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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance graphpart_clique-20
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)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 146.99999990 (ANTIGONE) 147.00000000 (BARON) 147.00000000 (COUENNE) 147.00000000 (CPLEX) 147.00000000 (GUROBI) 147.00000000 (LINDO) 147.00000000 (SCIP) 147.00000000 (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_clique_20.dimacs |
| Applicationⓘ | Graph Partitioning |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | BQP |
| #Variablesⓘ | 60 |
| #Binary Variablesⓘ | 60 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 60 |
| #Nonlinear Binary Variablesⓘ | 60 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | indefinite |
| #Nonzeros in Objectiveⓘ | 60 |
| #Nonlinear Nonzeros in Objectiveⓘ | 60 |
| #Constraintsⓘ | 20 |
| #Linear Constraintsⓘ | 20 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 60 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 1140 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 20 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 20 |
| Average blocksize in Hessian of Lagrangianⓘ | 20.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 1.9000e+01 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 21 21 0 0 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 61 1 60 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 121 61 60 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,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,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;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21;
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.. b49 + b50 + b51 =E= 1;
e18.. b52 + b53 + b54 =E= 1;
e19.. b55 + b56 + b57 =E= 1;
e20.. b58 + b59 + b60 =E= 1;
e21.. b1*b4 + 2*b1*b7 + 3*b1*b10 + 4*b1*b13 + 5*b1*b16 + 6*b1*b19 + 7*b1*b22 +
8*b1*b25 + 9*b1*b28 + 10*b1*b31 + 11*b1*b34 + 12*b1*b37 + 13*b1*b40 + 14*
b1*b43 + 15*b1*b46 + 16*b1*b49 + 17*b1*b52 + 18*b1*b55 + 19*b1*b58 + b2*
b5 + 2*b2*b8 + 3*b2*b11 + 4*b2*b14 + 5*b2*b17 + 6*b2*b20 + 7*b2*b23 + 8*
b2*b26 + 9*b2*b29 + 10*b2*b32 + 11*b2*b35 + 12*b2*b38 + 13*b2*b41 + 14*b2
*b44 + 15*b2*b47 + 16*b2*b50 + 17*b2*b53 + 18*b2*b56 + 19*b2*b59 + b3*b6
+ 2*b3*b9 + 3*b3*b12 + 4*b3*b15 + 5*b3*b18 + 6*b3*b21 + 7*b3*b24 + 8*b3*
b27 + 9*b3*b30 + 10*b3*b33 + 11*b3*b36 + 12*b3*b39 + 13*b3*b42 + 14*b3*
b45 + 15*b3*b48 + 16*b3*b51 + 17*b3*b54 + 18*b3*b57 + 19*b3*b60 + b4*b7
+ 2*b4*b10 + 3*b4*b13 + 4*b4*b16 + 5*b4*b19 + 6*b4*b22 + 7*b4*b25 + 8*b4
*b28 + 9*b4*b31 + 10*b4*b34 + 11*b4*b37 + 12*b4*b40 + 13*b4*b43 + 14*b4*
b46 + 15*b4*b49 + 16*b4*b52 + 17*b4*b55 + 18*b4*b58 + b5*b8 + 2*b5*b11 +
3*b5*b14 + 4*b5*b17 + 5*b5*b20 + 6*b5*b23 + 7*b5*b26 + 8*b5*b29 + 9*b5*
b32 + 10*b5*b35 + 11*b5*b38 + 12*b5*b41 + 13*b5*b44 + 14*b5*b47 + 15*b5*
b50 + 16*b5*b53 + 17*b5*b56 + 18*b5*b59 + b6*b9 + 2*b6*b12 + 3*b6*b15 + 4
*b6*b18 + 5*b6*b21 + 6*b6*b24 + 7*b6*b27 + 8*b6*b30 + 9*b6*b33 + 10*b6*
b36 + 11*b6*b39 + 12*b6*b42 + 13*b6*b45 + 14*b6*b48 + 15*b6*b51 + 16*b6*
b54 + 17*b6*b57 + 18*b6*b60 + b7*b10 + 2*b7*b13 + 3*b7*b16 + 4*b7*b19 + 5
*b7*b22 + 6*b7*b25 + 7*b7*b28 + 8*b7*b31 + 9*b7*b34 + 10*b7*b37 + 11*b7*
b40 + 12*b7*b43 + 13*b7*b46 + 14*b7*b49 + 15*b7*b52 + 16*b7*b55 + 17*b7*
b58 + b8*b11 + 2*b8*b14 + 3*b8*b17 + 4*b8*b20 + 5*b8*b23 + 6*b8*b26 + 7*
b8*b29 + 8*b8*b32 + 9*b8*b35 + 10*b8*b38 + 11*b8*b41 + 12*b8*b44 + 13*b8*
b47 + 14*b8*b50 + 15*b8*b53 + 16*b8*b56 + 17*b8*b59 + b9*b12 + 2*b9*b15
+ 3*b9*b18 + 4*b9*b21 + 5*b9*b24 + 6*b9*b27 + 7*b9*b30 + 8*b9*b33 + 9*b9
*b36 + 10*b9*b39 + 11*b9*b42 + 12*b9*b45 + 13*b9*b48 + 14*b9*b51 + 15*b9*
b54 + 16*b9*b57 + 17*b9*b60 + b10*b13 + 2*b10*b16 + 3*b10*b19 + 4*b10*b22
+ 5*b10*b25 + 6*b10*b28 + 7*b10*b31 + 8*b10*b34 + 9*b10*b37 + 10*b10*b40
+ 11*b10*b43 + 12*b10*b46 + 13*b10*b49 + 14*b10*b52 + 15*b10*b55 + 16*
b10*b58 + b11*b14 + 2*b11*b17 + 3*b11*b20 + 4*b11*b23 + 5*b11*b26 + 6*b11
*b29 + 7*b11*b32 + 8*b11*b35 + 9*b11*b38 + 10*b11*b41 + 11*b11*b44 + 12*
b11*b47 + 13*b11*b50 + 14*b11*b53 + 15*b11*b56 + 16*b11*b59 + b12*b15 + 2
*b12*b18 + 3*b12*b21 + 4*b12*b24 + 5*b12*b27 + 6*b12*b30 + 7*b12*b33 + 8*
b12*b36 + 9*b12*b39 + 10*b12*b42 + 11*b12*b45 + 12*b12*b48 + 13*b12*b51
+ 14*b12*b54 + 15*b12*b57 + 16*b12*b60 + b13*b16 + 2*b13*b19 + 3*b13*b22
+ 4*b13*b25 + 5*b13*b28 + 6*b13*b31 + 7*b13*b34 + 8*b13*b37 + 9*b13*b40
+ 10*b13*b43 + 11*b13*b46 + 12*b13*b49 + 13*b13*b52 + 14*b13*b55 + 15*
b13*b58 + b14*b17 + 2*b14*b20 + 3*b14*b23 + 4*b14*b26 + 5*b14*b29 + 6*b14
*b32 + 7*b14*b35 + 8*b14*b38 + 9*b14*b41 + 10*b14*b44 + 11*b14*b47 + 12*
b14*b50 + 13*b14*b53 + 14*b14*b56 + 15*b14*b59 + b15*b18 + 2*b15*b21 + 3*
b15*b24 + 4*b15*b27 + 5*b15*b30 + 6*b15*b33 + 7*b15*b36 + 8*b15*b39 + 9*
b15*b42 + 10*b15*b45 + 11*b15*b48 + 12*b15*b51 + 13*b15*b54 + 14*b15*b57
+ 15*b15*b60 + b16*b19 + 2*b16*b22 + 3*b16*b25 + 4*b16*b28 + 5*b16*b31
+ 6*b16*b34 + 7*b16*b37 + 8*b16*b40 + 9*b16*b43 + 10*b16*b46 + 11*b16*
b49 + 12*b16*b52 + 13*b16*b55 + 14*b16*b58 + b17*b20 + 2*b17*b23 + 3*b17*
b26 + 4*b17*b29 + 5*b17*b32 + 6*b17*b35 + 7*b17*b38 + 8*b17*b41 + 9*b17*
b44 + 10*b17*b47 + 11*b17*b50 + 12*b17*b53 + 13*b17*b56 + 14*b17*b59 +
b18*b21 + 2*b18*b24 + 3*b18*b27 + 4*b18*b30 + 5*b18*b33 + 6*b18*b36 + 7*
b18*b39 + 8*b18*b42 + 9*b18*b45 + 10*b18*b48 + 11*b18*b51 + 12*b18*b54 +
13*b18*b57 + 14*b18*b60 + b19*b22 + 2*b19*b25 + 3*b19*b28 + 4*b19*b31 + 5
*b19*b34 + 6*b19*b37 + 7*b19*b40 + 8*b19*b43 + 9*b19*b46 + 10*b19*b49 +
11*b19*b52 + 12*b19*b55 + 13*b19*b58 + b20*b23 + 2*b20*b26 + 3*b20*b29 +
4*b20*b32 + 5*b20*b35 + 6*b20*b38 + 7*b20*b41 + 8*b20*b44 + 9*b20*b47 +
10*b20*b50 + 11*b20*b53 + 12*b20*b56 + 13*b20*b59 + b21*b24 + 2*b21*b27
+ 3*b21*b30 + 4*b21*b33 + 5*b21*b36 + 6*b21*b39 + 7*b21*b42 + 8*b21*b45
+ 9*b21*b48 + 10*b21*b51 + 11*b21*b54 + 12*b21*b57 + 13*b21*b60 + b22*
b25 + 2*b22*b28 + 3*b22*b31 + 4*b22*b34 + 5*b22*b37 + 6*b22*b40 + 7*b22*
b43 + 8*b22*b46 + 9*b22*b49 + 10*b22*b52 + 11*b22*b55 + 12*b22*b58 + b23*
b26 + 2*b23*b29 + 3*b23*b32 + 4*b23*b35 + 5*b23*b38 + 6*b23*b41 + 7*b23*
b44 + 8*b23*b47 + 9*b23*b50 + 10*b23*b53 + 11*b23*b56 + 12*b23*b59 + b24*
b27 + 2*b24*b30 + 3*b24*b33 + 4*b24*b36 + 5*b24*b39 + 6*b24*b42 + 7*b24*
b45 + 8*b24*b48 + 9*b24*b51 + 10*b24*b54 + 11*b24*b57 + 12*b24*b60 + b25*
b28 + 2*b25*b31 + 3*b25*b34 + 4*b25*b37 + 5*b25*b40 + 6*b25*b43 + 7*b25*
b46 + 8*b25*b49 + 9*b25*b52 + 10*b25*b55 + 11*b25*b58 + b26*b29 + 2*b26*
b32 + 3*b26*b35 + 4*b26*b38 + 5*b26*b41 + 6*b26*b44 + 7*b26*b47 + 8*b26*
b50 + 9*b26*b53 + 10*b26*b56 + 11*b26*b59 + b27*b30 + 2*b27*b33 + 3*b27*
b36 + 4*b27*b39 + 5*b27*b42 + 6*b27*b45 + 7*b27*b48 + 8*b27*b51 + 9*b27*
b54 + 10*b27*b57 + 11*b27*b60 + b28*b31 + 2*b28*b34 + 3*b28*b37 + 4*b28*
b40 + 5*b28*b43 + 6*b28*b46 + 7*b28*b49 + 8*b28*b52 + 9*b28*b55 + 10*b28*
b58 + b29*b32 + 2*b29*b35 + 3*b29*b38 + 4*b29*b41 + 5*b29*b44 + 6*b29*b47
+ 7*b29*b50 + 8*b29*b53 + 9*b29*b56 + 10*b29*b59 + b30*b33 + 2*b30*b36
+ 3*b30*b39 + 4*b30*b42 + 5*b30*b45 + 6*b30*b48 + 7*b30*b51 + 8*b30*b54
+ 9*b30*b57 + 10*b30*b60 + b31*b34 + 2*b31*b37 + 3*b31*b40 + 4*b31*b43
+ 5*b31*b46 + 6*b31*b49 + 7*b31*b52 + 8*b31*b55 + 9*b31*b58 + b32*b35 +
2*b32*b38 + 3*b32*b41 + 4*b32*b44 + 5*b32*b47 + 6*b32*b50 + 7*b32*b53 + 8
*b32*b56 + 9*b32*b59 + b33*b36 + 2*b33*b39 + 3*b33*b42 + 4*b33*b45 + 5*
b33*b48 + 6*b33*b51 + 7*b33*b54 + 8*b33*b57 + 9*b33*b60 + b34*b37 + 2*b34
*b40 + 3*b34*b43 + 4*b34*b46 + 5*b34*b49 + 6*b34*b52 + 7*b34*b55 + 8*b34*
b58 + b35*b38 + 2*b35*b41 + 3*b35*b44 + 4*b35*b47 + 5*b35*b50 + 6*b35*b53
+ 7*b35*b56 + 8*b35*b59 + b36*b39 + 2*b36*b42 + 3*b36*b45 + 4*b36*b48 +
5*b36*b51 + 6*b36*b54 + 7*b36*b57 + 8*b36*b60 + b37*b40 + 2*b37*b43 + 3*
b37*b46 + 4*b37*b49 + 5*b37*b52 + 6*b37*b55 + 7*b37*b58 + b38*b41 + 2*b38
*b44 + 3*b38*b47 + 4*b38*b50 + 5*b38*b53 + 6*b38*b56 + 7*b38*b59 + b39*
b42 + 2*b39*b45 + 3*b39*b48 + 4*b39*b51 + 5*b39*b54 + 6*b39*b57 + 7*b39*
b60 + b40*b43 + 2*b40*b46 + 3*b40*b49 + 4*b40*b52 + 5*b40*b55 + 6*b40*b58
+ b41*b44 + 2*b41*b47 + 3*b41*b50 + 4*b41*b53 + 5*b41*b56 + 6*b41*b59 +
b42*b45 + 2*b42*b48 + 3*b42*b51 + 4*b42*b54 + 5*b42*b57 + 6*b42*b60 + b43
*b46 + 2*b43*b49 + 3*b43*b52 + 4*b43*b55 + 5*b43*b58 + b44*b47 + 2*b44*
b50 + 3*b44*b53 + 4*b44*b56 + 5*b44*b59 + b45*b48 + 2*b45*b51 + 3*b45*b54
+ 4*b45*b57 + 5*b45*b60 + b46*b49 + 2*b46*b52 + 3*b46*b55 + 4*b46*b58 +
b47*b50 + 2*b47*b53 + 3*b47*b56 + 4*b47*b59 + b48*b51 + 2*b48*b54 + 3*b48
*b57 + 4*b48*b60 + b49*b52 + 2*b49*b55 + 3*b49*b58 + b50*b53 + 2*b50*b56
+ 3*b50*b59 + b51*b54 + 2*b51*b57 + 3*b51*b60 + b52*b55 + 2*b52*b58 +
b53*b56 + 2*b53*b59 + b54*b57 + 2*b54*b60 + b55*b58 + b56*b59 + b57*b60
- 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;
Last updated: 2024-08-26 Git hash: 6cc1607f