - 10*b10 + x124 =L= 0; e156.. - 10*b11 + x126 =L= 0; e157.. - 10*b12 + x128 =L= 0; e158.. - 10*b13 + x130 =L= 0; e159.. - 10*b14 + x132 =L= 0; e160.. - 10*b15 + x134 =L= 0; e161.. - 10*b1 + x107 =L= 0; e162.. - 10*b2 + x109 =L= 0; e163.. - 10*b3 + x111 =L= 0; e164.. - 10*b4 + x113 =L= 0; e165.. - 10*b5 + x115 =L= 0; e166.. - 10*b6 + x117 =L= 0; e167.. - 10*b7 + x119 =L= 0; e168.. - 10*b8 + x121 =L= 0; e169.. - 10*b9 + x123 =L= 0; e170.. - 10*b10 + x125 =L= 0; e171.. - 10*b11 + x127 =L= 0; e172.. - 10*b12 + x129 =L= 0; e173.. - 10*b13 + x131 =L= 0; e174.. - 10*b14 + x133 =L= 0; e175.. - 10*b15 + x135 =L= 0; e176.. - 10*b16 + x136 =L= 0; e177.. - 10*b17 + x138 =L= 0; e178.. - 10*b18 + x140 =L= 0; e179.. - 10*b19 + x142 =L= 0; e180.. - 10*b20 + x144 =L= 0; e181.. - 10*b21 + x146 =L= 0; e182.. - 10*b22 + x148 =L= 0; e183.. - 10*b23 + x150 =L= 0; e184.. - 10*b24 + x152 =L= 0; e185.. - 10*b25 + x154 =L= 0; e186.. - 10*b26 + x156 =L= 0; e187.. - 10*b27 + x158 =L= 0; e188.. - 10*b28 + x160 =L= 0; e189.. - 10*b29 + x162 =L= 0; e190.. - 10*b30 + x164 =L= 0; e191.. - 10*b16 + x137 =L= 0; e192.. - 10*b17 + x139 =L= 0; e193.. - 10*b18 + x141 =L= 0; e194.. - 10*b19 + x143 =L= 0; e195.. - 10*b20 + x145 =L= 0; e196.. - 10*b21 + x147 =L= 0; e197.. - 10*b22 + x149 =L= 0; e198.. - 10*b23 + x151 =L= 0; e199.. - 10*b24 + x153 =L= 0; e200.. - 10*b25 + x155 =L= 0; e201.. - 10*b26 + x157 =L= 0; e202.. - 10*b27 + x159 =L= 0; e203.. - 10*b28 + x161 =L= 0; e204.. - 10*b29 + x163 =L= 0; e205.. - 10*b30 + x165 =L= 0; e206.. - 10*b31 + x166 =L= 0; e207.. - 10*b32 + x168 =L= 0; e208.. - 10*b33 + x170 =L= 0; e209.. - 10*b34 + x172 =L= 0; e210.. - 10*b35 + x174 =L= 0; e211.. - 10*b36 + x176 =L= 0; e212.. - 10*b37 + x178 =L= 0; e213.. - 10*b38 + x180 =L= 0; e214.. - 10*b39 + x182 =L= 0; e215.. - 10*b40 + x184 =L= 0; e216.. - 10*b41 + x186 =L= 0; e217.. - 10*b42 + x188 =L= 0; e218.. - 10*b43 + x190 =L= 0; e219.. - 10*b44 + x192 =L= 0; e220.. - 10*b45 + x194 =L= 0; e221.. - 10*b31 + x167 =L= 0; e222.. - 10*b32 + x169 =L= 0; e223.. - 10*b33 + x171 =L= 0; e224.. - 10*b34 + x173 =L= 0; e225.. - 10*b35 + x175 =L= 0; e226.. - 10*b36 + x177 =L= 0; e227.. - 10*b37 + x179 =L= 0; e228.. - 10*b38 + x181 =L= 0; e229.. - 10*b39 + x183 =L= 0; e230.. - 10*b40 + x185 =L= 0; e231.. - 10*b41 + x187 =L= 0; e232.. - 10*b42 + x189 =L= 0; e233.. - 10*b43 + x191 =L= 0; e234.. - 10*b44 + x193 =L= 0; e235.. - 10*b45 + x195 =L= 0; e236.. - 10*b46 + x196 =L= 0; e237.. - 10*b47 + x198 =L= 0; e238.. - 10*b48 + x200 =L= 0; e239.. - 10*b49 + x202 =L= 0; e240.. - 10*b50 + x204 =L= 0; e241.. - 10*b51 + x206 =L= 0; e242.. - 10*b52 + x208 =L= 0; e243.. - 10*b53 + x210 =L= 0; e244.. - 10*b54 + x212 =L= 0; e245.. - 10*b55 + x214 =L= 0; e246.. - 10*b56 + x216 =L= 0; e247.. - 10*b57 + x218 =L= 0; e248.. - 10*b58 + x220 =L= 0; e249.. - 10*b59 + x222 =L= 0; e250.. - 10*b60 + x224 =L= 0; e251.. - 10*b46 + x197 =L= 0; e252.. - 10*b47 + x199 =L= 0; e253.. - 10*b48 + x201 =L= 0; e254.. - 10*b49 + x203 =L= 0; e255.. - 10*b50 + x205 =L= 0; e256.. - 10*b51 + x207 =L= 0; e257.. - 10*b52 + x209 =L= 0; e258.. - 10*b53 + x211 =L= 0; e259.. - 10*b54 + x213 =L= 0; e260.. - 10*b55 + x215 =L= 0; e261.. - 10*b56 + x217 =L= 0; e262.. - 10*b57 + x219 =L= 0; e263.. - 10*b58 + x221 =L= 0; e264.. - 10*b59 + x223 =L= 0; e265.. - 10*b60 + x225 =L= 0; e266.. - 10*b61 + x226 =L= 0; e267.. - 10*b62 + x228 =L= 0; e268.. - 10*b63 + x230 =L= 0; e269.. - 10*b64 + x232 =L= 0; e270.. - 10*b65 + x234 =L= 0; e271.. - 10*b66 + x236 =L= 0; e272.. - 10*b67 + x238 =L= 0; e273.. - 10*b68 + x240 =L= 0; e274.. - 10*b69 + x242 =L= 0; e275.. - 10*b70 + x244 =L= 0; e276.. - 10*b71 + x246 =L= 0; e277.. - 10*b72 + x248 =L= 0; e278.. - 10*b73 + x250 =L= 0; e279.. - 10*b74 + x252 =L= 0; e280.. - 10*b75 + x254 =L= 0; e281.. - 10*b61 + x227 =L= 0; e282.. - 10*b62 + x229 =L= 0; e283.. - 10*b63 + x231 =L= 0; e284.. - 10*b64 + x233 =L= 0; e285.. - 10*b65 + x235 =L= 0; e286.. - 10*b66 + x237 =L= 0; e287.. - 10*b67 + x239 =L= 0; e288.. - 10*b68 + x241 =L= 0; e289.. - 10*b69 + x243 =L= 0; e290.. - 10*b70 + x245 =L= 0; e291.. - 10*b71 + x247 =L= 0; e292.. - 10*b72 + x249 =L= 0; e293.. - 10*b73 + x251 =L= 0; e294.. - 10*b74 + x253 =L= 0; e295.. - 10*b75 + x255 =L= 0; e296.. x76 - x77 =L= 0; e297.. x77 - x82 =L= 0; e298.. x82 - x86 =L= 0; e299.. x86 - x90 =L= 0; e300.. - x78 - x81 - x83 - x85 - x87 - x89 - x91 - x93 - x94 - x95 - x96 - x97 - x98 - x99 - x100 - x101 - x102 - x103 - x104 - x105 + objvar =E= 0; * set non-default bounds x76.up = 10; x77.up = 10; x78.up = 10; x79.up = 10; x80.up = 10; x81.up = 10; x82.up = 10; x83.up = 10; x84.up = 10; x85.up = 10; x86.up = 10; x87.up = 10; x88.up = 10; x89.up = 10; x90.up = 10; x91.up = 10; x92.up = 10; x93.up = 10; x94.up = 10; x95.up = 10; x96.up = 10; x97.up = 10; x98.up = 10; x99.up = 10; x100.up = 10; x101.up = 10; x102.up = 10; x103.up = 10; x104.up = 10; x105.up = 10; x106.up = 10; x107.up = 10; x108.up = 10; x109.up = 10; x110.up = 10; x111.up = 10; x112.up = 10; x113.up = 10; x114.up = 10; x115.up = 10; x116.up = 10; x117.up = 10; x118.up = 10; x119.up = 10; x120.up = 10; x121.up = 10; x122.up = 10; x123.up = 10; x124.up = 10; x125.up = 10; x126.up = 10; x127.up = 10; x128.up = 10; x129.up = 10; x130.up = 10; x131.up = 10; x132.up = 10; x133.up = 10; x134.up = 10; x135.up = 10; x136.up = 10; x137.up = 10; x138.up = 10; x139.up = 10; x140.up = 10; x141.up = 10; x142.up = 10; x143.up = 10; x144.up = 10; x145.up = 10; x146.up = 10; x147.up = 10; x148.up = 10; x149.up = 10; x150.up = 10; x151.up = 10; x152.up = 10; x153.up = 10; x154.up = 10; x155.up = 10; x156.up = 10; x157.up = 10; x158.up = 10; x159.up = 10; x160.up = 10; x161.up = 10; x162.up = 10; x163.up = 10; x164.up = 10; x165.up = 10; x166.up = 10; x167.up = 10; x168.up = 10; x169.up = 10; x170.up = 10; x171.up = 10; x172.up = 10; x173.up = 10; x174.up = 10; x175.up = 10; x176.up = 10; x177.up = 10; x178.up = 10; x179.up = 10; x180.up = 10; x181.up = 10; x182.up = 10; x183.up = 10; x184.up = 10; x185.up = 10; x186.up = 10; x187.up = 10; x188.up = 10; x189.up = 10; x190.up = 10; x191.up = 10; x192.up = 10; x193.up = 10; x194.up = 10; x195.up = 10; x196.up = 10; x197.up = 10; x198.up = 10; x199.up = 10; x200.up = 10; x201.up = 10; x202.up = 10; x203.up = 10; x204.up = 10; x205.up = 10; x206.up = 10; x207.up = 10; x208.up = 10; x209.up = 10; x210.up = 10; x211.up = 10; x212.up = 10; x213.up = 10; x214.up = 10; x215.up = 10; x216.up = 10; x217.up = 10; x218.up = 10; x219.up = 10; x220.up = 10; x221.up = 10; x222.up = 10; x223.up = 10; x224.up = 10; x225.up = 10; x226.up = 10; x227.up = 10; x228.up = 10; x229.up = 10; x230.up = 10; x231.up = 10; x232.up = 10; x233.up = 10; x234.up = 10; x235.up = 10; x236.up = 10; x237.up = 10; x238.up = 10; x239.up = 10; x240.up = 10; x241.up = 10; x242.up = 10; x243.up = 10; x244.up = 10; x245.up = 10; x246.up = 10; x247.up = 10; x248.up = 10; x249.up = 10; x250.up = 10; x251.up = 10; x252.up = 10; x253.up = 10; x254.up = 10; x255.up = 10; 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: 2024-12-17 Git hash: 8eaceb91