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Instance p_ball_20b_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 20 balls with radius one.
This is a big-M formulation.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
19.73646908 p1 ( gdx sol )
(infeas: 9e-16)
Other points (infeas > 1e-08)  
Dual Bounds
11.14081810 (ALPHAECP)
19.73643721 (ANTIGONE)
19.73646889 (BARON)
19.73645256 (COUENNE)
19.73646908 (CPLEX)
19.73617775 (GUROBI)
19.73646908 (LINDO)
19.73646717 (SCIP)
19.73646488 (SHOT)
References Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020.
Source p_ball_20b_5p_3d.gms, contributed by Jan Kronqvist and Ruth Misener
Application Geometry
Added to library 26 Aug 2020
Problem type MBQCP
#Variables 145
#Binary Variables 100
#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 189
#Linear Constraints 89
#Quadratic Constraints 100
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 788
#Nonlinear Nonzeros in Jacobian 300
#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 9.6649e-02
Maximal coefficient 1.8890e+02
Infeasibility of initial point 65.41
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
*        190        6        0      184        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        146       46      100        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        819      519      300        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,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,objvar;

Positive Variables  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;

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;

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;


e1..    x101 - x102 - x103 =L= 0;

e2..  - x101 + x102 - x103 =L= 0;

e3..    x104 - x105 - x106 =L= 0;

e4..  - x104 + x105 - x106 =L= 0;

e5..    x107 - x108 - x109 =L= 0;

e6..  - x107 + x108 - x109 =L= 0;

e7..    x101 - x110 - x111 =L= 0;

e8..  - x101 + x110 - x111 =L= 0;

e9..    x104 - x112 - x113 =L= 0;

e10..  - x104 + x112 - x113 =L= 0;

e11..    x107 - x114 - x115 =L= 0;

e12..  - x107 + x114 - x115 =L= 0;

e13..    x101 - x116 - x117 =L= 0;

e14..  - x101 + x116 - x117 =L= 0;

e15..    x104 - x118 - x119 =L= 0;

e16..  - x104 + x118 - x119 =L= 0;

e17..    x107 - x120 - x121 =L= 0;

e18..  - x107 + x120 - x121 =L= 0;

e19..    x101 - x122 - x123 =L= 0;

e20..  - x101 + x122 - x123 =L= 0;

e21..    x104 - x124 - x125 =L= 0;

e22..  - x104 + x124 - x125 =L= 0;

e23..    x107 - x126 - x127 =L= 0;

e24..  - x107 + x126 - x127 =L= 0;

e25..    x102 - x110 - x128 =L= 0;

e26..  - x102 + x110 - x128 =L= 0;

e27..    x105 - x112 - x129 =L= 0;

e28..  - x105 + x112 - x129 =L= 0;

e29..    x108 - x114 - x130 =L= 0;

e30..  - x108 + x114 - x130 =L= 0;

e31..    x102 - x116 - x131 =L= 0;

e32..  - x102 + x116 - x131 =L= 0;

e33..    x105 - x118 - x132 =L= 0;

e34..  - x105 + x118 - x132 =L= 0;

e35..    x108 - x120 - x133 =L= 0;

e36..  - x108 + x120 - x133 =L= 0;

e37..    x102 - x122 - x134 =L= 0;

e38..  - x102 + x122 - x134 =L= 0;

e39..    x105 - x124 - x135 =L= 0;

e40..  - x105 + x124 - x135 =L= 0;

e41..    x108 - x126 - x136 =L= 0;

e42..  - x108 + x126 - x136 =L= 0;

e43..    x110 - x116 - x137 =L= 0;

e44..  - x110 + x116 - x137 =L= 0;

e45..    x112 - x118 - x138 =L= 0;

e46..  - x112 + x118 - x138 =L= 0;

e47..    x114 - x120 - x139 =L= 0;

e48..  - x114 + x120 - x139 =L= 0;

e49..    x110 - x122 - x140 =L= 0;

e50..  - x110 + x122 - x140 =L= 0;

e51..    x112 - x124 - x141 =L= 0;

e52..  - x112 + x124 - x141 =L= 0;

e53..    x114 - x126 - x142 =L= 0;

e54..  - x114 + x126 - x142 =L= 0;

e55..    x116 - x122 - x143 =L= 0;

e56..  - x116 + x122 - x143 =L= 0;

e57..    x118 - x124 - x144 =L= 0;

e58..  - x118 + x124 - x144 =L= 0;

e59..    x120 - x126 - x145 =L= 0;

e60..  - x120 + x126 - x145 =L= 0;

e61.. sqr(0.483311857356823 - x101) + sqr(0.114242198506904 - x104) + sqr(
      7.12048883659032 - x107) + 188.522461227626*b1 =L= 189.522461227626;

e62.. sqr(5.2590135790233 - x101) + sqr(7.33259189570392 - x104) + sqr(
      5.312333476343 - x107) + 98.8166159288294*b2 =L= 99.8166159288294;

e63.. sqr(7.41517046461879 - x101) + sqr(9.62332773098117 - x104) + sqr(
      4.79943898486809 - x107) + 167.849028003939*b3 =L= 168.849028003939;

e64.. sqr(6.671843981803 - x101) + sqr(8.10658123259484 - x104) + sqr(
      8.43381689055527 - x107) + 144.62434214578*b4 =L= 145.62434214578;

e65.. sqr(9.05870575338678 - x101) + sqr(8.3311941216586 - x104) + sqr(
      2.43718333261179 - x107) + 188.522461227626*b5 =L= 189.522461227626;

e66.. sqr(2.45247392282192 - x101) + sqr(3.04490781414335 - x104) + sqr(
      3.74797873360784 - x107) + 119.618424440661*b6 =L= 120.618424440661;

e67.. sqr(3.17249885664207 - x101) + sqr(0.899014640298569 - x104) + sqr(
      6.53554769882638 - x107) + 128.282312211875*b7 =L= 129.282312211875;

e68.. sqr(7.19140474364188 - x101) + sqr(6.78752778006733 - x104) + sqr(
      7.10371917668867 - x107) + 108.45575250014*b8 =L= 109.45575250014;

e69.. sqr(0.581905599074722 - x101) + sqr(8.05664566308502 - x104) + sqr(
      0.465270839540525 - x107) + 163.557092366753*b9 =L= 164.557092366753;

e70.. sqr(2.89314656575976 - x101) + sqr(2.98350648433744 - x104) + sqr(
      4.94095686412664 - x107) + 101.809153524392*b10 =L= 102.809153524392;

e71.. sqr(2.18223181481477 - x101) + sqr(6.36734447251869 - x104) + sqr(
      6.99053555821422 - x107) + 135.200072571286*b11 =L= 136.200072571286;

e72.. sqr(8.39213303571845 - x101) + sqr(0.0966493493157039 - x104) + sqr(
      0.992650538147096 - x107) + 168.474583620344*b12 =L= 169.474583620344;

e73.. sqr(6.8673656213906 - x101) + sqr(8.47463209326542 - x104) + sqr(
      0.494039939513553 - x107) + 188.895677706624*b13 =L= 189.895677706624;

e74.. sqr(2.07334522686175 - x101) + sqr(0.611759422337085 - x104) + sqr(
      7.49872182399417 - x107) + 157.156134140441*b14 =L= 158.156134140441;

e75.. sqr(5.58287553353321 - x101) + sqr(7.41023187669618 - x104) + sqr(
      5.78186220125907 - x107) + 102.681819435286*b15 =L= 103.681819435286;

e76.. sqr(3.75663662491927 - x101) + sqr(2.16100057183036 - x104) + sqr(
      9.4954261517135 - x107) + 153.416411666872*b16 =L= 154.416411666872;

e77.. sqr(4.04360404243071 - x101) + sqr(7.5903513366217 - x104) + sqr(
      3.71685851137678 - x107) + 100.651007858618*b17 =L= 101.651007858618;

e78.. sqr(1.45072437530262 - x101) + sqr(1.11420059440894 - x104) + sqr(
      9.42819884441584 - x107) + 188.895677706624*b18 =L= 189.895677706624;

e79.. sqr(8.44626629441698 - x101) + sqr(8.81210793727421 - x104) + sqr(
      9.26767041565757 - x107) + 168.474583620344*b19 =L= 169.474583620344;

e80.. sqr(4.74415255019913 - x101) + sqr(2.8194183128037 - x104) + sqr(
      1.76655535189797 - x107) + 126.464760843581*b20 =L= 127.464760843581;

e81..    b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 + b11 + b12 + b13
       + b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;

e82.. sqr(0.483311857356823 - x102) + sqr(0.114242198506904 - x105) + sqr(
      7.12048883659032 - x108) + 188.522461227626*b21 =L= 189.522461227626;

e83.. sqr(5.2590135790233 - x102) + sqr(7.33259189570392 - x105) + sqr(
      5.312333476343 - x108) + 98.8166159288294*b22 =L= 99.8166159288294;

e84.. sqr(7.41517046461879 - x102) + sqr(9.62332773098117 - x105) + sqr(
      4.79943898486809 - x108) + 167.849028003939*b23 =L= 168.849028003939;

e85.. sqr(6.671843981803 - x102) + sqr(8.10658123259484 - x105) + sqr(
      8.43381689055527 - x108) + 144.62434214578*b24 =L= 145.62434214578;

e86.. sqr(9.05870575338678 - x102) + sqr(8.3311941216586 - x105) + sqr(
      2.43718333261179 - x108) + 188.522461227626*b25 =L= 189.522461227626;

e87.. sqr(2.45247392282192 - x102) + sqr(3.04490781414335 - x105) + sqr(
      3.74797873360784 - x108) + 119.618424440661*b26 =L= 120.618424440661;

e88.. sqr(3.17249885664207 - x102) + sqr(0.899014640298569 - x105) + sqr(
      6.53554769882638 - x108) + 128.282312211875*b27 =L= 129.282312211875;

e89.. sqr(7.19140474364188 - x102) + sqr(6.78752778006733 - x105) + sqr(
      7.10371917668867 - x108) + 108.45575250014*b28 =L= 109.45575250014;

e90.. sqr(0.581905599074722 - x102) + sqr(8.05664566308502 - x105) + sqr(
      0.465270839540525 - x108) + 163.557092366753*b29 =L= 164.557092366753;

e91.. sqr(2.89314656575976 - x102) + sqr(2.98350648433744 - x105) + sqr(
      4.94095686412664 - x108) + 101.809153524392*b30 =L= 102.809153524392;

e92.. sqr(2.18223181481477 - x102) + sqr(6.36734447251869 - x105) + sqr(
      6.99053555821422 - x108) + 135.200072571286*b31 =L= 136.200072571286;

e93.. sqr(8.39213303571845 - x102) + sqr(0.0966493493157039 - x105) + sqr(
      0.992650538147096 - x108) + 168.474583620344*b32 =L= 169.474583620344;

e94.. sqr(6.8673656213906 - x102) + sqr(8.47463209326542 - x105) + sqr(
      0.494039939513553 - x108) + 188.895677706624*b33 =L= 189.895677706624;

e95.. sqr(2.07334522686175 - x102) + sqr(0.611759422337085 - x105) + sqr(
      7.49872182399417 - x108) + 157.156134140441*b34 =L= 158.156134140441;

e96.. sqr(5.58287553353321 - x102) + sqr(7.41023187669618 - x105) + sqr(
      5.78186220125907 - x108) + 102.681819435286*b35 =L= 103.681819435286;

e97.. sqr(3.75663662491927 - x102) + sqr(2.16100057183036 - x105) + sqr(
      9.4954261517135 - x108) + 153.416411666872*b36 =L= 154.416411666872;

e98.. sqr(4.04360404243071 - x102) + sqr(7.5903513366217 - x105) + sqr(
      3.71685851137678 - x108) + 100.651007858618*b37 =L= 101.651007858618;

e99.. sqr(1.45072437530262 - x102) + sqr(1.11420059440894 - x105) + sqr(
      9.42819884441584 - x108) + 188.895677706624*b38 =L= 189.895677706624;

e100.. sqr(8.44626629441698 - x102) + sqr(8.81210793727421 - x105) + sqr(
       9.26767041565757 - x108) + 168.474583620344*b39 =L= 169.474583620344;

e101.. sqr(4.74415255019913 - x102) + sqr(2.8194183128037 - x105) + sqr(
       1.76655535189797 - x108) + 126.464760843581*b40 =L= 127.464760843581;

e102..    b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32
        + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;

e103.. sqr(0.483311857356823 - x110) + sqr(0.114242198506904 - x112) + sqr(
       7.12048883659032 - x114) + 188.522461227626*b41 =L= 189.522461227626;

e104.. sqr(5.2590135790233 - x110) + sqr(7.33259189570392 - x112) + sqr(
       5.312333476343 - x114) + 98.8166159288294*b42 =L= 99.8166159288294;

e105.. sqr(7.41517046461879 - x110) + sqr(9.62332773098117 - x112) + sqr(
       4.79943898486809 - x114) + 167.849028003939*b43 =L= 168.849028003939;

e106.. sqr(6.671843981803 - x110) + sqr(8.10658123259484 - x112) + sqr(
       8.43381689055527 - x114) + 144.62434214578*b44 =L= 145.62434214578;

e107.. sqr(9.05870575338678 - x110) + sqr(8.3311941216586 - x112) + sqr(
       2.43718333261179 - x114) + 188.522461227626*b45 =L= 189.522461227626;

e108.. sqr(2.45247392282192 - x110) + sqr(3.04490781414335 - x112) + sqr(
       3.74797873360784 - x114) + 119.618424440661*b46 =L= 120.618424440661;

e109.. sqr(3.17249885664207 - x110) + sqr(0.899014640298569 - x112) + sqr(
       6.53554769882638 - x114) + 128.282312211875*b47 =L= 129.282312211875;

e110.. sqr(7.19140474364188 - x110) + sqr(6.78752778006733 - x112) + sqr(
       7.10371917668867 - x114) + 108.45575250014*b48 =L= 109.45575250014;

e111.. sqr(0.581905599074722 - x110) + sqr(8.05664566308502 - x112) + sqr(
       0.465270839540525 - x114) + 163.557092366753*b49 =L= 164.557092366753;

e112.. sqr(2.89314656575976 - x110) + sqr(2.98350648433744 - x112) + sqr(
       4.94095686412664 - x114) + 101.809153524392*b50 =L= 102.809153524392;

e113.. sqr(2.18223181481477 - x110) + sqr(6.36734447251869 - x112) + sqr(
       6.99053555821422 - x114) + 135.200072571286*b51 =L= 136.200072571286;

e114.. sqr(8.39213303571845 - x110) + sqr(0.0966493493157039 - x112) + sqr(
       0.992650538147096 - x114) + 168.474583620344*b52 =L= 169.474583620344;

e115.. sqr(6.8673656213906 - x110) + sqr(8.47463209326542 - x112) + sqr(
       0.494039939513553 - x114) + 188.895677706624*b53 =L= 189.895677706624;

e116.. sqr(2.07334522686175 - x110) + sqr(0.611759422337085 - x112) + sqr(
       7.49872182399417 - x114) + 157.156134140441*b54 =L= 158.156134140441;

e117.. sqr(5.58287553353321 - x110) + sqr(7.41023187669618 - x112) + sqr(
       5.78186220125907 - x114) + 102.681819435286*b55 =L= 103.681819435286;

e118.. sqr(3.75663662491927 - x110) + sqr(2.16100057183036 - x112) + sqr(
       9.4954261517135 - x114) + 153.416411666872*b56 =L= 154.416411666872;

e119.. sqr(4.04360404243071 - x110) + sqr(7.5903513366217 - x112) + sqr(
       3.71685851137678 - x114) + 100.651007858618*b57 =L= 101.651007858618;

e120.. sqr(1.45072437530262 - x110) + sqr(1.11420059440894 - x112) + sqr(
       9.42819884441584 - x114) + 188.895677706624*b58 =L= 189.895677706624;

e121.. sqr(8.44626629441698 - x110) + sqr(8.81210793727421 - x112) + sqr(
       9.26767041565757 - x114) + 168.474583620344*b59 =L= 169.474583620344;

e122.. sqr(4.74415255019913 - x110) + sqr(2.8194183128037 - x112) + sqr(
       1.76655535189797 - x114) + 126.464760843581*b60 =L= 127.464760843581;

e123..    b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 + b51 + b52
        + b53 + b54 + b55 + b56 + b57 + b58 + b59 + b60 =E= 1;

e124.. sqr(0.483311857356823 - x116) + sqr(0.114242198506904 - x118) + sqr(
       7.12048883659032 - x120) + 188.522461227626*b61 =L= 189.522461227626;

e125.. sqr(5.2590135790233 - x116) + sqr(7.33259189570392 - x118) + sqr(
       5.312333476343 - x120) + 98.8166159288294*b62 =L= 99.8166159288294;

e126.. sqr(7.41517046461879 - x116) + sqr(9.62332773098117 - x118) + sqr(
       4.79943898486809 - x120) + 167.849028003939*b63 =L= 168.849028003939;

e127.. sqr(6.671843981803 - x116) + sqr(8.10658123259484 - x118) + sqr(
       8.43381689055527 - x120) + 144.62434214578*b64 =L= 145.62434214578;

e128.. sqr(9.05870575338678 - x116) + sqr(8.3311941216586 - x118) + sqr(
       2.43718333261179 - x120) + 188.522461227626*b65 =L= 189.522461227626;

e129.. sqr(2.45247392282192 - x116) + sqr(3.04490781414335 - x118) + sqr(
       3.74797873360784 - x120) + 119.618424440661*b66 =L= 120.618424440661;

e130.. sqr(3.17249885664207 - x116) + sqr(0.899014640298569 - x118) + sqr(
       6.53554769882638 - x120) + 128.282312211875*b67 =L= 129.282312211875;

e131.. sqr(7.19140474364188 - x116) + sqr(6.78752778006733 - x118) + sqr(
       7.10371917668867 - x120) + 108.45575250014*b68 =L= 109.45575250014;

e132.. sqr(0.581905599074722 - x116) + sqr(8.05664566308502 - x118) + sqr(
       0.465270839540525 - x120) + 163.557092366753*b69 =L= 164.557092366753;

e133.. sqr(2.89314656575976 - x116) + sqr(2.98350648433744 - x118) + sqr(
       4.94095686412664 - x120) + 101.809153524392*b70 =L= 102.809153524392;

e134.. sqr(2.18223181481477 - x116) + sqr(6.36734447251869 - x118) + sqr(
       6.99053555821422 - x120) + 135.200072571286*b71 =L= 136.200072571286;

e135.. sqr(8.39213303571845 - x116) + sqr(0.0966493493157039 - x118) + sqr(
       0.992650538147096 - x120) + 168.474583620344*b72 =L= 169.474583620344;

e136.. sqr(6.8673656213906 - x116) + sqr(8.47463209326542 - x118) + sqr(
       0.494039939513553 - x120) + 188.895677706624*b73 =L= 189.895677706624;

e137.. sqr(2.07334522686175 - x116) + sqr(0.611759422337085 - x118) + sqr(
       7.49872182399417 - x120) + 157.156134140441*b74 =L= 158.156134140441;

e138.. sqr(5.58287553353321 - x116) + sqr(7.41023187669618 - x118) + sqr(
       5.78186220125907 - x120) + 102.681819435286*b75 =L= 103.681819435286;

e139.. sqr(3.75663662491927 - x116) + sqr(2.16100057183036 - x118) + sqr(
       9.4954261517135 - x120) + 153.416411666872*b76 =L= 154.416411666872;

e140.. sqr(4.04360404243071 - x116) + sqr(7.5903513366217 - x118) + sqr(
       3.71685851137678 - x120) + 100.651007858618*b77 =L= 101.651007858618;

e141.. sqr(1.45072437530262 - x116) + sqr(1.11420059440894 - x118) + sqr(
       9.42819884441584 - x120) + 188.895677706624*b78 =L= 189.895677706624;

e142.. sqr(8.44626629441698 - x116) + sqr(8.81210793727421 - x118) + sqr(
       9.26767041565757 - x120) + 168.474583620344*b79 =L= 169.474583620344;

e143.. sqr(4.74415255019913 - x116) + sqr(2.8194183128037 - x118) + sqr(
       1.76655535189797 - x120) + 126.464760843581*b80 =L= 127.464760843581;

e144..    b61 + b62 + b63 + b64 + b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72
        + b73 + b74 + b75 + b76 + b77 + b78 + b79 + b80 =E= 1;

e145.. sqr(0.483311857356823 - x122) + sqr(0.114242198506904 - x124) + sqr(
       7.12048883659032 - x126) + 188.522461227626*b81 =L= 189.522461227626;

e146.. sqr(5.2590135790233 - x122) + sqr(7.33259189570392 - x124) + sqr(
       5.312333476343 - x126) + 98.8166159288294*b82 =L= 99.8166159288294;

e147.. sqr(7.41517046461879 - x122) + sqr(9.62332773098117 - x124) + sqr(
       4.79943898486809 - x126) + 167.849028003939*b83 =L= 168.849028003939;

e148.. sqr(6.671843981803 - x122) + sqr(8.10658123259484 - x124) + sqr(
       8.43381689055527 - x126) + 144.62434214578*b84 =L= 145.62434214578;

e149.. sqr(9.05870575338678 - x122) + sqr(8.3311941216586 - x124) + sqr(
       2.43718333261179 - x126) + 188.522461227626*b85 =L= 189.522461227626;

e150.. sqr(2.45247392282192 - x122) + sqr(3.04490781414335 - x124) + sqr(
       3.74797873360784 - x126) + 119.618424440661*b86 =L= 120.618424440661;

e151.. sqr(3.17249885664207 - x122) + sqr(0.899014640298569 - x124) + sqr(
       6.53554769882638 - x126) + 128.282312211875*b87 =L= 129.282312211875;

e152.. sqr(7.19140474364188 - x122) + sqr(6.78752778006733 - x124) + sqr(
       7.10371917668867 - x126) + 108.45575250014*b88 =L= 109.45575250014;

e153.. sqr(0.581905599074722 - x122) + sqr(8.05664566308502 - x124) + sqr(
       0.465270839540525 - x126) + 163.557092366753*b89 =L= 164.557092366753;

e154.. sqr(2.89314656575976 - x122) + sqr(2.98350648433744 - x124) + sqr(
       4.94095686412664 - x126) + 101.809153524392*b90 =L= 102.809153524392;

e155.. sqr(2.18223181481477 - x122) + sqr(6.36734447251869 - x124) + sqr(
       6.99053555821422 - x126) + 135.200072571286*b91 =L= 136.200072571286;

e156.. sqr(8.39213303571845 - x122) + sqr(0.0966493493157039 - x124) + sqr(
       0.992650538147096 - x126) + 168.474583620344*b92 =L= 169.474583620344;

e157.. sqr(6.8673656213906 - x122) + sqr(8.47463209326542 - x124) + sqr(
       0.494039939513553 - x126) + 188.895677706624*b93 =L= 189.895677706624;

e158.. sqr(2.07334522686175 - x122) + sqr(0.611759422337085 - x124) + sqr(
       7.49872182399417 - x126) + 157.156134140441*b94 =L= 158.156134140441;

e159.. sqr(5.58287553353321 - x122) + sqr(7.41023187669618 - x124) + sqr(
       5.78186220125907 - x126) + 102.681819435286*b95 =L= 103.681819435286;

e160.. sqr(3.75663662491927 - x122) + sqr(2.16100057183036 - x124) + sqr(
       9.4954261517135 - x126) + 153.416411666872*b96 =L= 154.416411666872;

e161.. sqr(4.04360404243071 - x122) + sqr(7.5903513366217 - x124) + sqr(
       3.71685851137678 - x126) + 100.651007858618*b97 =L= 101.651007858618;

e162.. sqr(1.45072437530262 - x122) + sqr(1.11420059440894 - x124) + sqr(
       9.42819884441584 - x126) + 188.895677706624*b98 =L= 189.895677706624;

e163.. sqr(8.44626629441698 - x122) + sqr(8.81210793727421 - x124) + sqr(
       9.26767041565757 - x126) + 168.474583620344*b99 =L= 169.474583620344;

e164.. sqr(4.74415255019913 - x122) + sqr(2.8194183128037 - x124) + sqr(
       1.76655535189797 - x126) + 126.464760843581*b100 =L= 127.464760843581;

e165..    b81 + b82 + b83 + b84 + b85 + b86 + b87 + b88 + b89 + b90 + b91 + b92
        + b93 + b94 + b95 + b96 + b97 + b98 + b99 + b100 =E= 1;

e166..    b1 + b21 + b41 + b61 + b81 =L= 1;

e167..    b2 + b22 + b42 + b62 + b82 =L= 1;

e168..    b3 + b23 + b43 + b63 + b83 =L= 1;

e169..    b4 + b24 + b44 + b64 + b84 =L= 1;

e170..    b5 + b25 + b45 + b65 + b85 =L= 1;

e171..    b6 + b26 + b46 + b66 + b86 =L= 1;

e172..    b7 + b27 + b47 + b67 + b87 =L= 1;

e173..    b8 + b28 + b48 + b68 + b88 =L= 1;

e174..    b9 + b29 + b49 + b69 + b89 =L= 1;

e175..    b10 + b30 + b50 + b70 + b90 =L= 1;

e176..    b11 + b31 + b51 + b71 + b91 =L= 1;

e177..    b12 + b32 + b52 + b72 + b92 =L= 1;

e178..    b13 + b33 + b53 + b73 + b93 =L= 1;

e179..    b14 + b34 + b54 + b74 + b94 =L= 1;

e180..    b15 + b35 + b55 + b75 + b95 =L= 1;

e181..    b16 + b36 + b56 + b76 + b96 =L= 1;

e182..    b17 + b37 + b57 + b77 + b97 =L= 1;

e183..    b18 + b38 + b58 + b78 + b98 =L= 1;

e184..    b19 + b39 + b59 + b79 + b99 =L= 1;

e185..    b20 + b40 + b60 + b80 + b100 =L= 1;

e186..    x101 - x102 =L= 0;

e187..    x102 - x110 =L= 0;

e188..    x110 - x116 =L= 0;

e189..    x116 - x122 =L= 0;

e190..  - x103 - x106 - x109 - x111 - x113 - x115 - x117 - x119 - x121 - x123
        - x125 - x127 - x128 - x129 - x130 - x131 - x132 - x133 - x134 - x135
        - x136 - x137 - x138 - x139 - x140 - x141 - x142 - x143 - x144 - x145
        + objvar =E= 0;

* set non-default bounds
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;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2022-08-11 Git hash: f176bd52
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