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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance sporttournament14
This is a quadratic model for the max-cut problem. The instance arises when minimizing so-called breaks in sports tournaments.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 96.00000010 (ANTIGONE) 96.00000010 (BARON) 96.00000000 (COUENNE) 96.00000000 (GUROBI) 96.00000001 (LINDO) 96.00000000 (SCIP) 256.00000000 (SHOT) |
| Referencesⓘ | Elf, Matthias, Jünger, Michael, and Rinaldi, Giovanni, Minimizing Breaks by Maximizing Cuts, Operations Research Letters, 31:5, 2003, 343-349. |
| Sourceⓘ | POLIP instance maxcut/sched-14-4711 |
| Applicationⓘ | Sports Tournament |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 92 |
| #Binary Variablesⓘ | 21 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 91 |
| #Nonlinear Binary Variablesⓘ | 21 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | max |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 1 |
| #Linear Constraintsⓘ | 0 |
| #Quadratic Constraintsⓘ | 1 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 92 |
| #Nonlinear Nonzeros in Jacobianⓘ | 91 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 336 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 91 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 91 |
| Average blocksize in Hessian of Lagrangianⓘ | 91.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 4.0000e+00 |
| Infeasibility of initial pointⓘ | 0 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 1 0 0 1 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 92 71 21 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 92 1 91 0
*
* Solve m using MINLP maximizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,objvar,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,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;
Positive Variables x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
,x36,x37,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,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;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21;
Equations e1;
e1.. 2*x43*x30 - 4*x30 - 2*x43 - 2*x43*x59 + 2*x59 + 2*x43*x69 + 2*x43*x70 + 2*
x46*x47 - 2*x46 - 4*x47 + 2*x46*x63 - 2*x63 + 2*x46*x84 - 2*x84 - 2*x46*
b14 + 2*x47*x64 - 2*x64 + 2*x47*x88 - 2*x88 + 2*x47*x74 + 2*x52*x54 + 2*
x52 - 4*x54 - 2*x52*x84 - 2*x52*x76 - 2*x52*b15 + 2*x54*x88 + 2*x54*x25 -
4*x25 + 2*x54*x78 + 2*x58*x60 - 2*x58 - 2*x60 + 2*x58*b12 - 4*b12 + 2*x60*
x62 - 2*x62 + 2*x60*x73 - 4*x73 - 2*x60*x83 + 2*x62*x77 - 4*x77 + 2*x63*
x37 - 2*x37 + 2*x64*x66 - 2*x66 + 2*x64*x84 - 2*x64*x82 + 2*x66*x67 - 2*
x67 - 2*x66*x26 - 2*x26 + 2*x66*x56 - 4*x56 + 2*x67*x90 - 4*x90 + 2*x67*
x57 + 2*x57 - 2*x67*x71 + 2*x73*x23 - 4*x23 + 2*x73*x32 - 4*x32 + 2*x73*
x85 + 2*x77*x81 - 2*x81 + 2*x77*x22 - 4*x22 + 2*x77*x83 + 2*x81*x23 + 2*
x84*x89 - 2*x89 + 2*x88*x90 - 2*x88*x79 + 2*x89*x90 + 2*x89*x39 - 4*x39 -
2*x89*x87 + 2*x90*x91 - 4*x91 + 2*x91*x42 + 2*x42 + 2*x91*x55 - 2*x55 + 2*
x91*x71 + 2*x92*x22 - 4*x92 + 2*x92*b3 - 2*b3 + 2*x92*x83 + 2*x92*x86 + 2*
x22*x34 - 4*x34 + 2*x22*b4 - 2*b4 + 2*x23*x24 - 2*x24 + 2*x23*x33 - 4*x33
+ 2*x24*x34 + 2*x25*x39 + 2*x25*x53 - 2*x53 + 2*x25*x55 + 2*x26*b1 - 2*b1
+ 2*x26*x55 + 2*x26*x87 + 2*x27*x39 - 2*x27 - 2*x27*x42 + 2*x27*x75 + 2*
x27*x79 + 2*x28*x29 - 4*x28 - 2*x29 + 2*x28*x30 + 2*x28*x41 - 2*x41 + 2*
x28*x56 - 2*x29*x31 - 2*x31 + 2*x29*x45 - 2*x45 + 2*x29*x71 + 2*x30*x31 +
2*x30*x75 + 2*x31*x32 + 2*x31*x85 + 2*x32*x33 + 2*x32*b9 - 2*b9 + 2*x33*
x49 - 4*x49 + 2*x33*b10 - 2*b10 + 2*x34*x35 - 2*x35 + 2*x34*x48 - 2*x48 +
2*x35*x49 - 2*x36*x74 + 2*x36 - 2*x36*b19 - 2*x37*b1 + 2*x37*x53 + 2*x37*
x76 + 2*b1*b17 + 2*b1*b19 + 2*x39*x41 + 2*x40*b2 - 4*b2 - 2*x40 - 2*x40*
x57 + 2*x40*x79 + 2*x40*x82 + 2*x41*b2 - 2*x41*b21 - 2*x42*x59 - 2*x42*b18
+ 2*b2*x72 + 2*b2*b18 - 2*x44*b3 + 2*x44 - 2*x44*x57 + 2*x44*x61 + 2*x61
- 2*x44*x71 - 2*x45*b4 + 2*x45*x70 + 2*x45*x72 + 2*b3*b4 + 2*b3*b18 + 2*
b4*x48 + 2*x48*x65 - 2*x65 - 2*x48*x70 + 2*x49*x50 - 2*x50 + 2*x49*b11 - 2
*b11 + 2*x50*x65 - 2*x51*b5 - 2*b5 + 2*x51 - 2*x51*x78 + 2*b5*b6 - 2*b6 +
2*b5*b14 + 2*b5*x87 + 2*x53*x74 - 2*x53*b16 - 2*b6*x78 + 2*b6*b16 + 2*b6*
b17 - 2*x55*b20 + 2*x56*b7 - 4*b7 + 2*x56*x82 - 2*x57*b8 - 2*b8 + 2*b7*x59
+ 2*b7*b8 + 2*b7*b20 - 2*x59*b9 + 2*b8*b9 + 2*b8*x86 - 2*x61*b10 - 2*x61*
x69 - 2*x61*x72 + 2*b9*b10 + 2*b10*b11 + 2*b11*b12 - 2*b11*x69 + 2*x65*b13
- 2*b13 - 2*x65*x68 + 2*b12*b13 + 2*b12*x68 + 2*x68*x69 - 2*x68*x70 - 2*
x72*x75 - 2*x74*x80 - 2*x75*b20 + 2*b15*b19 + 2*x78*x80 - 2*x79*b16 + 2*
b16*b21 - 2*x82*b17 - 2*x83*x85 - 2*b17*b21 - 2*x85*x86 - 2*x86*b18 - 2*
x87*b19 + 2*b20*b21 + objvar =L= 0;
* set non-default bounds
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.up = 1;
x29.up = 1;
x30.up = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1;
x39.up = 1;
x40.up = 1;
x41.up = 1;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 1;
x51.up = 1;
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 1;
x63.up = 1;
x64.up = 1;
x65.up = 1;
x66.up = 1;
x67.up = 1;
x68.up = 1;
x69.up = 1;
x70.up = 1;
x71.up = 1;
x72.up = 1;
x73.up = 1;
x74.up = 1;
x75.up = 1;
x76.up = 1;
x77.up = 1;
x78.up = 1;
x79.up = 1;
x80.up = 1;
x81.up = 1;
x82.up = 1;
x83.up = 1;
x84.up = 1;
x85.up = 1;
x86.up = 1;
x87.up = 1;
x88.up = 1;
x89.up = 1;
x90.up = 1;
x91.up = 1;
x92.up = 1;
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% maximizing objvar;
Last updated: 2025-08-07 Git hash: e62cedfc