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Instance p_ball_10b_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 10 balls with radius one.
This is a big-M formulation.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
44.00421681 p1 ( gdx sol )
(infeas: 4e-16)
Other points (infeas > 1e-08)  
Dual Bounds
44.00150856 (ALPHAECP)
44.00412070 (ANTIGONE)
44.00420628 (BARON)
44.00421667 (BONMIN)
44.00415948 (COUENNE)
44.00421679 (CPLEX)
44.00416942 (GUROBI)
44.00421681 (LINDO)
44.00421408 (SCIP)
44.00421681 (SHOT)
References Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020.
Source p_ball_10b_5p_3d.gms, contributed by Jan Kronqvist and Ruth Misener
Application Geometry
Added to library 26 Aug 2020
Problem type MBQCP
#Variables 95
#Binary Variables 50
#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 129
#Linear Constraints 79
#Quadratic Constraints 50
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 488
#Nonlinear Nonzeros in Jacobian 150
#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 5.0668e-01
Maximal coefficient 1.5258e+02
Infeasibility of initial point 57.28
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
*        130        6        0      124        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         96       46       50        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        519      369      150        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,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
          ,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
          ,x88,x89,x90,x91,x92,x93,x94,x95,objvar;

Positive Variables  x51,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64
          ,x65,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81
          ,x82,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95;

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;

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;


e1..    x51 - x52 - x53 =L= 0;

e2..  - x51 + x52 - x53 =L= 0;

e3..    x54 - x55 - x56 =L= 0;

e4..  - x54 + x55 - x56 =L= 0;

e5..    x57 - x58 - x59 =L= 0;

e6..  - x57 + x58 - x59 =L= 0;

e7..    x51 - x60 - x61 =L= 0;

e8..  - x51 + x60 - x61 =L= 0;

e9..    x54 - x62 - x63 =L= 0;

e10..  - x54 + x62 - x63 =L= 0;

e11..    x57 - x64 - x65 =L= 0;

e12..  - x57 + x64 - x65 =L= 0;

e13..    x51 - x66 - x67 =L= 0;

e14..  - x51 + x66 - x67 =L= 0;

e15..    x54 - x68 - x69 =L= 0;

e16..  - x54 + x68 - x69 =L= 0;

e17..    x57 - x70 - x71 =L= 0;

e18..  - x57 + x70 - x71 =L= 0;

e19..    x51 - x72 - x73 =L= 0;

e20..  - x51 + x72 - x73 =L= 0;

e21..    x54 - x74 - x75 =L= 0;

e22..  - x54 + x74 - x75 =L= 0;

e23..    x57 - x76 - x77 =L= 0;

e24..  - x57 + x76 - x77 =L= 0;

e25..    x52 - x60 - x78 =L= 0;

e26..  - x52 + x60 - x78 =L= 0;

e27..    x55 - x62 - x79 =L= 0;

e28..  - x55 + x62 - x79 =L= 0;

e29..    x58 - x64 - x80 =L= 0;

e30..  - x58 + x64 - x80 =L= 0;

e31..    x52 - x66 - x81 =L= 0;

e32..  - x52 + x66 - x81 =L= 0;

e33..    x55 - x68 - x82 =L= 0;

e34..  - x55 + x68 - x82 =L= 0;

e35..    x58 - x70 - x83 =L= 0;

e36..  - x58 + x70 - x83 =L= 0;

e37..    x52 - x72 - x84 =L= 0;

e38..  - x52 + x72 - x84 =L= 0;

e39..    x55 - x74 - x85 =L= 0;

e40..  - x55 + x74 - x85 =L= 0;

e41..    x58 - x76 - x86 =L= 0;

e42..  - x58 + x76 - x86 =L= 0;

e43..    x60 - x66 - x87 =L= 0;

e44..  - x60 + x66 - x87 =L= 0;

e45..    x62 - x68 - x88 =L= 0;

e46..  - x62 + x68 - x88 =L= 0;

e47..    x64 - x70 - x89 =L= 0;

e48..  - x64 + x70 - x89 =L= 0;

e49..    x60 - x72 - x90 =L= 0;

e50..  - x60 + x72 - x90 =L= 0;

e51..    x62 - x74 - x91 =L= 0;

e52..  - x62 + x74 - x91 =L= 0;

e53..    x64 - x76 - x92 =L= 0;

e54..  - x64 + x76 - x92 =L= 0;

e55..    x66 - x72 - x93 =L= 0;

e56..  - x66 + x72 - x93 =L= 0;

e57..    x68 - x74 - x94 =L= 0;

e58..  - x68 + x74 - x94 =L= 0;

e59..    x70 - x76 - x95 =L= 0;

e60..  - x70 + x76 - x95 =L= 0;

e61.. sqr(3.55441530772447 - x51) + sqr(2.6588399811956 - x54) + sqr(
      5.16713392802669 - x57) + 128.415159268527*b1 =L= 129.415159268527;

e62.. sqr(8.82094045941646 - x51) + sqr(9.51816335093057 - x54) + sqr(
      0.894770759747333 - x57) + 136.27463320812*b2 =L= 137.27463320812;

e63.. sqr(6.86229591973038 - x51) + sqr(4.74665709736901 - x54) + sqr(
      1.14651582775383 - x57) + 79.4930138069821*b3 =L= 80.4930138069821;

e64.. sqr(7.13880287505566 - x51) + sqr(0.923639199248324 - x54) + sqr(
      5.06906794010293 - x57) + 124.602073729487*b4 =L= 125.602073729487;

e65.. sqr(9.54873475130122 - x51) + sqr(9.730708594994 - x54) + sqr(
      0.506682101270036 - x57) + 152.575845479968*b5 =L= 153.575845479968;

e66.. sqr(2.60295575976191 - x51) + sqr(9.60525309364094 - x54) + sqr(
      5.33059723504087 - x57) + 115.609943222472*b6 =L= 116.609943222472;

e67.. sqr(8.7489239697277 - x51) + sqr(6.42418905563567 - x54) + sqr(
      6.53764526999883 - x57) + 102.276439512632*b7 =L= 103.276439512632;

e68.. sqr(2.98069751112782 - x51) + sqr(1.4913715136506 - x54) + sqr(
      2.04987567063475 - x57) + 134.705801750617*b8 =L= 135.705801750617;

e69.. sqr(1.65791995565741 - x51) + sqr(6.17322651944292 - x54) + sqr(
      7.01412219987569 - x57) + 138.925429422844*b9 =L= 139.925429422844;

e70.. sqr(2.41953526971379 - x51) + sqr(1.09500973629707 - x54) + sqr(
      2.60189595048839 - x57) + 152.575845479968*b10 =L= 153.575845479968;

e71..    b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 =E= 1;

e72.. sqr(3.55441530772447 - x52) + sqr(2.6588399811956 - x55) + sqr(
      5.16713392802669 - x58) + 128.415159268527*b11 =L= 129.415159268527;

e73.. sqr(8.82094045941646 - x52) + sqr(9.51816335093057 - x55) + sqr(
      0.894770759747333 - x58) + 136.27463320812*b12 =L= 137.27463320812;

e74.. sqr(6.86229591973038 - x52) + sqr(4.74665709736901 - x55) + sqr(
      1.14651582775383 - x58) + 79.4930138069821*b13 =L= 80.4930138069821;

e75.. sqr(7.13880287505566 - x52) + sqr(0.923639199248324 - x55) + sqr(
      5.06906794010293 - x58) + 124.602073729487*b14 =L= 125.602073729487;

e76.. sqr(9.54873475130122 - x52) + sqr(9.730708594994 - x55) + sqr(
      0.506682101270036 - x58) + 152.575845479968*b15 =L= 153.575845479968;

e77.. sqr(2.60295575976191 - x52) + sqr(9.60525309364094 - x55) + sqr(
      5.33059723504087 - x58) + 115.609943222472*b16 =L= 116.609943222472;

e78.. sqr(8.7489239697277 - x52) + sqr(6.42418905563567 - x55) + sqr(
      6.53764526999883 - x58) + 102.276439512632*b17 =L= 103.276439512632;

e79.. sqr(2.98069751112782 - x52) + sqr(1.4913715136506 - x55) + sqr(
      2.04987567063475 - x58) + 134.705801750617*b18 =L= 135.705801750617;

e80.. sqr(1.65791995565741 - x52) + sqr(6.17322651944292 - x55) + sqr(
      7.01412219987569 - x58) + 138.925429422844*b19 =L= 139.925429422844;

e81.. sqr(2.41953526971379 - x52) + sqr(1.09500973629707 - x55) + sqr(
      2.60189595048839 - x58) + 152.575845479968*b20 =L= 153.575845479968;

e82..    b11 + b12 + b13 + b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;

e83.. sqr(3.55441530772447 - x60) + sqr(2.6588399811956 - x62) + sqr(
      5.16713392802669 - x64) + 128.415159268527*b21 =L= 129.415159268527;

e84.. sqr(8.82094045941646 - x60) + sqr(9.51816335093057 - x62) + sqr(
      0.894770759747333 - x64) + 136.27463320812*b22 =L= 137.27463320812;

e85.. sqr(6.86229591973038 - x60) + sqr(4.74665709736901 - x62) + sqr(
      1.14651582775383 - x64) + 79.4930138069821*b23 =L= 80.4930138069821;

e86.. sqr(7.13880287505566 - x60) + sqr(0.923639199248324 - x62) + sqr(
      5.06906794010293 - x64) + 124.602073729487*b24 =L= 125.602073729487;

e87.. sqr(9.54873475130122 - x60) + sqr(9.730708594994 - x62) + sqr(
      0.506682101270036 - x64) + 152.575845479968*b25 =L= 153.575845479968;

e88.. sqr(2.60295575976191 - x60) + sqr(9.60525309364094 - x62) + sqr(
      5.33059723504087 - x64) + 115.609943222472*b26 =L= 116.609943222472;

e89.. sqr(8.7489239697277 - x60) + sqr(6.42418905563567 - x62) + sqr(
      6.53764526999883 - x64) + 102.276439512632*b27 =L= 103.276439512632;

e90.. sqr(2.98069751112782 - x60) + sqr(1.4913715136506 - x62) + sqr(
      2.04987567063475 - x64) + 134.705801750617*b28 =L= 135.705801750617;

e91.. sqr(1.65791995565741 - x60) + sqr(6.17322651944292 - x62) + sqr(
      7.01412219987569 - x64) + 138.925429422844*b29 =L= 139.925429422844;

e92.. sqr(2.41953526971379 - x60) + sqr(1.09500973629707 - x62) + sqr(
      2.60189595048839 - x64) + 152.575845479968*b30 =L= 153.575845479968;

e93..    b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 =E= 1;

e94.. sqr(3.55441530772447 - x66) + sqr(2.6588399811956 - x68) + sqr(
      5.16713392802669 - x70) + 128.415159268527*b31 =L= 129.415159268527;

e95.. sqr(8.82094045941646 - x66) + sqr(9.51816335093057 - x68) + sqr(
      0.894770759747333 - x70) + 136.27463320812*b32 =L= 137.27463320812;

e96.. sqr(6.86229591973038 - x66) + sqr(4.74665709736901 - x68) + sqr(
      1.14651582775383 - x70) + 79.4930138069821*b33 =L= 80.4930138069821;

e97.. sqr(7.13880287505566 - x66) + sqr(0.923639199248324 - x68) + sqr(
      5.06906794010293 - x70) + 124.602073729487*b34 =L= 125.602073729487;

e98.. sqr(9.54873475130122 - x66) + sqr(9.730708594994 - x68) + sqr(
      0.506682101270036 - x70) + 152.575845479968*b35 =L= 153.575845479968;

e99.. sqr(2.60295575976191 - x66) + sqr(9.60525309364094 - x68) + sqr(
      5.33059723504087 - x70) + 115.609943222472*b36 =L= 116.609943222472;

e100.. sqr(8.7489239697277 - x66) + sqr(6.42418905563567 - x68) + sqr(
       6.53764526999883 - x70) + 102.276439512632*b37 =L= 103.276439512632;

e101.. sqr(2.98069751112782 - x66) + sqr(1.4913715136506 - x68) + sqr(
       2.04987567063475 - x70) + 134.705801750617*b38 =L= 135.705801750617;

e102.. sqr(1.65791995565741 - x66) + sqr(6.17322651944292 - x68) + sqr(
       7.01412219987569 - x70) + 138.925429422844*b39 =L= 139.925429422844;

e103.. sqr(2.41953526971379 - x66) + sqr(1.09500973629707 - x68) + sqr(
       2.60189595048839 - x70) + 152.575845479968*b40 =L= 153.575845479968;

e104..    b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;

e105.. sqr(3.55441530772447 - x72) + sqr(2.6588399811956 - x74) + sqr(
       5.16713392802669 - x76) + 128.415159268527*b41 =L= 129.415159268527;

e106.. sqr(8.82094045941646 - x72) + sqr(9.51816335093057 - x74) + sqr(
       0.894770759747333 - x76) + 136.27463320812*b42 =L= 137.27463320812;

e107.. sqr(6.86229591973038 - x72) + sqr(4.74665709736901 - x74) + sqr(
       1.14651582775383 - x76) + 79.4930138069821*b43 =L= 80.4930138069821;

e108.. sqr(7.13880287505566 - x72) + sqr(0.923639199248324 - x74) + sqr(
       5.06906794010293 - x76) + 124.602073729487*b44 =L= 125.602073729487;

e109.. sqr(9.54873475130122 - x72) + sqr(9.730708594994 - x74) + sqr(
       0.506682101270036 - x76) + 152.575845479968*b45 =L= 153.575845479968;

e110.. sqr(2.60295575976191 - x72) + sqr(9.60525309364094 - x74) + sqr(
       5.33059723504087 - x76) + 115.609943222472*b46 =L= 116.609943222472;

e111.. sqr(8.7489239697277 - x72) + sqr(6.42418905563567 - x74) + sqr(
       6.53764526999883 - x76) + 102.276439512632*b47 =L= 103.276439512632;

e112.. sqr(2.98069751112782 - x72) + sqr(1.4913715136506 - x74) + sqr(
       2.04987567063475 - x76) + 134.705801750617*b48 =L= 135.705801750617;

e113.. sqr(1.65791995565741 - x72) + sqr(6.17322651944292 - x74) + sqr(
       7.01412219987569 - x76) + 138.925429422844*b49 =L= 139.925429422844;

e114.. sqr(2.41953526971379 - x72) + sqr(1.09500973629707 - x74) + sqr(
       2.60189595048839 - x76) + 152.575845479968*b50 =L= 153.575845479968;

e115..    b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 =E= 1;

e116..    b1 + b11 + b21 + b31 + b41 =L= 1;

e117..    b2 + b12 + b22 + b32 + b42 =L= 1;

e118..    b3 + b13 + b23 + b33 + b43 =L= 1;

e119..    b4 + b14 + b24 + b34 + b44 =L= 1;

e120..    b5 + b15 + b25 + b35 + b45 =L= 1;

e121..    b6 + b16 + b26 + b36 + b46 =L= 1;

e122..    b7 + b17 + b27 + b37 + b47 =L= 1;

e123..    b8 + b18 + b28 + b38 + b48 =L= 1;

e124..    b9 + b19 + b29 + b39 + b49 =L= 1;

e125..    b10 + b20 + b30 + b40 + b50 =L= 1;

e126..    x51 - x52 =L= 0;

e127..    x52 - x60 =L= 0;

e128..    x60 - x66 =L= 0;

e129..    x66 - x72 =L= 0;

e130..  - x53 - x56 - x59 - x61 - x63 - x65 - x67 - x69 - x71 - x73 - x75 - x77
        - x78 - x79 - x80 - x81 - x82 - x83 - x84 - x85 - x86 - x87 - x88 - x89
        - x90 - x91 - x92 - x93 - x94 - x95 + objvar =E= 0;

* set non-default bounds
x51.up = 10;
x52.up = 10;
x53.up = 10;
x54.up = 10;
x55.up = 10;
x56.up = 10;
x57.up = 10;
x58.up = 10;
x59.up = 10;
x60.up = 10;
x61.up = 10;
x62.up = 10;
x63.up = 10;
x64.up = 10;
x65.up = 10;
x66.up = 10;
x67.up = 10;
x68.up = 10;
x69.up = 10;
x70.up = 10;
x71.up = 10;
x72.up = 10;
x73.up = 10;
x74.up = 10;
x75.up = 10;
x76.up = 10;
x77.up = 10;
x78.up = 10;
x79.up = 10;
x80.up = 10;
x81.up = 10;
x82.up = 10;
x83.up = 10;
x84.up = 10;
x85.up = 10;
x86.up = 10;
x87.up = 10;
x88.up = 10;
x89.up = 10;
x90.up = 10;
x91.up = 10;
x92.up = 10;
x93.up = 10;
x94.up = 10;
x95.up = 10;

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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