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Instance sporttournament18
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ⓘ | 160.00000020 (ANTIGONE) 160.00000020 (BARON) 172.00000000 (COUENNE) 175.75342680 (CPLEX) 160.00000000 (GUROBI) 160.00000000 (LINDO) 160.00000000 (SCIP) 160.00000000 (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-18-4711 |
| Applicationⓘ | Sports Tournament |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 154 |
| #Binary Variablesⓘ | 153 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 153 |
| #Nonlinear Binary Variablesⓘ | 153 |
| #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ⓘ | 154 |
| #Nonlinear Nonzeros in Jacobianⓘ | 153 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 576 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 153 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 153 |
| Average blocksize in Hessian of Lagrangianⓘ | 153.0 |
| #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
* 154 1 153 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 154 1 153 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,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,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,b121,b122,b123,b124,b125,b126,b127
,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140
,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153;
Equations e1;
e1.. 2*b1*b7 - 2*b1 - 2*b7 + 2*b1*b10 - 2*b10 + 2*b1*b15 - 4*b15 - 2*b1*b48 + 2
*b48 + 2*b2*b81 - 2*b2 - 2*b81 + 2*b2*b112 + 2*b3*b108 - 2*b3 + 2*b3*b112
+ 2*b4*b33 - 2*b4 - 2*b33 + 2*b4*b108 + 2*b5*b33 - 2*b5 + 2*b5*b113 + 2*
b6*b21 - 2*b6 - 2*b21 + 2*b6*b78 - 4*b78 + 2*b7*b11 - 2*b11 + 2*b7*b110 -
2*b7*b127 + 2*b8*b18 - 2*b8 - 4*b18 + 2*b8*b28 - 4*b28 - 2*b8*b125 + 2*b8*
b133 - 2*b9*b60 - 2*b9 - 2*b60 + 2*b9*b81 + 2*b9*b114 + 2*b9*b123 + 2*b10*
b17 - 2*b17 + 2*b10*b117 - 2*b10*b124 + 2*b11*b26 - 4*b26 + 2*b11*b35 - 4*
b35 - 2*b11*b135 + 2*b12*b19 - 4*b12 - 4*b19 + 2*b12*b88 - 2*b88 + 2*b12*
b124 + 2*b12*b127 + 2*b13*b26 - 4*b13 + 2*b13*b28 + 2*b13*b37 - 4*b37 + 2*
b13*b125 + 2*b14*b44 - 2*b14 - 4*b44 + 2*b14*b129 + 2*b15*b16 - 4*b16 + 2*
b15*b107 + 2*b15*b134 + 2*b16*b109 + 2*b16*b123 + 2*b16*b140 + 2*b17*b35
+ 2*b17*b50 - 2*b50 - 2*b17*b140 + 2*b18*b27 - 4*b27 + 2*b18*b127 + 2*b18
*b131 + 2*b19*b35 + 2*b19*b37 + 2*b19*b53 - 4*b53 - 2*b20*b21 - 2*b20 + 2*
b20*b58 - 2*b58 + 2*b20*b136 + 2*b20*b142 + 2*b21*b22 - 2*b22 + 2*b21*b98
- 2*b98 + 2*b22*b58 + 2*b23*b24 + 2*b23 - 4*b24 - 2*b23*b48 - 2*b23*b113
- 2*b23*b144 + 2*b24*b25 - 2*b25 + 2*b24*b111 + 2*b24*b117 - 2*b25*b114
+ 2*b25*b135 + 2*b25*b140 + 2*b26*b36 - 2*b36 + 2*b26*b131 + 2*b27*b50 +
2*b27*b53 + 2*b27*b68 - 4*b68 + 2*b28*b38 - 4*b38 + 2*b28*b126 + 2*b29*b30
- 2*b29 - 2*b30 - 2*b29*b41 - 2*b41 + 2*b29*b95 - 2*b95 + 2*b29*b138 + 2*
b30*b57 - 2*b57 + 2*b30*b77 - 2*b77 - 2*b30*b129 + 2*b31*b32 - 2*b31 - 2*
b32 + 2*b31*b76 - 4*b76 - 2*b31*b138 + 2*b31*b139 + 2*b32*b77 - 2*b33*b83
+ 2*b83 + 2*b33*b107 - 2*b34*b110 + 4*b34 - 2*b34*b111 - 2*b34*b134 - 2*
b34*b145 + 2*b35*b52 - 2*b52 + 2*b36*b68 - 2*b36*b87 - 2*b87 + 2*b36*b89
- 4*b89 + 2*b37*b39 - 2*b39 + 2*b37*b91 + 2*b91 + 2*b38*b40 - 4*b40 + 2*
b38*b56 - 2*b56 + 2*b38*b90 - 4*b90 + 2*b39*b40 + 2*b39*b89 - 2*b39*b119
+ 2*b40*b41 + 2*b40*b103 + 2*b41*b74 - 2*b74 + 2*b41*b93 - 2*b93 - 2*b42*
b58 + 2*b42 - 2*b42*b75 - 2*b75 + 2*b42*b100 - 4*b100 - 2*b42*b102 + 2*b43
*b74 - 4*b43 + 2*b43*b100 + 2*b43*b129 + 2*b43*b142 + 2*b44*b45 - 2*b45 +
2*b44*b99 - 4*b99 + 2*b44*b138 + 2*b45*b100 + 2*b46*b47 - 2*b46 - 2*b47 +
2*b46*b144 + 2*b47*b59 - 2*b59 + 2*b47*b61 + 2*b61 - 2*b47*b134 + 2*b48*
b84 - 2*b84 - 2*b48*b148 + 2*b49*b64 - 2*b49 - 2*b64 + 2*b49*b66 - 2*b66
- 2*b49*b127 + 2*b49*b148 + 2*b50*b67 - 4*b67 - 2*b50*b141 + 2*b51*b66 -
4*b51 + 2*b51*b67 + 2*b51*b88 + 2*b51*b121 + 2*b52*b54 - 2*b54 + 2*b52*b89
- 2*b52*b149 + 2*b53*b55 - 4*b55 + 2*b53*b128 + 2*b54*b55 + 2*b54*b67 - 2
*b54*b105 + 2*b55*b119 + 2*b55*b146 + 2*b56*b104 + 2*b56*b105 - 2*b56*b137
- 2*b57*b94 - 2*b94 + 2*b57*b98 + 2*b57*b143 + 2*b58*b151 + 2*b59*b60 + 2
*b60*b62 - 2*b62 + 2*b60*b80 - 2*b80 - 2*b61*b108 - 2*b61*b123 - 2*b61*
b150 + 2*b62*b63 + 2*b63 - 2*b62*b112 + 2*b62*b150 - 2*b63*b64 - 2*b63*b83
- 2*b63*b117 + 2*b64*b65 - 2*b65 + 2*b64*b150 + 2*b65*b85 - 2*b85 + 2*b65
*b86 - 2*b86 - 2*b65*b124 - 2*b66*b132 + 2*b66*b149 + 2*b67*b69 - 2*b69 +
2*b68*b70 - 4*b70 + 2*b68*b126 + 2*b69*b70 + 2*b69*b105 - 2*b69*b153 + 2*
b70*b72 - 2*b72 + 2*b70*b115 - 2*b71*b73 + 2*b71 - 2*b73 - 2*b71*b91 + 2*
b71*b94 - 2*b71*b105 + 2*b72*b73 - 2*b72*b128 + 2*b72*b143 + 2*b73*b75 + 2
*b73*b136 + 2*b74*b76 - 2*b74*b118 + 2*b75*b76 + 2*b75*b118 + 2*b76*b78 +
2*b77*b79 - 2*b79 - 2*b77*b106 + 2*b78*b79 + 2*b78*b106 + 2*b80*b82 - 4*
b82 - 2*b81*b84 + 2*b81*b116 + 2*b82*b84 + 2*b82*b130 + 2*b82*b134 + 2*b83
*b144 - 2*b83*b147 + 2*b84*b147 + 2*b85*b122 - 2*b85*b123 + 2*b85*b147 + 2
*b86*b87 - 2*b86*b135 + 2*b86*b149 + 2*b87*b141 + 2*b87*b153 + 2*b88*b90
- 2*b88*b133 + 2*b89*b92 - 4*b92 + 2*b90*b92 + 2*b90*b153 - 2*b91*b93 - 2
*b91*b133 + 2*b92*b93 + 2*b92*b120 + 2*b93*b95 + 2*b94*b97 - 2*b97 + 2*b94
*b119 + 2*b95*b97 - 2*b95*b120 + 2*b96*b98 - 2*b96 + 2*b96*b99 - 2*b96*
b103 + 2*b96*b137 + 2*b97*b99 - 2*b97*b106 - 2*b98*b152 + 2*b99*b152 + 2*
b100*b101 - 2*b101 + 2*b101*b152 + 2*b102*b103 - 2*b102*b104 + 2*b102*b106
- 2*b103*b115 + 2*b104*b115 - 2*b104*b142 - 2*b107*b108 - 2*b107*b114 - 2
*b109*b110 + 2*b109*b121 - 2*b109*b131 + 2*b110*b114 - 2*b111*b112 + 2*
b111*b113 - 2*b113*b130 - 2*b115*b126 - 2*b116*b144 - 2*b117*b122 - 2*b118
*b119 + 2*b118*b120 - 2*b120*b128 - 2*b121*b122 - 2*b121*b125 + 2*b122*
b141 + 2*b124*b125 - 2*b126*b146 + 2*b128*b133 - 2*b129*b139 - 2*b131*b132
+ 2*b132*b145 + 2*b132*b148 + 2*b135*b145 - 2*b136*b137 - 2*b136*b138 + 2
*b137*b146 - 2*b140*b141 - 2*b142*b143 - 2*b143*b146 - 2*b145*b147 - 2*
b148*b150 - 2*b149*b153 - 2*b151*b152 + 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: 2024-12-17 Git hash: 8eaceb91