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Instance p_ball_10b_5p_2d_m

Select 5-points in 2-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)
18.71857799 p1 ( gdx sol )
(infeas: 4e-10)
Other points (infeas > 1e-08)  
Dual Bounds
18.71737986 (ALPHAECP)
18.71848326 (ANTIGONE)
18.71857768 (BARON)
18.71857793 (BONMIN)
18.71855872 (COUENNE)
18.71857799 (CPLEX)
18.71854375 (GUROBI)
18.71857799 (LINDO)
18.71857511 (SCIP)
18.71857799 (SHOT)
References Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020.
Source p_ball_10b_5p_2d.gms, contributed by Jan Kronqvist and Ruth Misener
Application Geometry
Added to library 26 Aug 2020
Problem type MBQCP
#Variables 80
#Binary Variables 50
#Integer Variables 0
#Nonlinear Variables 10
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 0
#Constraints 109
#Linear Constraints 59
#Quadratic Constraints 50
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 378
#Nonlinear Nonzeros in Jacobian 100
#Nonzeros in (Upper-Left) Hessian of Lagrangian 10
#Nonzeros in Diagonal of Hessian of Lagrangian 10
#Blocks in Hessian of Lagrangian 10
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 3.8028e-01
Maximal coefficient 1.2038e+02
Infeasibility of initial point 7.83e-05
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
*        110        6        0      104        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         81       31       50        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        399      299      100        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,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;

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;


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..    x51 - x57 - x58 =L= 0;

e6..  - x51 + x57 - x58 =L= 0;

e7..    x54 - x59 - x60 =L= 0;

e8..  - x54 + x59 - x60 =L= 0;

e9..    x51 - x61 - x62 =L= 0;

e10..  - x51 + x61 - x62 =L= 0;

e11..    x54 - x63 - x64 =L= 0;

e12..  - x54 + x63 - x64 =L= 0;

e13..    x51 - x65 - x66 =L= 0;

e14..  - x51 + x65 - x66 =L= 0;

e15..    x54 - x67 - x68 =L= 0;

e16..  - x54 + x67 - x68 =L= 0;

e17..    x52 - x57 - x69 =L= 0;

e18..  - x52 + x57 - x69 =L= 0;

e19..    x55 - x59 - x70 =L= 0;

e20..  - x55 + x59 - x70 =L= 0;

e21..    x52 - x61 - x71 =L= 0;

e22..  - x52 + x61 - x71 =L= 0;

e23..    x55 - x63 - x72 =L= 0;

e24..  - x55 + x63 - x72 =L= 0;

e25..    x52 - x65 - x73 =L= 0;

e26..  - x52 + x65 - x73 =L= 0;

e27..    x55 - x67 - x74 =L= 0;

e28..  - x55 + x67 - x74 =L= 0;

e29..    x57 - x61 - x75 =L= 0;

e30..  - x57 + x61 - x75 =L= 0;

e31..    x59 - x63 - x76 =L= 0;

e32..  - x59 + x63 - x76 =L= 0;

e33..    x57 - x65 - x77 =L= 0;

e34..  - x57 + x65 - x77 =L= 0;

e35..    x59 - x67 - x78 =L= 0;

e36..  - x59 + x67 - x78 =L= 0;

e37..    x61 - x65 - x79 =L= 0;

e38..  - x61 + x65 - x79 =L= 0;

e39..    x63 - x67 - x80 =L= 0;

e40..  - x63 + x67 - x80 =L= 0;

e41.. sqr(0.648386267690458 - x51) + sqr(5.34198386756466 - x54)
       + 109.233018040634*b1 =L= 110.233018040634;

e42.. sqr(0.38028139143083 - x51) + sqr(4.79200736168083 - x54)
       + 108.933937361066*b2 =L= 109.933937361066;

e43.. sqr(4.59553989190787 - x51) + sqr(2.92927044373959 - x54)
       + 54.6585416851302*b3 =L= 55.6585416851302;

e44.. sqr(7.79089239319392 - x51) + sqr(3.09688601355012 - x54)
       + 72.9946165089168*b4 =L= 73.9946165089168;

e45.. sqr(2.20597420581599 - x51) + sqr(0.880296019425143 - x54)
       + 103.212034038779*b5 =L= 104.212034038779;

e46.. sqr(4.31093077060147 - x51) + sqr(5.42555328385657 - x54)
       + 56.8881542099775*b6 =L= 57.8881542099775;

e47.. sqr(8.68776252232421 - x51) + sqr(7.42106012944621 - x54)
       + 103.212034038779*b7 =L= 104.212034038779;

e48.. sqr(3.86794113528858 - x51) + sqr(9.34863265837716 - x54)
       + 120.378073325993*b8 =L= 121.378073325993;

e49.. sqr(8.94294324678777 - x51) + sqr(0.712193380632226 - x54)
       + 120.378073325993*b9 =L= 121.378073325993;

e50.. sqr(1.56734614217404 - x51) + sqr(5.6469805099144 - x54)
       + 96.4999714251602*b10 =L= 97.4999714251602;

e51..    b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 =E= 1;

e52.. sqr(0.648386267690458 - x52) + sqr(5.34198386756466 - x55)
       + 109.233018040634*b11 =L= 110.233018040634;

e53.. sqr(0.38028139143083 - x52) + sqr(4.79200736168083 - x55)
       + 108.933937361066*b12 =L= 109.933937361066;

e54.. sqr(4.59553989190787 - x52) + sqr(2.92927044373959 - x55)
       + 54.6585416851302*b13 =L= 55.6585416851302;

e55.. sqr(7.79089239319392 - x52) + sqr(3.09688601355012 - x55)
       + 72.9946165089168*b14 =L= 73.9946165089168;

e56.. sqr(2.20597420581599 - x52) + sqr(0.880296019425143 - x55)
       + 103.212034038779*b15 =L= 104.212034038779;

e57.. sqr(4.31093077060147 - x52) + sqr(5.42555328385657 - x55)
       + 56.8881542099775*b16 =L= 57.8881542099775;

e58.. sqr(8.68776252232421 - x52) + sqr(7.42106012944621 - x55)
       + 103.212034038779*b17 =L= 104.212034038779;

e59.. sqr(3.86794113528858 - x52) + sqr(9.34863265837716 - x55)
       + 120.378073325993*b18 =L= 121.378073325993;

e60.. sqr(8.94294324678777 - x52) + sqr(0.712193380632226 - x55)
       + 120.378073325993*b19 =L= 121.378073325993;

e61.. sqr(1.56734614217404 - x52) + sqr(5.6469805099144 - x55)
       + 96.4999714251602*b20 =L= 97.4999714251602;

e62..    b11 + b12 + b13 + b14 + b15 + b16 + b17 + b18 + b19 + b20 =E= 1;

e63.. sqr(0.648386267690458 - x57) + sqr(5.34198386756466 - x59)
       + 109.233018040634*b21 =L= 110.233018040634;

e64.. sqr(0.38028139143083 - x57) + sqr(4.79200736168083 - x59)
       + 108.933937361066*b22 =L= 109.933937361066;

e65.. sqr(4.59553989190787 - x57) + sqr(2.92927044373959 - x59)
       + 54.6585416851302*b23 =L= 55.6585416851302;

e66.. sqr(7.79089239319392 - x57) + sqr(3.09688601355012 - x59)
       + 72.9946165089168*b24 =L= 73.9946165089168;

e67.. sqr(2.20597420581599 - x57) + sqr(0.880296019425143 - x59)
       + 103.212034038779*b25 =L= 104.212034038779;

e68.. sqr(4.31093077060147 - x57) + sqr(5.42555328385657 - x59)
       + 56.8881542099775*b26 =L= 57.8881542099775;

e69.. sqr(8.68776252232421 - x57) + sqr(7.42106012944621 - x59)
       + 103.212034038779*b27 =L= 104.212034038779;

e70.. sqr(3.86794113528858 - x57) + sqr(9.34863265837716 - x59)
       + 120.378073325993*b28 =L= 121.378073325993;

e71.. sqr(8.94294324678777 - x57) + sqr(0.712193380632226 - x59)
       + 120.378073325993*b29 =L= 121.378073325993;

e72.. sqr(1.56734614217404 - x57) + sqr(5.6469805099144 - x59)
       + 96.4999714251602*b30 =L= 97.4999714251602;

e73..    b21 + b22 + b23 + b24 + b25 + b26 + b27 + b28 + b29 + b30 =E= 1;

e74.. sqr(0.648386267690458 - x61) + sqr(5.34198386756466 - x63)
       + 109.233018040634*b31 =L= 110.233018040634;

e75.. sqr(0.38028139143083 - x61) + sqr(4.79200736168083 - x63)
       + 108.933937361066*b32 =L= 109.933937361066;

e76.. sqr(4.59553989190787 - x61) + sqr(2.92927044373959 - x63)
       + 54.6585416851302*b33 =L= 55.6585416851302;

e77.. sqr(7.79089239319392 - x61) + sqr(3.09688601355012 - x63)
       + 72.9946165089168*b34 =L= 73.9946165089168;

e78.. sqr(2.20597420581599 - x61) + sqr(0.880296019425143 - x63)
       + 103.212034038779*b35 =L= 104.212034038779;

e79.. sqr(4.31093077060147 - x61) + sqr(5.42555328385657 - x63)
       + 56.8881542099775*b36 =L= 57.8881542099775;

e80.. sqr(8.68776252232421 - x61) + sqr(7.42106012944621 - x63)
       + 103.212034038779*b37 =L= 104.212034038779;

e81.. sqr(3.86794113528858 - x61) + sqr(9.34863265837716 - x63)
       + 120.378073325993*b38 =L= 121.378073325993;

e82.. sqr(8.94294324678777 - x61) + sqr(0.712193380632226 - x63)
       + 120.378073325993*b39 =L= 121.378073325993;

e83.. sqr(1.56734614217404 - x61) + sqr(5.6469805099144 - x63)
       + 96.4999714251602*b40 =L= 97.4999714251602;

e84..    b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 =E= 1;

e85.. sqr(0.648386267690458 - x65) + sqr(5.34198386756466 - x67)
       + 109.233018040634*b41 =L= 110.233018040634;

e86.. sqr(0.38028139143083 - x65) + sqr(4.79200736168083 - x67)
       + 108.933937361066*b42 =L= 109.933937361066;

e87.. sqr(4.59553989190787 - x65) + sqr(2.92927044373959 - x67)
       + 54.6585416851302*b43 =L= 55.6585416851302;

e88.. sqr(7.79089239319392 - x65) + sqr(3.09688601355012 - x67)
       + 72.9946165089168*b44 =L= 73.9946165089168;

e89.. sqr(2.20597420581599 - x65) + sqr(0.880296019425143 - x67)
       + 103.212034038779*b45 =L= 104.212034038779;

e90.. sqr(4.31093077060147 - x65) + sqr(5.42555328385657 - x67)
       + 56.8881542099775*b46 =L= 57.8881542099775;

e91.. sqr(8.68776252232421 - x65) + sqr(7.42106012944621 - x67)
       + 103.212034038779*b47 =L= 104.212034038779;

e92.. sqr(3.86794113528858 - x65) + sqr(9.34863265837716 - x67)
       + 120.378073325993*b48 =L= 121.378073325993;

e93.. sqr(8.94294324678777 - x65) + sqr(0.712193380632226 - x67)
       + 120.378073325993*b49 =L= 121.378073325993;

e94.. sqr(1.56734614217404 - x65) + sqr(5.6469805099144 - x67)
       + 96.4999714251602*b50 =L= 97.4999714251602;

e95..    b41 + b42 + b43 + b44 + b45 + b46 + b47 + b48 + b49 + b50 =E= 1;

e96..    b1 + b11 + b21 + b31 + b41 =L= 1;

e97..    b2 + b12 + b22 + b32 + b42 =L= 1;

e98..    b3 + b13 + b23 + b33 + b43 =L= 1;

e99..    b4 + b14 + b24 + b34 + b44 =L= 1;

e100..    b5 + b15 + b25 + b35 + b45 =L= 1;

e101..    b6 + b16 + b26 + b36 + b46 =L= 1;

e102..    b7 + b17 + b27 + b37 + b47 =L= 1;

e103..    b8 + b18 + b28 + b38 + b48 =L= 1;

e104..    b9 + b19 + b29 + b39 + b49 =L= 1;

e105..    b10 + b20 + b30 + b40 + b50 =L= 1;

e106..    x51 - x52 =L= 0;

e107..    x52 - x57 =L= 0;

e108..    x57 - x61 =L= 0;

e109..    x61 - x65 =L= 0;

e110..  - x53 - x56 - x58 - x60 - x62 - x64 - x66 - x68 - x69 - x70 - x71 - x72
        - x73 - x74 - x75 - x76 - x77 - x78 - x79 - x80 + 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;

* set non-default levels
b2.l = 1;
b11.l = 1;
b30.l = 1;
b36.l = 1;
b43.l = 1;
x51.l = 1.37695009606239;
x52.l = 1.42378547420432;
x53.l = 0.0468353781419294;
x54.l = 4.71045051597106;
x55.l = 4.71045051597106;
x57.l = 1.91800199645783;
x58.l = 0.541051900395441;
x59.l = 4.71045051597106;
x61.l = 3.61191140798068;
x62.l = 2.23496131191829;
x63.l = 4.71045051597106;
x65.l = 3.89283484794216;
x66.l = 2.51588475187977;
x67.l = 3.64078525445372;
x68.l = 1.06966526151734;
x69.l = 0.494216522253511;
x71.l = 2.18812593377636;
x73.l = 2.46904937373784;
x74.l = 1.06966526151734;
x75.l = 1.69390941152285;
x77.l = 1.97483285148432;
x78.l = 1.06966526151734;
x79.l = 0.280923439961476;
x80.l = 1.06966526151734;

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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