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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)ⓘ | |
| 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 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: 2025-08-07 Git hash: e62cedfc