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Instance sporttournament06

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)
12.00000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
12.00000001 (ANTIGONE)
12.00000002 (BARON)
12.00000000 (COUENNE)
12.00000026 (CPLEX)
12.00000000 (GUROBI)
12.00000000 (LINDO)
12.00000000 (SCIP)
12.00000000 (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-6-4711
Application Sports Tournament
Added to library 26 Feb 2014
Problem type MBQCP
#Variables 16
#Binary Variables 15
#Integer Variables 0
#Nonlinear Variables 15
#Nonlinear Binary Variables 15
#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 16
#Nonlinear Nonzeros in Jacobian 15
#Nonzeros in (Upper-Left) Hessian of Lagrangian 48
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 15
Maximal blocksize in Hessian of Lagrangian 15
Average blocksize in Hessian of Lagrangian 15.0
#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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of 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
*         16        1       15        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         16        1       15        0
*
*  Solve m using MINLP maximizing objvar;


Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,objvar;

Binary Variables  b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15;

Equations  e1;


e1.. 2*b1*b3 - 2*b1 + 2*b3 + 2*b1*b7 - 2*b7 + 2*b2*b5 - 2*b2 - 2*b5 + 2*b2*b10
      - 4*b10 - 2*b3*b4 + 2*b4 - 2*b3*b12 - 2*b3*b14 - 2*b4*b5 + 2*b4*b9 - 2*b9
      - 2*b4*b15 + 2*b5*b6 - 2*b6 + 2*b5*b8 - 2*b8 + 2*b6*b9 - 2*b7*b8 + 2*b7*
     b12 + 2*b7*b13 + 2*b8*b10 + 2*b8*b15 + 2*b9*b11 - 2*b11 - 2*b9*b12 + 2*b10
     *b11 + 2*b10*b12 - 2*b13*b15 + 2*b14*b15 + 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: 2022-10-14 Git hash: 2be6d7c0
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