MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics

Instance graphpart_2g-0044-1601

This is a quadratic model for the graph partitioning problem. The
graphs are taken from the publication of Ghaddar et al. We used 3
parts of the partition to generate the quadratic instances. The model
assigns each node to one of the three parts. Hence, the model is
symmetric, which should probably be used in a solution algorithm.

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	-954077.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-954077.00100000 (ANTIGONE) -954077.00000000 (BARON) -954077.00000000 (COUENNE) -954077.00000000 (CPLEX) -954077.00000000 (GUROBI) -954077.00000000 (LINDO) -954077.00000000 (SCIP) -954077.00000000 (SHOT)
Referencesⓘ	Ghaddar, Bissan, Anjos, Miguel F, and Liers, Frauke, A Branch-and-Cut Algorithm based on Semidefinite Programming for the Minimum k-Partition Problem, Annals of Operations Research, 188:1, 2011, 155-174.
Sourceⓘ	POLIP instance graphpart/data_2g_44_1601.dimacs
Applicationⓘ	Graph Partitioning
Added to libraryⓘ	26 Feb 2014
Problem typeⓘ	BQP
#Variablesⓘ	48
#Binary Variablesⓘ	48
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	48
#Nonlinear Binary Variablesⓘ	48
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	48
#Nonlinear Nonzeros in Objectiveⓘ	48
#Constraintsⓘ	16
#Linear Constraintsⓘ	16
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	linear
#Nonzeros in Jacobianⓘ	48
#Nonlinear Nonzeros in Jacobianⓘ	0
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	192
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	3
Minimal blocksize in Hessian of Lagrangianⓘ	16
Maximal blocksize in Hessian of Lagrangianⓘ	16
Average blocksize in Hessian of Lagrangianⓘ	16.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.7850e+05
Infeasibility of initial pointⓘ	1
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         17       17        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         49        1       48        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         97       49       48        0
*
*  Solve m using MINLP minimizing 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,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;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17;


e1..    b1 + b2 + b3 =E= 1;

e2..    b4 + b5 + b6 =E= 1;

e3..    b7 + b8 + b9 =E= 1;

e4..    b10 + b11 + b12 =E= 1;

e5..    b13 + b14 + b15 =E= 1;

e6..    b16 + b17 + b18 =E= 1;

e7..    b19 + b20 + b21 =E= 1;

e8..    b22 + b23 + b24 =E= 1;

e9..    b25 + b26 + b27 =E= 1;

e10..    b28 + b29 + b30 =E= 1;

e11..    b31 + b32 + b33 =E= 1;

e12..    b34 + b35 + b36 =E= 1;

e13..    b37 + b38 + b39 =E= 1;

e14..    b40 + b41 + b42 =E= 1;

e15..    b43 + b44 + b45 =E= 1;

e16..    b46 + b47 + b48 =E= 1;

e17.. 13960*b1*b4 + 132180*b1*b10 - 45455*b1*b13 + 21397*b1*b37 + 13960*b2*b5
       + 132180*b2*b11 - 45455*b2*b14 + 21397*b2*b38 + 13960*b3*b6 + 132180*b3*
      b12 - 45455*b3*b15 + 21397*b3*b39 - 30411*b4*b7 - 101527*b4*b16 - 8896*b4
      *b40 - 30411*b5*b8 - 101527*b5*b17 - 8896*b5*b41 - 30411*b6*b9 - 101527*
      b6*b18 - 8896*b6*b42 - 122332*b7*b10 + 30058*b7*b19 + 33114*b7*b43 - 
      122332*b8*b11 + 30058*b8*b20 + 33114*b8*b44 - 122332*b9*b12 + 30058*b9*
      b21 + 33114*b9*b45 - 13676*b10*b22 + 124553*b10*b46 - 13676*b11*b23 + 
      124553*b11*b47 - 13676*b12*b24 + 124553*b12*b48 + 17153*b13*b16 + 73691*
      b13*b22 - 32022*b13*b25 + 17153*b14*b17 + 73691*b14*b23 - 32022*b14*b26
       + 17153*b15*b18 + 73691*b15*b24 - 32022*b15*b27 - 106129*b16*b19 - 
      101395*b16*b28 - 106129*b17*b20 - 101395*b17*b29 - 106129*b18*b21 - 
      101395*b18*b30 - 10958*b19*b22 - 41751*b19*b31 - 10958*b20*b23 - 41751*
      b20*b32 - 10958*b21*b24 - 41751*b21*b33 - 30446*b22*b34 - 30446*b23*b35
       - 30446*b24*b36 + 94519*b25*b28 + 44613*b25*b34 + 70141*b25*b37 + 94519*
      b26*b29 + 44613*b26*b35 + 70141*b26*b38 + 94519*b27*b30 + 44613*b27*b36
       + 70141*b27*b39 + 73611*b28*b31 - 54792*b28*b40 + 73611*b29*b32 - 54792*
      b29*b41 + 73611*b30*b33 - 54792*b30*b42 + 57663*b31*b34 - 147596*b31*b43
       + 57663*b32*b35 - 147596*b32*b44 + 57663*b33*b36 - 147596*b33*b45 + 
      70863*b34*b46 + 70863*b35*b47 + 70863*b36*b48 + 24474*b37*b40 - 178500*
      b37*b46 + 24474*b38*b41 - 178500*b38*b47 + 24474*b39*b42 - 178500*b39*b48
       + 118713*b40*b43 + 118713*b41*b44 + 118713*b42*b45 + 34279*b43*b46 + 
      34279*b44*b47 + 34279*b45*b48 - objvar =E= 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% minimizing objvar;