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Instance sporttournament16
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ⓘ | 130.00000010 (ANTIGONE) 130.00000010 (BARON) 130.00000000 (COUENNE) 139.18698880 (CPLEX) 130.00000000 (GUROBI) 130.00000000 (LINDO) 130.00000000 (SCIP) 130.00000000 (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-16-4711 |
| Applicationⓘ | Sports Tournament |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 121 |
| #Binary Variablesⓘ | 120 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 120 |
| #Nonlinear Binary Variablesⓘ | 120 |
| #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ⓘ | 121 |
| #Nonlinear Nonzeros in Jacobianⓘ | 120 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 448 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 120 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 120 |
| Average blocksize in Hessian of Lagrangianⓘ | 120.0 |
| #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
* 121 1 120 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 121 1 120 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,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,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,objvar;
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,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85
,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101
,b102,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114
,b115,b116,b117,b118,b119,b120;
Equations e1;
e1.. 2*b1*b3 - 2*b1 - 2*b3 + 2*b1*b5 - 4*b5 + 2*b1*b38 + 2*b38 - 2*b1*b50 + 4*
b50 + 2*b2*b5 - 2*b2 + 2*b2*b7 - 4*b7 + 2*b2*b25 - 2*b25 - 2*b2*b68 + 2*
b68 - 2*b3*b6 - 2*b6 + 2*b3*b26 - 2*b26 + 2*b3*b39 - 2*b39 + 2*b4*b7 - 4*
b4 + 2*b4*b10 - 2*b10 + 2*b4*b18 - 2*b18 + 2*b4*b19 - 4*b19 + 2*b5*b8 - 4*
b8 + 2*b5*b39 + 2*b6*b7 + 2*b6*b15 - 4*b15 + 2*b6*b99 + 2*b7*b11 - 2*b11
+ 2*b8*b10 + 2*b8*b15 + 2*b8*b20 - 4*b20 + 2*b9*b23 - 2*b9 - 2*b23 + 2*b9
*b64 - 4*b64 + 2*b10*b14 - 2*b14 - 2*b10*b100 + 2*b11*b20 + 2*b11*b27 - 4*
b27 - 2*b11*b71 - 2*b71 + 2*b12*b20 - 2*b12 + 2*b12*b29 - 4*b29 - 2*b12*
b99 + 2*b12*b104 + 2*b13*b18 - 2*b13 + 2*b13*b25 + 2*b14*b27 + 2*b14*b40
- 2*b40 - 2*b14*b51 - 2*b51 + 2*b15*b21 - 4*b21 + 2*b15*b75 - 2*b75 + 2*
b16*b27 - 4*b16 + 2*b16*b29 + 2*b16*b43 - 4*b43 + 2*b16*b99 + 2*b17*b48 -
2*b17 - 2*b48 + 2*b17*b102 + 2*b18*b26 - 2*b18*b98 + 2*b19*b26 + 2*b19*
b103 + 2*b19*b106 + 2*b20*b28 - 2*b28 + 2*b21*b40 + 2*b21*b43 + 2*b21*b54
- 4*b54 - 2*b22*b23 - 2*b22 + 2*b22*b47 - 4*b47 + 2*b22*b63 - 2*b63 + 2*
b22*b107 + 2*b23*b24 - 2*b24 + 2*b23*b62 - 4*b62 + 2*b24*b63 + 2*b25*b105
- 2*b25*b112 - 2*b26*b114 + 2*b27*b42 - 2*b42 + 2*b28*b54 - 2*b28*b74 - 2
*b74 + 2*b28*b76 - 4*b76 + 2*b29*b30 - 2*b30 + 2*b29*b78 - 2*b78 + 2*b30*
b31 - 4*b31 + 2*b30*b76 - 2*b30*b80 + 2*b80 + 2*b31*b32 - 2*b32 + 2*b31*
b78 + 2*b31*b90 + 2*b32*b61 - 2*b61 + 2*b32*b81 - 2*b81 - 2*b32*b107 + 2*
b33*b35 - 2*b33 - 2*b35 + 2*b33*b60 - 2*b60 + 2*b33*b108 - 2*b33*b110 - 2*
b34*b48 + 2*b34 + 2*b34*b87 - 4*b87 - 2*b34*b89 - 2*b34*b94 + 2*b35*b61 +
2*b35*b87 - 2*b35*b102 + 2*b36*b37 - 2*b36 - 2*b37 + 2*b36*b86 - 4*b86 - 2
*b36*b108 + 2*b36*b109 + 2*b37*b87 - 2*b38*b105 - 2*b38*b106 - 2*b38*b116
+ 2*b39*b41 - 4*b41 - 2*b39*b99 + 2*b40*b53 - 4*b53 - 2*b40*b73 - 2*b73
+ 2*b41*b52 - 2*b52 + 2*b41*b53 + 2*b41*b75 + 2*b42*b44 - 2*b44 + 2*b42*
b76 - 2*b42*b115 + 2*b43*b45 - 2*b45 + 2*b43*b56 + 2*b56 + 2*b44*b45 + 2*
b44*b53 - 2*b44*b92 - 2*b45*b96 + 2*b45*b111 + 2*b46*b83 - 2*b46 - 2*b83
- 2*b46*b97 + 2*b46*b107 + 2*b46*b111 + 2*b47*b82 - 2*b82 + 2*b47*b85 - 2
*b85 + 2*b47*b110 + 2*b48*b108 + 2*b48*b118 - 2*b49*b68 + 2*b49 - 2*b49*
b117 - 2*b50*b66 + 2*b66 - 2*b50*b69 - 2*b69 - 2*b50*b103 + 2*b51*b69 + 2*
b51*b72 - 4*b72 + 2*b51*b116 + 2*b52*b70 - 4*b70 - 2*b52*b114 + 2*b52*b115
+ 2*b53*b55 - 2*b55 + 2*b54*b57 - 4*b57 + 2*b54*b101 + 2*b55*b57 + 2*b55*
b92 - 2*b55*b120 - 2*b56*b59 - 2*b59 - 2*b56*b97 - 2*b56*b104 + 2*b57*b59
+ 2*b57*b96 - 2*b58*b60 + 2*b58 - 2*b58*b92 + 2*b58*b95 - 2*b58*b101 + 2*
b59*b60 + 2*b59*b110 + 2*b60*b94 + 2*b61*b62 - 2*b61*b91 + 2*b62*b64 + 2*
b62*b94 + 2*b63*b65 - 2*b65 - 2*b63*b93 + 2*b64*b65 + 2*b64*b93 - 2*b66*
b113 + 2*b67*b68 - 2*b67 + 2*b67*b113 - 2*b68*b100 + 2*b69*b71 + 2*b69*
b117 + 2*b70*b73 + 2*b70*b112 + 2*b70*b116 + 2*b71*b73 + 2*b71*b100 + 2*
b72*b74 + 2*b72*b114 + 2*b72*b115 + 2*b73*b74 + 2*b74*b120 + 2*b75*b77 - 4
*b77 - 2*b75*b104 + 2*b76*b79 - 4*b79 + 2*b77*b78 + 2*b77*b79 + 2*b77*b120
- 2*b78*b81 + 2*b79*b80 + 2*b79*b81 - 2*b80*b82 - 2*b80*b90 + 2*b81*b82
+ 2*b82*b84 - 2*b84 + 2*b83*b85 + 2*b83*b86 - 2*b83*b95 + 2*b84*b86 - 2*
b84*b93 + 2*b84*b95 + 2*b85*b102 - 2*b85*b119 + 2*b86*b119 + 2*b87*b88 - 2
*b88 + 2*b88*b119 + 2*b89*b90 - 2*b89*b91 + 2*b89*b93 - 2*b90*b94 + 2*b91*
b96 + 2*b91*b97 + 2*b92*b97 - 2*b95*b96 + 2*b98*b117 + 2*b100*b113 + 2*
b101*b104 - 2*b101*b111 - 2*b102*b109 - 2*b107*b108 - 2*b110*b111 - 2*b112
*b113 + 2*b112*b114 - 2*b115*b120 - 2*b116*b117 - 2*b118*b119 + objvar
=L= 0;
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