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Instance sporttournament12

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)ⓘ	68.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	68.00000007 (ANTIGONE) 68.00000007 (BARON) 68.00000000 (COUENNE) 68.00000064 (CPLEX) 68.00000000 (GUROBI) 68.00000000 (LINDO) 68.00000000 (SCIP) 68.00000000 (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-12-4711
Applicationⓘ	Sports Tournament
Added to libraryⓘ	26 Feb 2014
Problem typeⓘ	MBQCP
#Variablesⓘ	67
#Binary Variablesⓘ	66
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	66
#Nonlinear Binary Variablesⓘ	66
#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ⓘ	67
#Nonlinear Nonzeros in Jacobianⓘ	66
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	240
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	66
Maximal blocksize in Hessian of Lagrangianⓘ	66
Average blocksize in Hessian of Lagrangianⓘ	66.0
#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
*         67        1       66        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         67        1       66        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,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;

Equations  e1;


e1.. 2*b1*b16 - 2*b1 - 4*b16 + 2*b1*b48 + 2*b1*b49 - 2*b1*b54 + 2*b2*b4 - 2*b2
      - 2*b4 + 2*b2*b45 - 4*b45 + 2*b3*b8 - 2*b3 - 4*b8 + 2*b3*b38 - 2*b38 - 2*
     b3*b50 + 2*b3*b60 + 2*b4*b5 - 2*b5 + 2*b4*b10 - 4*b10 - 2*b4*b61 + 2*b5*
     b11 - 4*b11 + 2*b6*b7 - 2*b6 - 2*b7 + 2*b6*b13 - 2*b13 + 2*b7*b8 + 2*b7*
     b22 - 2*b22 - 2*b7*b63 + 2*b8*b9 - 4*b9 + 2*b8*b52 + 2*b9*b25 + 2*b25 + 2*
     b9*b36 - 2*b36 + 2*b9*b50 + 2*b10*b20 - 4*b20 + 2*b10*b30 - 2*b30 + 2*b10*
     b62 + 2*b11*b12 - 2*b12 + 2*b11*b19 - 4*b19 + 2*b11*b61 + 2*b12*b20 + 2*
     b13*b36 + 2*b13*b55 - 2*b13*b58 + 2*b14*b36 + 2*b14 - 2*b14*b55 - 2*b14*
     b60 - 2*b14*b64 + 2*b15*b16 + 2*b15 - 2*b15*b23 - 2*b23 - 2*b15*b56 - 2*
     b15*b65 + 2*b16*b17 - 2*b17 + 2*b16*b38 + 2*b17*b18 - 4*b18 + 2*b17*b27 - 
     2*b27 - 2*b17*b62 + 2*b18*b19 + 2*b18*b41 - 2*b41 + 2*b18*b61 + 2*b19*b32
      - 4*b32 + 2*b19*b42 - 2*b42 + 2*b20*b21 - 2*b21 + 2*b20*b31 - 2*b31 + 2*
     b21*b32 + 2*b22*b23 + 2*b22*b24 - 2*b24 - 2*b22*b57 + 2*b23*b26 - 2*b26 + 
     2*b23*b58 + 2*b24*b26 + 2*b24*b38 - 2*b24*b66 - 2*b25*b27 - 2*b25*b37 - 2*
     b37 - 2*b25*b59 + 2*b26*b27 - 2*b26*b54 + 2*b27*b29 - 4*b29 - 2*b28*b30 - 
     2*b28 + 2*b28*b49 + 2*b28*b56 + 2*b28*b59 + 2*b29*b30 + 2*b29*b40 - 2*b40
      + 2*b29*b62 + 2*b30*b31 + 2*b31*b44 - 2*b44 - 2*b31*b49 + 2*b32*b33 - 2*
     b33 + 2*b32*b43 - 2*b43 + 2*b33*b44 - 2*b34*b52 + 2*b34 - 2*b34*b57 - 2*
     b35*b53 + 2*b35 - 2*b35*b58 + 2*b35*b64 - 2*b35*b66 - 2*b36*b65 + 2*b37*
     b39 - 4*b39 + 2*b37*b58 + 2*b37*b60 - 2*b38*b40 + 2*b39*b40 + 2*b39*b54 + 
     2*b39*b65 + 2*b40*b41 + 2*b41*b42 - 2*b41*b59 + 2*b42*b43 - 2*b42*b51 + 2*
     b43*b45 - 2*b43*b48 + 2*b44*b46 - 2*b46 - 2*b44*b47 + 2*b45*b46 + 2*b45*
     b47 + 2*b47*b48 - 2*b47*b49 - 2*b48*b51 - 2*b50*b56 + 2*b50*b59 + 2*b51*
     b54 + 2*b51*b56 + 2*b52*b53 - 2*b52*b60 + 2*b57*b63 + 2*b57*b66 - 2*b61*
     b62 + 2*b65*b66 + 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;