MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance p_ball_15b_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 15 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ⓘ | 6.59760891 (ALPHAECP) 6.59982978 (ANTIGONE) 6.59984991 (BARON) 6.59986761 (BONMIN) 6.59981397 (COUENNE) 6.59986393 (CPLEX) 6.59979141 (GUROBI) 6.59986773 (LINDO) 6.59986272 (SCIP) 6.59986772 (SHOT) |
| Referencesⓘ | Kronqvist, Jan and Misener, Ruth, A disjunctive cut strengthening technique for convex MINLP, Tech. Rep., 2020. |
| Sourceⓘ | p_ball_15b_5p_2d.gms, contributed by Jan Kronqvist and Ruth Misener |
| Applicationⓘ | Geometry |
| Added to libraryⓘ | 26 Aug 2020 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 105 |
| #Binary Variablesⓘ | 75 |
| #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ⓘ | 139 |
| #Linear Constraintsⓘ | 64 |
| #Quadratic Constraintsⓘ | 75 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 503 |
| #Nonlinear Nonzeros in Jacobianⓘ | 150 |
| #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ⓘ | 3.0308e-01 |
| Maximal coefficientⓘ | 1.4420e+02 |
| Infeasibility of initial pointⓘ | 8.326e-05 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 140 6 0 134 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 106 31 75 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 524 374 150 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,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,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103
,x104,x105,objvar;
Positive Variables x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87,x88,x89
,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103,x104
,x105;
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;
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;
e1.. x76 - x77 - x78 =L= 0;
e2.. - x76 + x77 - x78 =L= 0;
e3.. x79 - x80 - x81 =L= 0;
e4.. - x79 + x80 - x81 =L= 0;
e5.. x76 - x82 - x83 =L= 0;
e6.. - x76 + x82 - x83 =L= 0;
e7.. x79 - x84 - x85 =L= 0;
e8.. - x79 + x84 - x85 =L= 0;
e9.. x76 - x86 - x87 =L= 0;
e10.. - x76 + x86 - x87 =L= 0;
e11.. x79 - x88 - x89 =L= 0;
e12.. - x79 + x88 - x89 =L= 0;
e13.. x76 - x90 - x91 =L= 0;
e14.. - x76 + x90 - x91 =L= 0;
e15.. x79 - x92 - x93 =L= 0;
e16.. - x79 + x92 - x93 =L= 0;
e17.. x77 - x82 - x94 =L= 0;
e18.. - x77 + x82 - x94 =L= 0;
e19.. x80 - x84 - x95 =L= 0;
e20.. - x80 + x84 - x95 =L= 0;
e21.. x77 - x86 - x96 =L= 0;
e22.. - x77 + x86 - x96 =L= 0;
e23.. x80 - x88 - x97 =L= 0;
e24.. - x80 + x88 - x97 =L= 0;
e25.. x77 - x90 - x98 =L= 0;
e26.. - x77 + x90 - x98 =L= 0;
e27.. x80 - x92 - x99 =L= 0;
e28.. - x80 + x92 - x99 =L= 0;
e29.. x82 - x86 - x100 =L= 0;
e30.. - x82 + x86 - x100 =L= 0;
e31.. x84 - x88 - x101 =L= 0;
e32.. - x84 + x88 - x101 =L= 0;
e33.. x82 - x90 - x102 =L= 0;
e34.. - x82 + x90 - x102 =L= 0;
e35.. x84 - x92 - x103 =L= 0;
e36.. - x84 + x92 - x103 =L= 0;
e37.. x86 - x90 - x104 =L= 0;
e38.. - x86 + x90 - x104 =L= 0;
e39.. x88 - x92 - x105 =L= 0;
e40.. - x88 + x92 - x105 =L= 0;
e41.. sqr(8.68340342427357 - x76) + sqr(8.57974596088368 - x79)
+ 122.913026025479*b1 =L= 123.913026025479;
e42.. sqr(9.63614333912176 - x76) + sqr(8.80176337918095 - x79)
+ 144.203684439948*b2 =L= 145.203684439948;
e43.. sqr(3.68142205418198 - x76) + sqr(1.1692321814062 - x79)
+ 113.075460968432*b3 =L= 114.075460968432;
e44.. sqr(9.7121756733827 - x76) + sqr(7.68772804421774 - x79)
+ 132.715787162747*b4 =L= 133.715787162747;
e45.. sqr(3.2772228491781 - x76) + sqr(8.20105404549271 - x79)
+ 71.5990957077621*b5 =L= 72.5990957077621;
e46.. sqr(8.95169370625893 - x76) + sqr(5.71833771240185 - x79)
+ 101.022453999802*b6 =L= 102.022453999802;
e47.. sqr(6.39713701672676 - x76) + sqr(2.19374777991393 - x79)
+ 76.9700130269697*b7 =L= 77.9700130269697;
e48.. sqr(8.63324272987351 - x76) + sqr(2.92174290170279 - x79)
+ 86.0532928024441*b8 =L= 87.0532928024441;
e49.. sqr(3.63244627881363 - x76) + sqr(1.91739848753332 - x79)
+ 101.707832966379*b9 =L= 102.707832966379;
e50.. sqr(0.303084489788861 - x76) + sqr(2.88588654972735 - x79)
+ 144.203684439948*b10 =L= 145.203684439948;
e51.. sqr(9.32557624217471 - x76) + sqr(5.59175556022082 - x79)
+ 107.566095593812*b11 =L= 108.566095593812;
e52.. sqr(8.52118108549064 - x76) + sqr(5.32332318998315 - x79)
+ 90.6220952924323*b12 =L= 91.6220952924323;
e53.. sqr(4.01861330995576 - x76) + sqr(9.65380890252737 - x79)
+ 97.233140568496*b13 =L= 98.233140568496;
e54.. sqr(2.49020328922613 - x76) + sqr(0.874596139412213 - x79)
+ 135.249644224288*b14 =L= 136.249644224288;
e55.. sqr(0.545671492825244 - x76) + sqr(3.81401698819633 - x79)
+ 128.252112242799*b15 =L= 129.252112242799;
e56.. b1 + b2 + b3 + b4 + b5 + b6 + b7 + b8 + b9 + b10 + b11 + b12 + b13
+ b14 + b15 =E= 1;
e57.. sqr(8.68340342427357 - x77) + sqr(8.57974596088368 - x80)
+ 122.913026025479*b16 =L= 123.913026025479;
e58.. sqr(9.63614333912176 - x77) + sqr(8.80176337918095 - x80)
+ 144.203684439948*b17 =L= 145.203684439948;
e59.. sqr(3.68142205418198 - x77) + sqr(1.1692321814062 - x80)
+ 113.075460968432*b18 =L= 114.075460968432;
e60.. sqr(9.7121756733827 - x77) + sqr(7.68772804421774 - x80)
+ 132.715787162747*b19 =L= 133.715787162747;
e61.. sqr(3.2772228491781 - x77) + sqr(8.20105404549271 - x80)
+ 71.5990957077621*b20 =L= 72.5990957077621;
e62.. sqr(8.95169370625893 - x77) + sqr(5.71833771240185 - x80)
+ 101.022453999802*b21 =L= 102.022453999802;
e63.. sqr(6.39713701672676 - x77) + sqr(2.19374777991393 - x80)
+ 76.9700130269697*b22 =L= 77.9700130269697;
e64.. sqr(8.63324272987351 - x77) + sqr(2.92174290170279 - x80)
+ 86.0532928024441*b23 =L= 87.0532928024441;
e65.. sqr(3.63244627881363 - x77) + sqr(1.91739848753332 - x80)
+ 101.707832966379*b24 =L= 102.707832966379;
e66.. sqr(0.303084489788861 - x77) + sqr(2.88588654972735 - x80)
+ 144.203684439948*b25 =L= 145.203684439948;
e67.. sqr(9.32557624217471 - x77) + sqr(5.59175556022082 - x80)
+ 107.566095593812*b26 =L= 108.566095593812;
e68.. sqr(8.52118108549064 - x77) + sqr(5.32332318998315 - x80)
+ 90.6220952924323*b27 =L= 91.6220952924323;
e69.. sqr(4.01861330995576 - x77) + sqr(9.65380890252737 - x80)
+ 97.233140568496*b28 =L= 98.233140568496;
e70.. sqr(2.49020328922613 - x77) + sqr(0.874596139412213 - x80)
+ 135.249644224288*b29 =L= 136.249644224288;
e71.. sqr(0.545671492825244 - x77) + sqr(3.81401698819633 - x80)
+ 128.252112242799*b30 =L= 129.252112242799;
e72.. b16 + b17 + b18 + b19 + b20 + b21 + b22 + b23 + b24 + b25 + b26 + b27
+ b28 + b29 + b30 =E= 1;
e73.. sqr(8.68340342427357 - x82) + sqr(8.57974596088368 - x84)
+ 122.913026025479*b31 =L= 123.913026025479;
e74.. sqr(9.63614333912176 - x82) + sqr(8.80176337918095 - x84)
+ 144.203684439948*b32 =L= 145.203684439948;
e75.. sqr(3.68142205418198 - x82) + sqr(1.1692321814062 - x84)
+ 113.075460968432*b33 =L= 114.075460968432;
e76.. sqr(9.7121756733827 - x82) + sqr(7.68772804421774 - x84)
+ 132.715787162747*b34 =L= 133.715787162747;
e77.. sqr(3.2772228491781 - x82) + sqr(8.20105404549271 - x84)
+ 71.5990957077621*b35 =L= 72.5990957077621;
e78.. sqr(8.95169370625893 - x82) + sqr(5.71833771240185 - x84)
+ 101.022453999802*b36 =L= 102.022453999802;
e79.. sqr(6.39713701672676 - x82) + sqr(2.19374777991393 - x84)
+ 76.9700130269697*b37 =L= 77.9700130269697;
e80.. sqr(8.63324272987351 - x82) + sqr(2.92174290170279 - x84)
+ 86.0532928024441*b38 =L= 87.0532928024441;
e81.. sqr(3.63244627881363 - x82) + sqr(1.91739848753332 - x84)
+ 101.707832966379*b39 =L= 102.707832966379;
e82.. sqr(0.303084489788861 - x82) + sqr(2.88588654972735 - x84)
+ 144.203684439948*b40 =L= 145.203684439948;
e83.. sqr(9.32557624217471 - x82) + sqr(5.59175556022082 - x84)
+ 107.566095593812*b41 =L= 108.566095593812;
e84.. sqr(8.52118108549064 - x82) + sqr(5.32332318998315 - x84)
+ 90.6220952924323*b42 =L= 91.6220952924323;
e85.. sqr(4.01861330995576 - x82) + sqr(9.65380890252737 - x84)
+ 97.233140568496*b43 =L= 98.233140568496;
e86.. sqr(2.49020328922613 - x82) + sqr(0.874596139412213 - x84)
+ 135.249644224288*b44 =L= 136.249644224288;
e87.. sqr(0.545671492825244 - x82) + sqr(3.81401698819633 - x84)
+ 128.252112242799*b45 =L= 129.252112242799;
e88.. b31 + b32 + b33 + b34 + b35 + b36 + b37 + b38 + b39 + b40 + b41 + b42
+ b43 + b44 + b45 =E= 1;
e89.. sqr(8.68340342427357 - x86) + sqr(8.57974596088368 - x88)
+ 122.913026025479*b46 =L= 123.913026025479;
e90.. sqr(9.63614333912176 - x86) + sqr(8.80176337918095 - x88)
+ 144.203684439948*b47 =L= 145.203684439948;
e91.. sqr(3.68142205418198 - x86) + sqr(1.1692321814062 - x88)
+ 113.075460968432*b48 =L= 114.075460968432;
e92.. sqr(9.7121756733827 - x86) + sqr(7.68772804421774 - x88)
+ 132.715787162747*b49 =L= 133.715787162747;
e93.. sqr(3.2772228491781 - x86) + sqr(8.20105404549271 - x88)
+ 71.5990957077621*b50 =L= 72.5990957077621;
e94.. sqr(8.95169370625893 - x86) + sqr(5.71833771240185 - x88)
+ 101.022453999802*b51 =L= 102.022453999802;
e95.. sqr(6.39713701672676 - x86) + sqr(2.19374777991393 - x88)
+ 76.9700130269697*b52 =L= 77.9700130269697;
e96.. sqr(8.63324272987351 - x86) + sqr(2.92174290170279 - x88)
+ 86.0532928024441*b53 =L= 87.0532928024441;
e97.. sqr(3.63244627881363 - x86) + sqr(1.91739848753332 - x88)
+ 101.707832966379*b54 =L= 102.707832966379;
e98.. sqr(0.303084489788861 - x86) + sqr(2.88588654972735 - x88)
+ 144.203684439948*b55 =L= 145.203684439948;
e99.. sqr(9.32557624217471 - x86) + sqr(5.59175556022082 - x88)
+ 107.566095593812*b56 =L= 108.566095593812;
e100.. sqr(8.52118108549064 - x86) + sqr(5.32332318998315 - x88)
+ 90.6220952924323*b57 =L= 91.6220952924323;
e101.. sqr(4.01861330995576 - x86) + sqr(9.65380890252737 - x88)
+ 97.233140568496*b58 =L= 98.233140568496;
e102.. sqr(2.49020328922613 - x86) + sqr(0.874596139412213 - x88)
+ 135.249644224288*b59 =L= 136.249644224288;
e103.. sqr(0.545671492825244 - x86) + sqr(3.81401698819633 - x88)
+ 128.252112242799*b60 =L= 129.252112242799;
e104.. b46 + b47 + b48 + b49 + b50 + b51 + b52 + b53 + b54 + b55 + b56 + b57
+ b58 + b59 + b60 =E= 1;
e105.. sqr(8.68340342427357 - x90) + sqr(8.57974596088368 - x92)
+ 122.913026025479*b61 =L= 123.913026025479;
e106.. sqr(9.63614333912176 - x90) + sqr(8.80176337918095 - x92)
+ 144.203684439948*b62 =L= 145.203684439948;
e107.. sqr(3.68142205418198 - x90) + sqr(1.1692321814062 - x92)
+ 113.075460968432*b63 =L= 114.075460968432;
e108.. sqr(9.7121756733827 - x90) + sqr(7.68772804421774 - x92)
+ 132.715787162747*b64 =L= 133.715787162747;
e109.. sqr(3.2772228491781 - x90) + sqr(8.20105404549271 - x92)
+ 71.5990957077621*b65 =L= 72.5990957077621;
e110.. sqr(8.95169370625893 - x90) + sqr(5.71833771240185 - x92)
+ 101.022453999802*b66 =L= 102.022453999802;
e111.. sqr(6.39713701672676 - x90) + sqr(2.19374777991393 - x92)
+ 76.9700130269697*b67 =L= 77.9700130269697;
e112.. sqr(8.63324272987351 - x90) + sqr(2.92174290170279 - x92)
+ 86.0532928024441*b68 =L= 87.0532928024441;
e113.. sqr(3.63244627881363 - x90) + sqr(1.91739848753332 - x92)
+ 101.707832966379*b69 =L= 102.707832966379;
e114.. sqr(0.303084489788861 - x90) + sqr(2.88588654972735 - x92)
+ 144.203684439948*b70 =L= 145.203684439948;
e115.. sqr(9.32557624217471 - x90) + sqr(5.59175556022082 - x92)
+ 107.566095593812*b71 =L= 108.566095593812;
e116.. sqr(8.52118108549064 - x90) + sqr(5.32332318998315 - x92)
+ 90.6220952924323*b72 =L= 91.6220952924323;
e117.. sqr(4.01861330995576 - x90) + sqr(9.65380890252737 - x92)
+ 97.233140568496*b73 =L= 98.233140568496;
e118.. sqr(2.49020328922613 - x90) + sqr(0.874596139412213 - x92)
+ 135.249644224288*b74 =L= 136.249644224288;
e119.. sqr(0.545671492825244 - x90) + sqr(3.81401698819633 - x92)
+ 128.252112242799*b75 =L= 129.252112242799;
e120.. b61 + b62 + b63 + b64 + b65 + b66 + b67 + b68 + b69 + b70 + b71 + b72
+ b73 + b74 + b75 =E= 1;
e121.. b1 + b16 + b31 + b46 + b61 =L= 1;
e122.. b2 + b17 + b32 + b47 + b62 =L= 1;
e123.. b3 + b18 + b33 + b48 + b63 =L= 1;
e124.. b4 + b19 + b34 + b49 + b64 =L= 1;
e125.. b5 + b20 + b35 + b50 + b65 =L= 1;
e126.. b6 + b21 + b36 + b51 + b66 =L= 1;
e127.. b7 + b22 + b37 + b52 + b67 =L= 1;
e128.. b8 + b23 + b38 + b53 + b68 =L= 1;
e129.. b9 + b24 + b39 + b54 + b69 =L= 1;
e130.. b10 + b25 + b40 + b55 + b70 =L= 1;
e131.. b11 + b26 + b41 + b56 + b71 =L= 1;
e132.. b12 + b27 + b42 + b57 + b72 =L= 1;
e133.. b13 + b28 + b43 + b58 + b73 =L= 1;
e134.. b14 + b29 + b44 + b59 + b74 =L= 1;
e135.. b15 + b30 + b45 + b60 + b75 =L= 1;
e136.. x76 - x77 =L= 0;
e137.. x77 - x82 =L= 0;
e138.. x82 - x86 =L= 0;
e139.. x86 - x90 =L= 0;
e140.. - x78 - x81 - x83 - x85 - x87 - x89 - x91 - x93 - x94 - x95 - x96 - x97
- x98 - x99 - x100 - x101 - x102 - x103 - x104 - x105 + objvar =E= 0;
* set non-default bounds
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;
x96.up = 10;
x97.up = 10;
x98.up = 10;
x99.up = 10;
x100.up = 10;
x101.up = 10;
x102.up = 10;
x103.up = 10;
x104.up = 10;
x105.up = 10;
* set non-default levels
b1.l = 1;
b19.l = 1;
b42.l = 1;
b56.l = 1;
b66.l = 1;
x76.l = 8.95906267878703;
x77.l = 8.95906267878703;
x79.l = 7.61846710348714;
x80.l = 7.02977358343362;
x81.l = 0.58869352005352;
x82.l = 8.95906267878703;
x84.l = 6.22238510231117;
x85.l = 1.39608200117597;
x86.l = 8.95906267878703;
x87.l = 1.11022302462516E-16;
x88.l = 6.52219222156143;
x89.l = 1.0962748819257;
x90.l = 8.95906267878703;
x92.l = 6.52219222156143;
x93.l = 1.0962748819257;
x95.l = 0.807388481122451;
x97.l = 0.507581361872184;
x99.l = 0.507581361872184;
x101.l = 0.299807119250266;
x103.l = 0.299807119250266;
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