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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance clay0304hfsg
Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized. Equivalent perspective reformulation of clay0304.
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 40262.38753000 (ALPHAECP) 7298.20051100 (ANTIGONE) 40262.38747000 (BARON) 40262.38753000 (BONMIN) 40262.38646000 (COUENNE) 40262.38753000 (LINDO) 40262.38747000 (SCIP) 40262.38440000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. Kevin C. Furman, Nicolas W. Sawaya, Ignacio E. Grossmann, A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function, Tech. Rep., 2019. |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 25 Sep 2019 |
| Problem typeⓘ | MBNLP |
| #Variablesⓘ | 176 |
| #Binary Variablesⓘ | 36 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 36 |
| #Nonlinear Binary Variablesⓘ | 12 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 12 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 258 |
| #Linear Constraintsⓘ | 210 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 48 |
| Operands in Gen. Nonlin. Functionsⓘ | div mul sqr |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 716 |
| #Nonlinear Nonzeros in Jacobianⓘ | 144 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 84 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 36 |
| #Blocks in Hessian of Lagrangianⓘ | 12 |
| 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-03 |
| Maximal coefficientⓘ | 6.8890e+03 |
| Infeasibility of initial pointⓘ | 12.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 259 43 24 192 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 177 141 36 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 729 585 144 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,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b160,b161,b162,b163,b164,x165,x166,x167,x168
,x169,x170,x171,x172,x173,x174,x175,x176,objvar;
Positive Variables 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,x165,x166,x167,x168
,x169,x170,x171,x172,x173,x174,x175,x176;
Binary Variables b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140
,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153
,b154,b155,b156,b157,b158,b159,b160,b161,b162,b163,b164;
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;
e1.. - 300*x165 - 240*x166 - 210*x167 - 100*x168 - 150*x169 - 120*x170
- 300*x171 - 240*x172 - 210*x173 - 100*x174 - 150*x175 - 120*x176
+ objvar =E= 0;
e2.. - x1 + x2 + x165 =G= 0;
e3.. - x1 + x3 + x166 =G= 0;
e4.. - x1 + x4 + x167 =G= 0;
e5.. - x2 + x3 + x168 =G= 0;
e6.. - x2 + x4 + x169 =G= 0;
e7.. - x3 + x4 + x170 =G= 0;
e8.. x1 - x2 + x165 =G= 0;
e9.. x1 - x3 + x166 =G= 0;
e10.. x1 - x4 + x167 =G= 0;
e11.. x2 - x3 + x168 =G= 0;
e12.. x2 - x4 + x169 =G= 0;
e13.. x3 - x4 + x170 =G= 0;
e14.. - x5 + x6 + x171 =G= 0;
e15.. - x5 + x7 + x172 =G= 0;
e16.. - x5 + x8 + x173 =G= 0;
e17.. - x6 + x7 + x174 =G= 0;
e18.. - x6 + x8 + x175 =G= 0;
e19.. - x7 + x8 + x176 =G= 0;
e20.. x5 - x6 + x171 =G= 0;
e21.. x5 - x7 + x172 =G= 0;
e22.. x5 - x8 + x173 =G= 0;
e23.. x6 - x7 + x174 =G= 0;
e24.. x6 - x8 + x175 =G= 0;
e25.. x7 - x8 + x176 =G= 0;
e26.. x1 - x9 - x12 - x15 - x18 =E= 0;
e27.. x1 - x10 - x13 - x16 - x19 =E= 0;
e28.. x1 - x11 - x14 - x17 - x20 =E= 0;
e29.. x2 - x21 - x24 - x27 - x30 =E= 0;
e30.. x2 - x22 - x25 - x28 - x31 =E= 0;
e31.. x2 - x23 - x26 - x29 - x32 =E= 0;
e32.. x3 - x33 - x36 - x39 - x42 =E= 0;
e33.. x3 - x34 - x37 - x40 - x43 =E= 0;
e34.. x3 - x35 - x38 - x41 - x44 =E= 0;
e35.. x4 - x45 - x48 - x51 - x54 =E= 0;
e36.. x4 - x46 - x49 - x52 - x55 =E= 0;
e37.. x4 - x47 - x50 - x53 - x56 =E= 0;
e38.. x5 - x57 - x60 - x63 - x66 =E= 0;
e39.. x5 - x58 - x61 - x64 - x67 =E= 0;
e40.. x5 - x59 - x62 - x65 - x68 =E= 0;
e41.. x6 - x69 - x72 - x75 - x78 =E= 0;
e42.. x6 - x70 - x73 - x76 - x79 =E= 0;
e43.. x6 - x71 - x74 - x77 - x80 =E= 0;
e44.. x7 - x81 - x84 - x87 - x90 =E= 0;
e45.. x7 - x82 - x85 - x88 - x91 =E= 0;
e46.. x7 - x83 - x86 - x89 - x92 =E= 0;
e47.. x8 - x93 - x96 - x99 - x102 =E= 0;
e48.. x8 - x94 - x97 - x100 - x103 =E= 0;
e49.. x8 - x95 - x98 - x101 - x104 =E= 0;
e50.. x9 - 52.5*b129 =L= 0;
e51.. x10 - 52.5*b130 =L= 0;
e52.. x11 - 52.5*b131 =L= 0;
e53.. x12 - 52.5*b135 =L= 0;
e54.. x13 - 52.5*b136 =L= 0;
e55.. x14 - 52.5*b137 =L= 0;
e56.. x15 - 52.5*b141 =L= 0;
e57.. x16 - 52.5*b142 =L= 0;
e58.. x17 - 52.5*b143 =L= 0;
e59.. x18 - 52.5*b147 =L= 0;
e60.. x19 - 52.5*b148 =L= 0;
e61.. x20 - 52.5*b149 =L= 0;
e62.. x21 - 52.5*b129 =L= 0;
e63.. x22 - 51.5*b132 =L= 0;
e64.. x23 - 51.5*b133 =L= 0;
e65.. x24 - 52.5*b135 =L= 0;
e66.. x25 - 51.5*b138 =L= 0;
e67.. x26 - 51.5*b139 =L= 0;
e68.. x27 - 52.5*b141 =L= 0;
e69.. x28 - 51.5*b144 =L= 0;
e70.. x29 - 51.5*b145 =L= 0;
e71.. x30 - 52.5*b147 =L= 0;
e72.. x31 - 51.5*b150 =L= 0;
e73.. x32 - 51.5*b151 =L= 0;
e74.. x33 - 52.5*b130 =L= 0;
e75.. x34 - 51.5*b132 =L= 0;
e76.. x35 - 53.5*b134 =L= 0;
e77.. x36 - 52.5*b136 =L= 0;
e78.. x37 - 51.5*b138 =L= 0;
e79.. x38 - 53.5*b140 =L= 0;
e80.. x39 - 52.5*b142 =L= 0;
e81.. x40 - 51.5*b144 =L= 0;
e82.. x41 - 53.5*b146 =L= 0;
e83.. x42 - 52.5*b148 =L= 0;
e84.. x43 - 51.5*b150 =L= 0;
e85.. x44 - 53.5*b152 =L= 0;
e86.. x45 - 52.5*b131 =L= 0;
e87.. x46 - 51.5*b133 =L= 0;
e88.. x47 - 53.5*b134 =L= 0;
e89.. x48 - 52.5*b137 =L= 0;
e90.. x49 - 51.5*b139 =L= 0;
e91.. x50 - 53.5*b140 =L= 0;
e92.. x51 - 52.5*b143 =L= 0;
e93.. x52 - 51.5*b145 =L= 0;
e94.. x53 - 53.5*b146 =L= 0;
e95.. x54 - 52.5*b149 =L= 0;
e96.. x55 - 51.5*b151 =L= 0;
e97.. x56 - 53.5*b152 =L= 0;
e98.. x57 - 82*b129 =L= 0;
e99.. x58 - 82*b130 =L= 0;
e100.. x59 - 82*b131 =L= 0;
e101.. x60 - 82*b135 =L= 0;
e102.. x61 - 82*b136 =L= 0;
e103.. x62 - 82*b137 =L= 0;
e104.. x63 - 82*b141 =L= 0;
e105.. x64 - 82*b142 =L= 0;
e106.. x65 - 82*b143 =L= 0;
e107.. x66 - 82*b147 =L= 0;
e108.. x67 - 82*b148 =L= 0;
e109.. x68 - 82*b149 =L= 0;
e110.. x69 - 82*b129 =L= 0;
e111.. x70 - 82.5*b132 =L= 0;
e112.. x71 - 82.5*b133 =L= 0;
e113.. x72 - 82*b135 =L= 0;
e114.. x73 - 82.5*b138 =L= 0;
e115.. x74 - 82.5*b139 =L= 0;
e116.. x75 - 82*b141 =L= 0;
e117.. x76 - 82.5*b144 =L= 0;
e118.. x77 - 82.5*b145 =L= 0;
e119.. x78 - 82*b147 =L= 0;
e120.. x79 - 82.5*b150 =L= 0;
e121.. x80 - 82.5*b151 =L= 0;
e122.. x81 - 82*b130 =L= 0;
e123.. x82 - 82.5*b132 =L= 0;
e124.. x83 - 83.5*b134 =L= 0;
e125.. x84 - 82*b136 =L= 0;
e126.. x85 - 82.5*b138 =L= 0;
e127.. x86 - 83.5*b140 =L= 0;
e128.. x87 - 82*b142 =L= 0;
e129.. x88 - 82.5*b144 =L= 0;
e130.. x89 - 83.5*b146 =L= 0;
e131.. x90 - 82*b148 =L= 0;
e132.. x91 - 82.5*b150 =L= 0;
e133.. x92 - 83.5*b152 =L= 0;
e134.. x93 - 82*b131 =L= 0;
e135.. x94 - 82.5*b133 =L= 0;
e136.. x95 - 83.5*b134 =L= 0;
e137.. x96 - 82*b137 =L= 0;
e138.. x97 - 82.5*b139 =L= 0;
e139.. x98 - 83.5*b140 =L= 0;
e140.. x99 - 82*b143 =L= 0;
e141.. x100 - 82.5*b145 =L= 0;
e142.. x101 - 83.5*b146 =L= 0;
e143.. x102 - 82*b149 =L= 0;
e144.. x103 - 82.5*b151 =L= 0;
e145.. x104 - 83.5*b152 =L= 0;
e146.. x9 - x21 + 6*b129 =L= 0;
e147.. x10 - x33 + 4*b130 =L= 0;
e148.. x11 - x45 + 3.5*b131 =L= 0;
e149.. x22 - x34 + 5*b132 =L= 0;
e150.. x23 - x46 + 4.5*b133 =L= 0;
e151.. x35 - x47 + 2.5*b134 =L= 0;
e152.. - x12 + x24 + 6*b135 =L= 0;
e153.. - x13 + x36 + 4*b136 =L= 0;
e154.. - x14 + x48 + 3.5*b137 =L= 0;
e155.. - x25 + x37 + 5*b138 =L= 0;
e156.. - x26 + x49 + 4.5*b139 =L= 0;
e157.. - x38 + x50 + 2.5*b140 =L= 0;
e158.. x63 - x75 + 5.5*b141 =L= 0;
e159.. x64 - x87 + 4.5*b142 =L= 0;
e160.. x65 - x99 + 4.5*b143 =L= 0;
e161.. x76 - x88 + 4*b144 =L= 0;
e162.. x77 - x100 + 4*b145 =L= 0;
e163.. x89 - x101 + 3*b146 =L= 0;
e164.. - x66 + x78 + 5.5*b147 =L= 0;
e165.. - x67 + x90 + 4.5*b148 =L= 0;
e166.. - x68 + x102 + 4.5*b149 =L= 0;
e167.. - x79 + x91 + 4*b150 =L= 0;
e168.. - x80 + x103 + 4*b151 =L= 0;
e169.. - x92 + x104 + 3*b152 =L= 0;
e170.. b129 + b135 + b141 + b147 =E= 1;
e171.. b130 + b136 + b142 + b148 =E= 1;
e172.. b131 + b137 + b143 + b149 =E= 1;
e173.. b132 + b138 + b144 + b150 =E= 1;
e174.. b133 + b139 + b145 + b151 =E= 1;
e175.. b134 + b140 + b146 + b152 =E= 1;
e176.. x1 - x105 - x109 - x113 =E= 0;
e177.. x2 - x106 - x110 - x114 =E= 0;
e178.. x3 - x107 - x111 - x115 =E= 0;
e179.. x4 - x108 - x112 - x116 =E= 0;
e180.. x5 - x117 - x121 - x125 =E= 0;
e181.. x6 - x118 - x122 - x126 =E= 0;
e182.. x7 - x119 - x123 - x127 =E= 0;
e183.. x8 - x120 - x124 - x128 =E= 0;
e184.. x105 - 18.5*b153 =L= 0;
e185.. x106 - 17.5*b154 =L= 0;
e186.. x107 - 19.5*b155 =L= 0;
e187.. x108 - 20*b156 =L= 0;
e188.. x109 - 52.5*b157 =L= 0;
e189.. x110 - 51.5*b158 =L= 0;
e190.. x111 - 53.5*b159 =L= 0;
e191.. x112 - 54*b160 =L= 0;
e192.. x113 - 31.5*b161 =L= 0;
e193.. x114 - 30.5*b162 =L= 0;
e194.. x115 - 32.5*b163 =L= 0;
e195.. x116 - 33*b164 =L= 0;
e196.. x117 - 13*b153 =L= 0;
e197.. x118 - 13.5*b154 =L= 0;
e198.. x119 - 14.5*b155 =L= 0;
e199.. x120 - 14.5*b156 =L= 0;
e200.. x121 - 82*b157 =L= 0;
e201.. x122 - 82.5*b158 =L= 0;
e202.. x123 - 83.5*b159 =L= 0;
e203.. x124 - 83.5*b160 =L= 0;
e204.. x125 - 51*b161 =L= 0;
e205.. x126 - 51.5*b162 =L= 0;
e206.. x127 - 52.5*b163 =L= 0;
e207.. x128 - 52.5*b164 =L= 0;
e208.. (sqr(x105/(0.001 + 0.999*b153)) - 35*x105/(0.001 + 0.999*b153) + sqr(
x117/(0.001 + 0.999*b153)) - 14*x117/(0.001 + 0.999*b153))*(0.001 +
0.999*b153) + 306.25*b153 + 49*b153 - 36*b153 =L= 0;
e209.. (sqr(x106/(0.001 + 0.999*b154)) - 37*x106/(0.001 + 0.999*b154) + sqr(
x118/(0.001 + 0.999*b154)) - 15*x118/(0.001 + 0.999*b154))*(0.001 +
0.999*b154) + 342.25*b154 + 56.25*b154 - 36*b154 =L= 0;
e210.. (sqr(x107/(0.001 + 0.999*b155)) - 33*x107/(0.001 + 0.999*b155) + sqr(
x119/(0.001 + 0.999*b155)) - 17*x119/(0.001 + 0.999*b155))*(0.001 +
0.999*b155) + 272.25*b155 + 72.25*b155 - 36*b155 =L= 0;
e211.. (sqr(x108/(0.001 + 0.999*b156)) - 32*x108/(0.001 + 0.999*b156) + sqr(
x120/(0.001 + 0.999*b156)) - 17*x120/(0.001 + 0.999*b156))*(0.001 +
0.999*b156) + 256*b156 + 72.25*b156 - 36*b156 =L= 0;
e212.. (sqr(x109/(0.001 + 0.999*b157)) - 105*x109/(0.001 + 0.999*b157) + sqr(
x121/(0.001 + 0.999*b157)) - 154*x121/(0.001 + 0.999*b157))*(0.001 +
0.999*b157) + 2756.25*b157 + 5929*b157 - 25*b157 =L= 0;
e213.. (sqr(x110/(0.001 + 0.999*b158)) - 107*x110/(0.001 + 0.999*b158) + sqr(
x122/(0.001 + 0.999*b158)) - 155*x122/(0.001 + 0.999*b158))*(0.001 +
0.999*b158) + 2862.25*b158 + 6006.25*b158 - 25*b158 =L= 0;
e214.. (sqr(x111/(0.001 + 0.999*b159)) - 103*x111/(0.001 + 0.999*b159) + sqr(
x123/(0.001 + 0.999*b159)) - 157*x123/(0.001 + 0.999*b159))*(0.001 +
0.999*b159) + 2652.25*b159 + 6162.25*b159 - 25*b159 =L= 0;
e215.. (sqr(x112/(0.001 + 0.999*b160)) - 102*x112/(0.001 + 0.999*b160) + sqr(
x124/(0.001 + 0.999*b160)) - 157*x124/(0.001 + 0.999*b160))*(0.001 +
0.999*b160) + 2601*b160 + 6162.25*b160 - 25*b160 =L= 0;
e216.. (sqr(x113/(0.001 + 0.999*b161)) - 65*x113/(0.001 + 0.999*b161) + sqr(
x125/(0.001 + 0.999*b161)) - 94*x125/(0.001 + 0.999*b161))*(0.001 +
0.999*b161) + 1056.25*b161 + 2209*b161 - 16*b161 =L= 0;
e217.. (sqr(x114/(0.001 + 0.999*b162)) - 67*x114/(0.001 + 0.999*b162) + sqr(
x126/(0.001 + 0.999*b162)) - 95*x126/(0.001 + 0.999*b162))*(0.001 +
0.999*b162) + 1122.25*b162 + 2256.25*b162 - 16*b162 =L= 0;
e218.. (sqr(x115/(0.001 + 0.999*b163)) - 63*x115/(0.001 + 0.999*b163) + sqr(
x127/(0.001 + 0.999*b163)) - 97*x127/(0.001 + 0.999*b163))*(0.001 +
0.999*b163) + 992.25*b163 + 2352.25*b163 - 16*b163 =L= 0;
e219.. (sqr(x116/(0.001 + 0.999*b164)) - 62*x116/(0.001 + 0.999*b164) + sqr(
x128/(0.001 + 0.999*b164)) - 97*x128/(0.001 + 0.999*b164))*(0.001 +
0.999*b164) + 961*b164 + 2352.25*b164 - 16*b164 =L= 0;
e220.. (sqr(x105/(0.001 + 0.999*b153)) - 35*x105/(0.001 + 0.999*b153) + sqr(
x117/(0.001 + 0.999*b153)) - 26*x117/(0.001 + 0.999*b153))*(0.001 +
0.999*b153) + 306.25*b153 + 169*b153 - 36*b153 =L= 0;
e221.. (sqr(x106/(0.001 + 0.999*b154)) - 37*x106/(0.001 + 0.999*b154) + sqr(
x118/(0.001 + 0.999*b154)) - 25*x118/(0.001 + 0.999*b154))*(0.001 +
0.999*b154) + 342.25*b154 + 156.25*b154 - 36*b154 =L= 0;
e222.. (sqr(x107/(0.001 + 0.999*b155)) - 33*x107/(0.001 + 0.999*b155) + sqr(
x119/(0.001 + 0.999*b155)) - 23*x119/(0.001 + 0.999*b155))*(0.001 +
0.999*b155) + 272.25*b155 + 132.25*b155 - 36*b155 =L= 0;
e223.. (sqr(x108/(0.001 + 0.999*b156)) - 32*x108/(0.001 + 0.999*b156) + sqr(
x120/(0.001 + 0.999*b156)) - 23*x120/(0.001 + 0.999*b156))*(0.001 +
0.999*b156) + 256*b156 + 132.25*b156 - 36*b156 =L= 0;
e224.. (sqr(x109/(0.001 + 0.999*b157)) - 105*x109/(0.001 + 0.999*b157) + sqr(
x121/(0.001 + 0.999*b157)) - 166*x121/(0.001 + 0.999*b157))*(0.001 +
0.999*b157) + 2756.25*b157 + 6889*b157 - 25*b157 =L= 0;
e225.. (sqr(x110/(0.001 + 0.999*b158)) - 107*x110/(0.001 + 0.999*b158) + sqr(
x122/(0.001 + 0.999*b158)) - 165*x122/(0.001 + 0.999*b158))*(0.001 +
0.999*b158) + 2862.25*b158 + 6806.25*b158 - 25*b158 =L= 0;
e226.. (sqr(x111/(0.001 + 0.999*b159)) - 103*x111/(0.001 + 0.999*b159) + sqr(
x123/(0.001 + 0.999*b159)) - 163*x123/(0.001 + 0.999*b159))*(0.001 +
0.999*b159) + 2652.25*b159 + 6642.25*b159 - 25*b159 =L= 0;
e227.. (sqr(x112/(0.001 + 0.999*b160)) - 102*x112/(0.001 + 0.999*b160) + sqr(
x124/(0.001 + 0.999*b160)) - 163*x124/(0.001 + 0.999*b160))*(0.001 +
0.999*b160) + 2601*b160 + 6642.25*b160 - 25*b160 =L= 0;
e228.. (sqr(x113/(0.001 + 0.999*b161)) - 65*x113/(0.001 + 0.999*b161) + sqr(
x125/(0.001 + 0.999*b161)) - 106*x125/(0.001 + 0.999*b161))*(0.001 +
0.999*b161) + 1056.25*b161 + 2809*b161 - 16*b161 =L= 0;
e229.. (sqr(x114/(0.001 + 0.999*b162)) - 67*x114/(0.001 + 0.999*b162) + sqr(
x126/(0.001 + 0.999*b162)) - 105*x126/(0.001 + 0.999*b162))*(0.001 +
0.999*b162) + 1122.25*b162 + 2756.25*b162 - 16*b162 =L= 0;
e230.. (sqr(x115/(0.001 + 0.999*b163)) - 63*x115/(0.001 + 0.999*b163) + sqr(
x127/(0.001 + 0.999*b163)) - 103*x127/(0.001 + 0.999*b163))*(0.001 +
0.999*b163) + 992.25*b163 + 2652.25*b163 - 16*b163 =L= 0;
e231.. (sqr(x116/(0.001 + 0.999*b164)) - 62*x116/(0.001 + 0.999*b164) + sqr(
x128/(0.001 + 0.999*b164)) - 103*x128/(0.001 + 0.999*b164))*(0.001 +
0.999*b164) + 961*b164 + 2652.25*b164 - 16*b164 =L= 0;
e232.. (sqr(x105/(0.001 + 0.999*b153)) - 25*x105/(0.001 + 0.999*b153) + sqr(
x117/(0.001 + 0.999*b153)) - 14*x117/(0.001 + 0.999*b153))*(0.001 +
0.999*b153) + 156.25*b153 + 49*b153 - 36*b153 =L= 0;
e233.. (sqr(x106/(0.001 + 0.999*b154)) - 23*x106/(0.001 + 0.999*b154) + sqr(
x118/(0.001 + 0.999*b154)) - 15*x118/(0.001 + 0.999*b154))*(0.001 +
0.999*b154) + 132.25*b154 + 56.25*b154 - 36*b154 =L= 0;
e234.. (sqr(x107/(0.001 + 0.999*b155)) - 27*x107/(0.001 + 0.999*b155) + sqr(
x119/(0.001 + 0.999*b155)) - 17*x119/(0.001 + 0.999*b155))*(0.001 +
0.999*b155) + 182.25*b155 + 72.25*b155 - 36*b155 =L= 0;
e235.. (sqr(x108/(0.001 + 0.999*b156)) - 28*x108/(0.001 + 0.999*b156) + sqr(
x120/(0.001 + 0.999*b156)) - 17*x120/(0.001 + 0.999*b156))*(0.001 +
0.999*b156) + 196*b156 + 72.25*b156 - 36*b156 =L= 0;
e236.. (sqr(x109/(0.001 + 0.999*b157)) - 95*x109/(0.001 + 0.999*b157) + sqr(
x121/(0.001 + 0.999*b157)) - 154*x121/(0.001 + 0.999*b157))*(0.001 +
0.999*b157) + 2256.25*b157 + 5929*b157 - 25*b157 =L= 0;
e237.. (sqr(x110/(0.001 + 0.999*b158)) - 93*x110/(0.001 + 0.999*b158) + sqr(
x122/(0.001 + 0.999*b158)) - 155*x122/(0.001 + 0.999*b158))*(0.001 +
0.999*b158) + 2162.25*b158 + 6006.25*b158 - 25*b158 =L= 0;
e238.. (sqr(x111/(0.001 + 0.999*b159)) - 97*x111/(0.001 + 0.999*b159) + sqr(
x123/(0.001 + 0.999*b159)) - 157*x123/(0.001 + 0.999*b159))*(0.001 +
0.999*b159) + 2352.25*b159 + 6162.25*b159 - 25*b159 =L= 0;
e239.. (sqr(x112/(0.001 + 0.999*b160)) - 98*x112/(0.001 + 0.999*b160) + sqr(
x124/(0.001 + 0.999*b160)) - 157*x124/(0.001 + 0.999*b160))*(0.001 +
0.999*b160) + 2401*b160 + 6162.25*b160 - 25*b160 =L= 0;
e240.. (sqr(x113/(0.001 + 0.999*b161)) - 55*x113/(0.001 + 0.999*b161) + sqr(
x125/(0.001 + 0.999*b161)) - 94*x125/(0.001 + 0.999*b161))*(0.001 +
0.999*b161) + 756.25*b161 + 2209*b161 - 16*b161 =L= 0;
e241.. (sqr(x114/(0.001 + 0.999*b162)) - 53*x114/(0.001 + 0.999*b162) + sqr(
x126/(0.001 + 0.999*b162)) - 95*x126/(0.001 + 0.999*b162))*(0.001 +
0.999*b162) + 702.25*b162 + 2256.25*b162 - 16*b162 =L= 0;
e242.. (sqr(x115/(0.001 + 0.999*b163)) - 57*x115/(0.001 + 0.999*b163) + sqr(
x127/(0.001 + 0.999*b163)) - 97*x127/(0.001 + 0.999*b163))*(0.001 +
0.999*b163) + 812.25*b163 + 2352.25*b163 - 16*b163 =L= 0;
e243.. (sqr(x116/(0.001 + 0.999*b164)) - 58*x116/(0.001 + 0.999*b164) + sqr(
x128/(0.001 + 0.999*b164)) - 97*x128/(0.001 + 0.999*b164))*(0.001 +
0.999*b164) + 841*b164 + 2352.25*b164 - 16*b164 =L= 0;
e244.. (sqr(x105/(0.001 + 0.999*b153)) - 25*x105/(0.001 + 0.999*b153) + sqr(
x117/(0.001 + 0.999*b153)) - 26*x117/(0.001 + 0.999*b153))*(0.001 +
0.999*b153) + 156.25*b153 + 169*b153 - 36*b153 =L= 0;
e245.. (sqr(x106/(0.001 + 0.999*b154)) - 23*x106/(0.001 + 0.999*b154) + sqr(
x118/(0.001 + 0.999*b154)) - 25*x118/(0.001 + 0.999*b154))*(0.001 +
0.999*b154) + 132.25*b154 + 156.25*b154 - 36*b154 =L= 0;
e246.. (sqr(x107/(0.001 + 0.999*b155)) - 27*x107/(0.001 + 0.999*b155) + sqr(
x119/(0.001 + 0.999*b155)) - 23*x119/(0.001 + 0.999*b155))*(0.001 +
0.999*b155) + 182.25*b155 + 132.25*b155 - 36*b155 =L= 0;
e247.. (sqr(x108/(0.001 + 0.999*b156)) - 28*x108/(0.001 + 0.999*b156) + sqr(
x120/(0.001 + 0.999*b156)) - 23*x120/(0.001 + 0.999*b156))*(0.001 +
0.999*b156) + 196*b156 + 132.25*b156 - 36*b156 =L= 0;
e248.. (sqr(x109/(0.001 + 0.999*b157)) - 95*x109/(0.001 + 0.999*b157) + sqr(
x121/(0.001 + 0.999*b157)) - 166*x121/(0.001 + 0.999*b157))*(0.001 +
0.999*b157) + 2256.25*b157 + 6889*b157 - 25*b157 =L= 0;
e249.. (sqr(x110/(0.001 + 0.999*b158)) - 93*x110/(0.001 + 0.999*b158) + sqr(
x122/(0.001 + 0.999*b158)) - 165*x122/(0.001 + 0.999*b158))*(0.001 +
0.999*b158) + 2162.25*b158 + 6806.25*b158 - 25*b158 =L= 0;
e250.. (sqr(x111/(0.001 + 0.999*b159)) - 97*x111/(0.001 + 0.999*b159) + sqr(
x123/(0.001 + 0.999*b159)) - 163*x123/(0.001 + 0.999*b159))*(0.001 +
0.999*b159) + 2352.25*b159 + 6642.25*b159 - 25*b159 =L= 0;
e251.. (sqr(x112/(0.001 + 0.999*b160)) - 98*x112/(0.001 + 0.999*b160) + sqr(
x124/(0.001 + 0.999*b160)) - 163*x124/(0.001 + 0.999*b160))*(0.001 +
0.999*b160) + 2401*b160 + 6642.25*b160 - 25*b160 =L= 0;
e252.. (sqr(x113/(0.001 + 0.999*b161)) - 55*x113/(0.001 + 0.999*b161) + sqr(
x125/(0.001 + 0.999*b161)) - 106*x125/(0.001 + 0.999*b161))*(0.001 +
0.999*b161) + 756.25*b161 + 2809*b161 - 16*b161 =L= 0;
e253.. (sqr(x114/(0.001 + 0.999*b162)) - 53*x114/(0.001 + 0.999*b162) + sqr(
x126/(0.001 + 0.999*b162)) - 105*x126/(0.001 + 0.999*b162))*(0.001 +
0.999*b162) + 702.25*b162 + 2756.25*b162 - 16*b162 =L= 0;
e254.. (sqr(x115/(0.001 + 0.999*b163)) - 57*x115/(0.001 + 0.999*b163) + sqr(
x127/(0.001 + 0.999*b163)) - 103*x127/(0.001 + 0.999*b163))*(0.001 +
0.999*b163) + 812.25*b163 + 2652.25*b163 - 16*b163 =L= 0;
e255.. (sqr(x116/(0.001 + 0.999*b164)) - 58*x116/(0.001 + 0.999*b164) + sqr(
x128/(0.001 + 0.999*b164)) - 103*x128/(0.001 + 0.999*b164))*(0.001 +
0.999*b164) + 841*b164 + 2652.25*b164 - 16*b164 =L= 0;
e256.. b153 + b157 + b161 =E= 1;
e257.. b154 + b158 + b162 =E= 1;
e258.. b155 + b159 + b163 =E= 1;
e259.. b156 + b160 + b164 =E= 1;
* set non-default bounds
x1.lo = 11.5; x1.up = 52.5;
x2.lo = 12.5; x2.up = 51.5;
x3.lo = 10.5; x3.up = 53.5;
x4.lo = 10; x4.up = 54;
x5.lo = 7; x5.up = 82;
x6.lo = 6.5; x6.up = 82.5;
x7.lo = 5.5; x7.up = 83.5;
x8.lo = 5.5; x8.up = 83.5;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc