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Instance p_ball_30b_5p_3d_m
Select 5-points in 3-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 30 balls with radius one. This is a big-M formulation.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 0.00000000 (ALPHAECP) 8.21823207 (ANTIGONE) 8.21826651 (BARON) 8.21829027 (BONMIN) 8.21826149 (COUENNE) 8.21829037 (CPLEX) 8.21820006 (GUROBI) 8.21829037 (LINDO) 8.21828601 (SCIP) 8.21829037 (SHOT) |
| Referencesⓘ | Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020. |
| Sourceⓘ | p_ball_30b_5p_3d.gms, contributed by Jan Kronqvist and Ruth Misener |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 26 Aug 2020 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 195 |
| #Binary Variablesⓘ | 150 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 15 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 30 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 249 |
| #Linear Constraintsⓘ | 99 |
| #Quadratic Constraintsⓘ | 150 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 1088 |
| #Nonlinear Nonzeros in Jacobianⓘ | 450 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 15 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 15 |
| #Blocks in Hessian of Lagrangianⓘ | 15 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 8.0236e-02 |
| Maximal coefficientⓘ | 1.7909e+02 |
| Infeasibility of initial pointⓘ | 28.27 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 250 6 0 244 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 196 46 150 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1119 669 450 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,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,objvar;
Positive Variables 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;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51
,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68
,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85
,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101
,b102,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114
,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127
,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140
,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150;
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;
e1.. x151 - x152 - x153 =L= 0;
e2.. - x151 + x152 - x153 =L= 0;
e3.. x154 - x155 - x156 =L= 0;
e4.. - x154 + x155 - x156 =L= 0;
e5.. x157 - x158 - x159 =L= 0;
e6.. - x157 + x158 - x159 =L= 0;
e7.. x151 - x160 - x161 =L= 0;
e8.. - x151 + x160 - x161 =L= 0;
e9.. x154 - x162 - x163 =L= 0;
e10.. - x154 + x162 - x163 =L= 0;
e11.. x157 - x164 - x165 =L= 0;
e12.. - x157 + x164 - x165 =L= 0;
e13.. x151 - x166 - x167 =L= 0;
e14.. - x151 + x166 - x167 =L= 0;
e15.. x154 - x168 - x169 =L= 0;
e16.. - x154 + x168 - x169 =L= 0;
e17.. x157 - x170 - x171 =L= 0;
e18.. - x157 + x170 - x171 =L= 0;
e19.. x151 - x172 - x173 =L= 0;
e20.. - x151 + x172 - x173 =L= 0;
e21.. x154 - x174 - x175 =L= 0;
e22.. - x154 + x174 - x175 =L= 0;
e23.. x157 - x176 - x177 =L= 0;
e24.. - x157 + x176 - x177 =L= 0;
e25.. x152 - x160 - x178 =L= 0;
e26.. - x152 + x160 - x178 =L= 0;
e27.. x155 - x162 - x179 =L= 0;
e28.. - x155 + x162 - x179 =L= 0;
e29.. x158 - x164 - x180 =L= 0;
e30.. - x158 + x164 - x180 =L= 0;
e31.. x152 - x166 - x181 =L= 0;
e32.. - x152 + x166 - x181 =L= 0;
e33.. x155 - x168 - x182 =L= 0;
e34.. - x155 + x168 - x182 =L= 0;
e35.. x158 - x170 - x183 =L= 0;
e36.. - x158 + x170 - x183 =L= 0;
e37.. x152 - x172 - x184 =L= 0;
e38.. - x152 + x172 - x184 =L= 0;
e39.. x155 - x174 - x185 =L= 0;
e40.. - x155 + x174 - x185 =L= 0;
e41.. x158 - x176 - x186 =L= 0;
e42.. - x158 + x176 - x186 =L= 0;
e43.. x160 - x166 - x187 =L= 0;
e44.. - x160 + x166 - x187 =L= 0;
e45.. x162 - x168 - x188 =L= 0;
e46.. - x162 + x168 - x188 =L= 0;
e47.. x164 - x170 - x189 =L= 0;
e48.. - x164 + x170 - x189 =L= 0;
e49.. x160 - x172 - x190 =L= 0;
e50.. - x160 + x172 - x190 =L= 0;
e51.. x162 - x174 - x191 =L= 0;
e52.. - x162 + x174 - x191 =L= 0;
e53.. x164 - x176 - x192 =L= 0;
e54.. - x164 + x176 - x192 =L= 0;
e55.. x166 - x172 - x193 =L= 0;
e56.. - x166 + x172 - x193 =L= 0;
e57.. x168 - x174 - x194 =L= 0;
e58.. - x168 + x174 - x194 =L= 0;
e59.. x170 - x176 - x195 =L= 0;
e60.. - x170 + x176 - x195 =L= 0;
e61.. sqr(4.83202054247519 - x151) + sqr(5.08041476544912 - x154) + sqr(
6.32621379041806 - x157) + 75.9704013248235*b1 =L= 76.9704013248235;
e62.. sqr(6.86422157586402 - x151) + sqr(7.66428209799864 - x154) + sqr(
0.09709175573132 - x157) + 140.659182931282*b2 =L= 141.659182931282;
e63.. sqr(4.84862000711289 - x151) + sqr(3.45257195120785 - x154) + sqr(
7.39094773970617 - x157) + 109.037662329134*b3 =L= 110.037662329134;
e64.. sqr(1.90653576175828 - x151) + sqr(9.06815267710453 - x154) + sqr(
0.329270310437709 - x157) + 179.094987294124*b4 =L= 180.094987294124;
e65.. sqr(8.91873287322862 - x151) + sqr(3.005493222209 - x154) + sqr(
6.72603314933737 - x157) + 149.370448589907*b5 =L= 150.370448589907;
e66.. sqr(2.79219011695411 - x151) + sqr(0.0802363505466042 - x154) + sqr(
5.8239689013093 - x157) + 161.969348685106*b6 =L= 162.969348685106;
e67.. sqr(8.45192604487847 - x151) + sqr(0.960982267180915 - x154) + sqr(
7.08846749273086 - x157) + 179.094987294124*b7 =L= 180.094987294124;
e68.. sqr(9.76694746975659 - x151) + sqr(1.64767982343444 - x154) + sqr(
3.89461195866276 - x157) + 152.326136990614*b8 =L= 153.326136990614;
e69.. sqr(3.92650027388399 - x151) + sqr(8.57900429288824 - x154) + sqr(
9.23525817101371 - x157) + 147.501061227256*b9 =L= 148.501061227256;
e70.. sqr(0.679990404106158 - x151) + sqr(7.93354548453717 - x154) + sqr(
6.24827514848977 - x157) + 150.218840203818*b10 =L= 151.218840203818;
e71.. sqr(3.80282662917579 - x151) + sqr(5.00336142496769 - x154) + sqr(
6.01003348085459 - x157) + 79.871242402384*b11 =L= 80.871242402384;
e72.. sqr(6.54293331034743 - x151) + sqr(1.49363772657694 - x154) + sqr(
3.58497465463316 - x157) + 108.386687957096*b12 =L= 109.386687957096;
e73.. sqr(5.20241765093859 - x151) + sqr(5.86977990966318 - x154) + sqr(
6.440337805336 - x157) + 73.72646594677*b13 =L= 74.72646594677;
e74.. sqr(5.87470028021075 - x151) + sqr(2.67028689434427 - x154) + sqr(
0.749156996429077 - x157) + 131.767274170968*b14 =L= 132.767274170968;
e75.. sqr(2.89776733906328 - x151) + sqr(5.22108290497701 - x154) + sqr(
7.57016691626461 - x157) + 107.46773494331*b15 =L= 108.46773494331;
e76.. sqr(3.25002624472116 - x151) + sqr(6.977422017743 - x154) + sqr(
0.695695115140367 - x157) + 124.533164159302*b16 =L= 125.533164159302;
e77.. sqr(8.47049713128073 - x151) + sqr(4.20582102463618 - x154) + sqr(
4.93941262529365 - x157) + 106.740936443786*b17 =L= 107.740936443786;
e78.. sqr(0.786615440794736 - x151) + sqr(1.54813106254315 - x154) + sqr(
2.98963379540322 - x157) + 150.565522268974*b18 =L= 151.565522268974;
e79.. sqr(5.17568572881879 - x151) + sqr(2.02627806544288 - x154) + sqr(
9.2740633418688 - x157) + 163.973027168021*b19 =L= 164.973027168021;
e80.. sqr(9.11874181180651 - x151) + sqr(9.07966816070985 - x154) + sqr(
1.64995049320116 - x157) + 161.969348685106*b20 =L= 162.969348685106;
e81.. sqr(8.26392769674786 - x151) + sqr(4.29716878332203 - x154) + sqr(
3.06511979366618 - x157) + 98.8575703440414*b21 =L= 99.8575703440414;
e82.. sqr(2.95522257480442 - x151) + sqr(1.29725120442498 - x154) + sqr(
0.799527585103169 - x157) + 147.501061227256*b22 =L= 148.501061227256;
e83.. sqr(5.59281220526297 - x151) + sqr(5.08387949672858 - x154) + sqr(
0.547463810150197 - x157) + 109.493435167956*b23 =L= 110.493435167956;
e84.. sqr(5.5713321706538 - x151) + sqr(3.89813512317444 - x154) + sqr(
0.378899938163517 - x157) + 123.353905785717*b24 =L= 124.353905785717;
e85.. sqr(1.47483805835463 - x151) + sqr(0.989752492299246 - x154) + sqr(
5.36717263813865 - x157) + 161.162335824934*b25 =L= 162.162335824934;
e86.. sqr(4.61507078501251 - x151) + sqr(0.234707301612243 - x154) + sqr(
3.97342857514894 - x157) + 124.302670822369*b26 =L= 125.302670822369;
e87.. sqr(9.15405801517484 - x151) + sqr(4.26169733166395 - x154) + sqr(
4.89911772871142 - x157) + 116.160211358947*b27 =L= 117.160211358947;
e88.. sqr(6.23408727244271 - x151) + sqr(0.755925845511098 - x154) + sqr(
5.40595672236618 - x157) + 134.909618001418*b28 =L= 135.909618001418;
e89.. sqr(5.16744991507397 - x151) + sqr(5.25535097293888 - x154) + sqr(
3.81062986996748 - x157) + 54.9767406737741*b29 =L= 55.9767406737741;
e90.. sqr(7.23609076996082 - x151) + sqr(3.30048962157922 - x154) + sqr(
8.05002431260521 - x157) + 143.305588261876*b30 =L= 144.305588261876;
e91.. 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 =E= 1;
e92.. sqr(4.83202054247519 - x152) + sqr(5.08041476544912 - x155) + sqr(
6.32621379041806 - x158) + 75.9704013248235*b31 =L= 76.9704013248235;
e93.. sqr(6.86422157586402 - x152) + sqr(7.66428209799864 - x155) + sqr(
0.09709175573132 - x158) + 140.659182931282*b32 =L= 141.659182931282;
e94.. sqr(4.84862000711289 - x152) + sqr(3.45257195120785 - x155) + sqr(
7.39094773970617 - x158) + 109.037662329134*b33 =L= 110.037662329134;
e95.. sqr(1.90653576175828 - x152) + sqr(9.06815267710453 - x155) + sqr(
0.329270310437709 - x158) + 179.094987294124*b34 =L= 180.094987294124;
e96.. sqr(8.91873287322862 - x152) + sqr(3.005493222209 - x155) + sqr(
6.72603314933737 - x158) + 149.370448589907*b35 =L= 150.370448589907;
e97.. sqr(2.79219011695411 - x152) + sqr(0.0802363505466042 - x155) + sqr(
5.8239689013093 - x158) + 161.969348685106*b36 =L= 162.969348685106;
e98.. sqr(8.45192604487847 - x152) + sqr(0.960982267180915 - x155) + sqr(
7.08846749273086 - x158) + 179.094987294124*b37 =L= 180.094987294124;
e99.. sqr(9.76694746975659 - x152) + sqr(1.64767982343444 - x155) + sqr(
3.89461195866276 - x158) + 152.326136990614*b38 =L= 153.326136990614;
e100.. sqr(3.92650027388399 - x152) + sqr(8.57900429288824 - x155) + sqr(
9.23525817101371 - x158) + 147.501061227256*b39 =L= 148.501061227256;
e101.. sqr(0.679990404106158 - x152) + sqr(7.93354548453717 - x155) + sqr(
6.24827514848977 - x158) + 150.218840203818*b40 =L= 151.218840203818;
e102.. sqr(3.80282662917579 - x152) + sqr(5.00336142496769 - x155) + sqr(
6.01003348085459 - x158) + 79.871242402384*b41 =L= 80.871242402384;
e103.. sqr(6.54293331034743 - x152) + sqr(1.49363772657694 - x155) + sqr(
3.58497465463316 - x158) + 108.386687957096*b42 =L= 109.386687957096;
e104.. sqr(5.20241765093859 - x152) + sqr(5.86977990966318 - x155) + sqr(
6.440337805336 - x158) + 73.72646594677*b43 =L= 74.72646594677;
e105.. sqr(5.87470028021075 - x152) + sqr(2.67028689434427 - x155) + sqr(
0.749156996429077 - x158) + 131.767274170968*b44 =L= 132.767274170968;
e106.. sqr(2.89776733906328 - x152) + sqr(5.22108290497701 - x155) + sqr(
7.57016691626461 - x158) + 107.46773494331*b45 =L= 108.46773494331;
e107.. sqr(3.25002624472116 - x152) + sqr(6.977422017743 - x155) + sqr(
0.695695115140367 - x158) + 124.533164159302*b46 =L= 125.533164159302;
e108.. sqr(8.47049713128073 - x152) + sqr(4.20582102463618 - x155) + sqr(
4.93941262529365 - x158) + 106.740936443786*b47 =L= 107.740936443786;
e109.. sqr(0.786615440794736 - x152) + sqr(1.54813106254315 - x155) + sqr(
2.98963379540322 - x158) + 150.565522268974*b48 =L= 151.565522268974;
e110.. sqr(5.17568572881879 - x152) + sqr(2.02627806544288 - x155) + sqr(
9.2740633418688 - x158) + 163.973027168021*b49 =L= 164.973027168021;
e111.. sqr(9.11874181180651 - x152) + sqr(9.07966816070985 - x155) + sqr(
1.64995049320116 - x158) + 161.969348685106*b50 =L= 162.969348685106;
e112.. sqr(8.26392769674786 - x152) + sqr(4.29716878332203 - x155) + sqr(
3.06511979366618 - x158) + 98.8575703440414*b51 =L= 99.8575703440414;
e113.. sqr(2.95522257480442 - x152) + sqr(1.29725120442498 - x155) + sqr(
0.799527585103169 - x158) + 147.501061227256*b52 =L= 148.501061227256;
e114.. sqr(5.59281220526297 - x152) + sqr(5.08387949672858 - x155) + sqr(
0.547463810150197 - x158) + 109.493435167956*b53 =L= 110.493435167956;
e115.. sqr(5.5713321706538 - x152) + sqr(3.89813512317444 - x155) + sqr(
0.378899938163517 - x158) + 123.353905785717*b54 =L= 124.353905785717;
e116.. sqr(1.47483805835463 - x152) + sqr(0.989752492299246 - x155) + sqr(
5.36717263813865 - x158) + 161.162335824934*b55 =L= 162.162335824934;
e117.. sqr(4.61507078501251 - x152) + sqr(0.234707301612243 - x155) + sqr(
3.97342857514894 - x158) + 124.302670822369*b56 =L= 125.302670822369;
e118.. sqr(9.15405801517484 - x152) + sqr(4.26169733166395 - x155) + sqr(
4.89911772871142 - x158) + 116.160211358947*b57 =L= 117.160211358947;
e119.. sqr(6.23408727244271 - x152) + sqr(0.755925845511098 - x155) + sqr(
5.40595672236618 - x158) + 134.909618001418*b58 =L= 135.909618001418;
e120.. sqr(5.16744991507397 - x152) + sqr(5.25535097293888 - x155) + sqr(
3.81062986996748 - x158) + 54.9767406737741*b59 =L= 55.9767406737741;
e121.. sqr(7.23609076996082 - x152) + sqr(3.30048962157922 - x155) + sqr(
8.05002431260521 - x158) + 143.305588261876*b60 =L= 144.305588261876;
e122.. 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 =E= 1;
e123.. sqr(4.83202054247519 - x160) + sqr(5.08041476544912 - x162) + sqr(
6.32621379041806 - x164) + 75.9704013248235*b61 =L= 76.9704013248235;
e124.. sqr(6.86422157586402 - x160) + sqr(7.66428209799864 - x162) + sqr(
0.09709175573132 - x164) + 140.659182931282*b62 =L= 141.659182931282;
e125.. sqr(4.84862000711289 - x160) + sqr(3.45257195120785 - x162) + sqr(
7.39094773970617 - x164) + 109.037662329134*b63 =L= 110.037662329134;
e126.. sqr(1.90653576175828 - x160) + sqr(9.06815267710453 - x162) + sqr(
0.329270310437709 - x164) + 179.094987294124*b64 =L= 180.094987294124;
e127.. sqr(8.91873287322862 - x160) + sqr(3.005493222209 - x162) + sqr(
6.72603314933737 - x164) + 149.370448589907*b65 =L= 150.370448589907;
e128.. sqr(2.79219011695411 - x160) + sqr(0.0802363505466042 - x162) + sqr(
5.8239689013093 - x164) + 161.969348685106*b66 =L= 162.969348685106;
e129.. sqr(8.45192604487847 - x160) + sqr(0.960982267180915 - x162) + sqr(
7.08846749273086 - x164) + 179.094987294124*b67 =L= 180.094987294124;
e130.. sqr(9.76694746975659 - x160) + sqr(1.64767982343444 - x162) + sqr(
3.89461195866276 - x164) + 152.326136990614*b68 =L= 153.326136990614;
e131.. sqr(3.92650027388399 - x160) + sqr(8.57900429288824 - x162) + sqr(
9.23525817101371 - x164) + 147.501061227256*b69 =L= 148.501061227256;
e132.. sqr(0.679990404106158 - x160) + sqr(7.93354548453717 - x162) + sqr(
6.24827514848977 - x164) + 150.218840203818*b70 =L= 151.218840203818;
e133.. sqr(3.80282662917579 - x160) + sqr(5.00336142496769 - x162) + sqr(
6.01003348085459 - x164) + 79.871242402384*b71 =L= 80.871242402384;
e134.. sqr(6.54293331034743 - x160) + sqr(1.49363772657694 - x162) + sqr(
3.58497465463316 - x164) + 108.386687957096*b72 =L= 109.386687957096;
e135.. sqr(5.20241765093859 - x160) + sqr(5.86977990966318 - x162) + sqr(
6.440337805336 - x164) + 73.72646594677*b73 =L= 74.72646594677;
e136.. sqr(5.87470028021075 - x160) + sqr(2.67028689434427 - x162) + sqr(
0.749156996429077 - x164) + 131.767274170968*b74 =L= 132.767274170968;
e137.. sqr(2.89776733906328 - x160) + sqr(5.22108290497701 - x162) + sqr(
7.57016691626461 - x164) + 107.46773494331*b75 =L= 108.46773494331;
e138.. sqr(3.25002624472116 - x160) + sqr(6.977422017743 - x162) + sqr(
0.695695115140367 - x164) + 124.533164159302*b76 =L= 125.533164159302;
e139.. sqr(8.47049713128073 - x160) + sqr(4.20582102463618 - x162) + sqr(
4.93941262529365 - x164) + 106.740936443786*b77 =L= 107.740936443786;
e140.. sqr(0.786615440794736 - x160) + sqr(1.54813106254315 - x162) + sqr(
2.98963379540322 - x164) + 150.565522268974*b78 =L= 151.565522268974;
e141.. sqr(5.17568572881879 - x160) + sqr(2.02627806544288 - x162) + sqr(
9.2740633418688 - x164) + 163.973027168021*b79 =L= 164.973027168021;
e142.. sqr(9.11874181180651 - x160) + sqr(9.07966816070985 - x162) + sqr(
1.64995049320116 - x164) + 161.969348685106*b80 =L= 162.969348685106;
e143.. sqr(8.26392769674786 - x160) + sqr(4.29716878332203 - x162) + sqr(
3.06511979366618 - x164) + 98.8575703440414*b81 =L= 99.8575703440414;
e144.. sqr(2.95522257480442 - x160) + sqr(1.29725120442498 - x162) + sqr(
0.799527585103169 - x164) + 147.501061227256*b82 =L= 148.501061227256;
e145.. sqr(5.59281220526297 - x160) + sqr(5.08387949672858 - x162) + sqr(
0.547463810150197 - x164) + 109.493435167956*b83 =L= 110.493435167956;
e146.. sqr(5.5713321706538 - x160) + sqr(3.89813512317444 - x162) + sqr(
0.378899938163517 - x164) + 123.353905785717*b84 =L= 124.353905785717;
e147.. sqr(1.47483805835463 - x160) + sqr(0.989752492299246 - x162) + sqr(
5.36717263813865 - x164) + 161.162335824934*b85 =L= 162.162335824934;
e148.. sqr(4.61507078501251 - x160) + sqr(0.234707301612243 - x162) + sqr(
3.97342857514894 - x164) + 124.302670822369*b86 =L= 125.302670822369;
e149.. sqr(9.15405801517484 - x160) + sqr(4.26169733166395 - x162) + sqr(
4.89911772871142 - x164) + 116.160211358947*b87 =L= 117.160211358947;
e150.. sqr(6.23408727244271 - x160) + sqr(0.755925845511098 - x162) + sqr(
5.40595672236618 - x164) + 134.909618001418*b88 =L= 135.909618001418;
e151.. sqr(5.16744991507397 - x160) + sqr(5.25535097293888 - x162) + sqr(
3.81062986996748 - x164) + 54.9767406737741*b89 =L= 55.9767406737741;
e152.. sqr(7.23609076996082 - x160) + sqr(3.30048962157922 - x162) + sqr(
8.05002431260521 - x164) + 143.305588261876*b90 =L= 144.305588261876;
e153.. b61 + b62 + b63 + b64 + b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72
+ b73 + b74 + b75 + b76 + b77 + b78 + b79 + b80 + b81 + b82 + b83 + b84
+ b85 + b86 + b87 + b88 + b89 + b90 =E= 1;
e154.. sqr(4.83202054247519 - x166) + sqr(5.08041476544912 - x168) + sqr(
6.32621379041806 - x170) + 75.9704013248235*b91 =L= 76.9704013248235;
e155.. sqr(6.86422157586402 - x166) + sqr(7.66428209799864 - x168) + sqr(
0.09709175573132 - x170) + 140.659182931282*b92 =L= 141.659182931282;
e156.. sqr(4.84862000711289 - x166) + sqr(3.45257195120785 - x168) + sqr(
7.39094773970617 - x170) + 109.037662329134*b93 =L= 110.037662329134;
e157.. sqr(1.90653576175828 - x166) + sqr(9.06815267710453 - x168) + sqr(
0.329270310437709 - x170) + 179.094987294124*b94 =L= 180.094987294124;
e158.. sqr(8.91873287322862 - x166) + sqr(3.005493222209 - x168) + sqr(
6.72603314933737 - x170) + 149.370448589907*b95 =L= 150.370448589907;
e159.. sqr(2.79219011695411 - x166) + sqr(0.0802363505466042 - x168) + sqr(
5.8239689013093 - x170) + 161.969348685106*b96 =L= 162.969348685106;
e160.. sqr(8.45192604487847 - x166) + sqr(0.960982267180915 - x168) + sqr(
7.08846749273086 - x170) + 179.094987294124*b97 =L= 180.094987294124;
e161.. sqr(9.76694746975659 - x166) + sqr(1.64767982343444 - x168) + sqr(
3.89461195866276 - x170) + 152.326136990614*b98 =L= 153.326136990614;
e162.. sqr(3.92650027388399 - x166) + sqr(8.57900429288824 - x168) + sqr(
9.23525817101371 - x170) + 147.501061227256*b99 =L= 148.501061227256;
e163.. sqr(0.679990404106158 - x166) + sqr(7.93354548453717 - x168) + sqr(
6.24827514848977 - x170) + 150.218840203818*b100 =L= 151.218840203818;
e164.. sqr(3.80282662917579 - x166) + sqr(5.00336142496769 - x168) + sqr(
6.01003348085459 - x170) + 79.871242402384*b101 =L= 80.871242402384;
e165.. sqr(6.54293331034743 - x166) + sqr(1.49363772657694 - x168) + sqr(
3.58497465463316 - x170) + 108.386687957096*b102 =L= 109.386687957096;
e166.. sqr(5.20241765093859 - x166) + sqr(5.86977990966318 - x168) + sqr(
6.440337805336 - x170) + 73.72646594677*b103 =L= 74.72646594677;
e167.. sqr(5.87470028021075 - x166) + sqr(2.67028689434427 - x168) + sqr(
0.749156996429077 - x170) + 131.767274170968*b104 =L= 132.767274170968;
e168.. sqr(2.89776733906328 - x166) + sqr(5.22108290497701 - x168) + sqr(
7.57016691626461 - x170) + 107.46773494331*b105 =L= 108.46773494331;
e169.. sqr(3.25002624472116 - x166) + sqr(6.977422017743 - x168) + sqr(
0.695695115140367 - x170) + 124.533164159302*b106 =L= 125.533164159302;
e170.. sqr(8.47049713128073 - x166) + sqr(4.20582102463618 - x168) + sqr(
4.93941262529365 - x170) + 106.740936443786*b107 =L= 107.740936443786;
e171.. sqr(0.786615440794736 - x166) + sqr(1.54813106254315 - x168) + sqr(
2.98963379540322 - x170) + 150.565522268974*b108 =L= 151.565522268974;
e172.. sqr(5.17568572881879 - x166) + sqr(2.02627806544288 - x168) + sqr(
9.2740633418688 - x170) + 163.973027168021*b109 =L= 164.973027168021;
e173.. sqr(9.11874181180651 - x166) + sqr(9.07966816070985 - x168) + sqr(
1.64995049320116 - x170) + 161.969348685106*b110 =L= 162.969348685106;
e174.. sqr(8.26392769674786 - x166) + sqr(4.29716878332203 - x168) + sqr(
3.06511979366618 - x170) + 98.8575703440414*b111 =L= 99.8575703440414;
e175.. sqr(2.95522257480442 - x166) + sqr(1.29725120442498 - x168) + sqr(
0.799527585103169 - x170) + 147.501061227256*b112 =L= 148.501061227256;
e176.. sqr(5.59281220526297 - x166) + sqr(5.08387949672858 - x168) + sqr(
0.547463810150197 - x170) + 109.493435167956*b113 =L= 110.493435167956;
e177.. sqr(5.5713321706538 - x166) + sqr(3.89813512317444 - x168) + sqr(
0.378899938163517 - x170) + 123.353905785717*b114 =L= 124.353905785717;
e178.. sqr(1.47483805835463 - x166) + sqr(0.989752492299246 - x168) + sqr(
5.36717263813865 - x170) + 161.162335824934*b115 =L= 162.162335824934;
e179.. sqr(4.61507078501251 - x166) + sqr(0.234707301612243 - x168) + sqr(
3.97342857514894 - x170) + 124.302670822369*b116 =L= 125.302670822369;
e180.. sqr(9.15405801517484 - x166) + sqr(4.26169733166395 - x168) + sqr(
4.89911772871142 - x170) + 116.160211358947*b117 =L= 117.160211358947;
e181.. sqr(6.23408727244271 - x166) + sqr(0.755925845511098 - x168) + sqr(
5.40595672236618 - x170) + 134.909618001418*b118 =L= 135.909618001418;
e182.. sqr(5.16744991507397 - x166) + sqr(5.25535097293888 - x168) + sqr(
3.81062986996748 - x170) + 54.9767406737741*b119 =L= 55.9767406737741;
e183.. sqr(7.23609076996082 - x166) + sqr(3.30048962157922 - x168) + sqr(
8.05002431260521 - x170) + 143.305588261876*b120 =L= 144.305588261876;
e184.. b91 + b92 + b93 + b94 + b95 + b96 + b97 + b98 + b99 + b100 + b101
+ b102 + b103 + b104 + b105 + b106 + b107 + b108 + b109 + b110 + b111
+ b112 + b113 + b114 + b115 + b116 + b117 + b118 + b119 + b120 =E= 1;
e185.. sqr(4.83202054247519 - x172) + sqr(5.08041476544912 - x174) + sqr(
6.32621379041806 - x176) + 75.9704013248235*b121 =L= 76.9704013248235;
e186.. sqr(6.86422157586402 - x172) + sqr(7.66428209799864 - x174) + sqr(
0.09709175573132 - x176) + 140.659182931282*b122 =L= 141.659182931282;
e187.. sqr(4.84862000711289 - x172) + sqr(3.45257195120785 - x174) + sqr(
7.39094773970617 - x176) + 109.037662329134*b123 =L= 110.037662329134;
e188.. sqr(1.90653576175828 - x172) + sqr(9.06815267710453 - x174) + sqr(
0.329270310437709 - x176) + 179.094987294124*b124 =L= 180.094987294124;
e189.. sqr(8.91873287322862 - x172) + sqr(3.005493222209 - x174) + sqr(
6.72603314933737 - x176) + 149.370448589907*b125 =L= 150.370448589907;
e190.. sqr(2.79219011695411 - x172) + sqr(0.0802363505466042 - x174) + sqr(
5.8239689013093 - x176) + 161.969348685106*b126 =L= 162.969348685106;
e191.. sqr(8.45192604487847 - x172) + sqr(0.960982267180915 - x174) + sqr(
7.08846749273086 - x176) + 179.094987294124*b127 =L= 180.094987294124;
e192.. sqr(9.76694746975659 - x172) + sqr(1.64767982343444 - x174) + sqr(
3.89461195866276 - x176) + 152.326136990614*b128 =L= 153.326136990614;
e193.. sqr(3.92650027388399 - x172) + sqr(8.57900429288824 - x174) + sqr(
9.23525817101371 - x176) + 147.501061227256*b129 =L= 148.501061227256;
e194.. sqr(0.679990404106158 - x172) + sqr(7.93354548453717 - x174) + sqr(
6.24827514848977 - x176) + 150.218840203818*b130 =L= 151.218840203818;
e195.. sqr(3.80282662917579 - x172) + sqr(5.00336142496769 - x174) + sqr(
6.01003348085459 - x176) + 79.871242402384*b131 =L= 80.871242402384;
e196.. sqr(6.54293331034743 - x172) + sqr(1.49363772657694 - x174) + sqr(
3.58497465463316 - x176) + 108.386687957096*b132 =L= 109.386687957096;
e197.. sqr(5.20241765093859 - x172) + sqr(5.86977990966318 - x174) + sqr(
6.440337805336 - x176) + 73.72646594677*b133 =L= 74.72646594677;
e198.. sqr(5.87470028021075 - x172) + sqr(2.67028689434427 - x174) + sqr(
0.749156996429077 - x176) + 131.767274170968*b134 =L= 132.767274170968;
e199.. sqr(2.89776733906328 - x172) + sqr(5.22108290497701 - x174) + sqr(
7.57016691626461 - x176) + 107.46773494331*b135 =L= 108.46773494331;
e200.. sqr(3.25002624472116 - x172) + sqr(6.977422017743 - x174) + sqr(
0.695695115140367 - x176) + 124.533164159302*b136 =L= 125.533164159302;
e201.. sqr(8.47049713128073 - x172) + sqr(4.20582102463618 - x174) + sqr(
4.93941262529365 - x176) + 106.740936443786*b137 =L= 107.740936443786;
e202.. sqr(0.786615440794736 - x172) + sqr(1.54813106254315 - x174) + sqr(
2.98963379540322 - x176) + 150.565522268974*b138 =L= 151.565522268974;
e203.. sqr(5.17568572881879 - x172) + sqr(2.02627806544288 - x174) + sqr(
9.2740633418688 - x176) + 163.973027168021*b139 =L= 164.973027168021;
e204.. sqr(9.11874181180651 - x172) + sqr(9.07966816070985 - x174) + sqr(
1.64995049320116 - x176) + 161.969348685106*b140 =L= 162.969348685106;
e205.. sqr(8.26392769674786 - x172) + sqr(4.29716878332203 - x174) + sqr(
3.06511979366618 - x176) + 98.8575703440414*b141 =L= 99.8575703440414;
e206.. sqr(2.95522257480442 - x172) + sqr(1.29725120442498 - x174) + sqr(
0.799527585103169 - x176) + 147.501061227256*b142 =L= 148.501061227256;
e207.. sqr(5.59281220526297 - x172) + sqr(5.08387949672858 - x174) + sqr(
0.547463810150197 - x176) + 109.493435167956*b143 =L= 110.493435167956;
e208.. sqr(5.5713321706538 - x172) + sqr(3.89813512317444 - x174) + sqr(
0.378899938163517 - x176) + 123.353905785717*b144 =L= 124.353905785717;
e209.. sqr(1.47483805835463 - x172) + sqr(0.989752492299246 - x174) + sqr(
5.36717263813865 - x176) + 161.162335824934*b145 =L= 162.162335824934;
e210.. sqr(4.61507078501251 - x172) + sqr(0.234707301612243 - x174) + sqr(
3.97342857514894 - x176) + 124.302670822369*b146 =L= 125.302670822369;
e211.. sqr(9.15405801517484 - x172) + sqr(4.26169733166395 - x174) + sqr(
4.89911772871142 - x176) + 116.160211358947*b147 =L= 117.160211358947;
e212.. sqr(6.23408727244271 - x172) + sqr(0.755925845511098 - x174) + sqr(
5.40595672236618 - x176) + 134.909618001418*b148 =L= 135.909618001418;
e213.. sqr(5.16744991507397 - x172) + sqr(5.25535097293888 - x174) + sqr(
3.81062986996748 - x176) + 54.9767406737741*b149 =L= 55.9767406737741;
e214.. sqr(7.23609076996082 - x172) + sqr(3.30048962157922 - x174) + sqr(
8.05002431260521 - x176) + 143.305588261876*b150 =L= 144.305588261876;
e215.. b121 + b122 + b123 + b124 + b125 + b126 + b127 + b128 + b129 + b130
+ b131 + b132 + b133 + b134 + b135 + b136 + b137 + b138 + b139 + b140
+ b141 + b142 + b143 + b144 + b145 + b146 + b147 + b148 + b149 + b150
=E= 1;
e216.. b1 + b31 + b61 + b91 + b121 =L= 1;
e217.. b2 + b32 + b62 + b92 + b122 =L= 1;
e218.. b3 + b33 + b63 + b93 + b123 =L= 1;
e219.. b4 + b34 + b64 + b94 + b124 =L= 1;
e220.. b5 + b35 + b65 + b95 + b125 =L= 1;
e221.. b6 + b36 + b66 + b96 + b126 =L= 1;
e222.. b7 + b37 + b67 + b97 + b127 =L= 1;
e223.. b8 + b38 + b68 + b98 + b128 =L= 1;
e224.. b9 + b39 + b69 + b99 + b129 =L= 1;
e225.. b10 + b40 + b70 + b100 + b130 =L= 1;
e226.. b11 + b41 + b71 + b101 + b131 =L= 1;
e227.. b12 + b42 + b72 + b102 + b132 =L= 1;
e228.. b13 + b43 + b73 + b103 + b133 =L= 1;
e229.. b14 + b44 + b74 + b104 + b134 =L= 1;
e230.. b15 + b45 + b75 + b105 + b135 =L= 1;
e231.. b16 + b46 + b76 + b106 + b136 =L= 1;
e232.. b17 + b47 + b77 + b107 + b137 =L= 1;
e233.. b18 + b48 + b78 + b108 + b138 =L= 1;
e234.. b19 + b49 + b79 + b109 + b139 =L= 1;
e235.. b20 + b50 + b80 + b110 + b140 =L= 1;
e236.. b21 + b51 + b81 + b111 + b141 =L= 1;
e237.. b22 + b52 + b82 + b112 + b142 =L= 1;
e238.. b23 + b53 + b83 + b113 + b143 =L= 1;
e239.. b24 + b54 + b84 + b114 + b144 =L= 1;
e240.. b25 + b55 + b85 + b115 + b145 =L= 1;
e241.. b26 + b56 + b86 + b116 + b146 =L= 1;
e242.. b27 + b57 + b87 + b117 + b147 =L= 1;
e243.. b28 + b58 + b88 + b118 + b148 =L= 1;
e244.. b29 + b59 + b89 + b119 + b149 =L= 1;
e245.. b30 + b60 + b90 + b120 + b150 =L= 1;
e246.. x151 - x152 =L= 0;
e247.. x152 - x160 =L= 0;
e248.. x160 - x166 =L= 0;
e249.. x166 - x172 =L= 0;
e250.. - x153 - x156 - x159 - x161 - x163 - x165 - x167 - x169 - x171 - x173
- x175 - x177 - x178 - x179 - x180 - x181 - x182 - x183 - x184 - x185
- x186 - x187 - x188 - x189 - x190 - x191 - x192 - x193 - x194 - x195
+ objvar =E= 0;
* set non-default bounds
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;
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