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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)
8.21829037 p1 ( gdx sol )
(infeas: 6e-16)
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 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
*        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: 2022-04-26 Git hash: de668763
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