MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance: graphpart_2pm-0077-0777

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
Primal Bounds
-40.00000000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-40.00000004 (ANTIGONE)
-40.00000000 (BARON)
-40.00000000 (COUENNE)
-40.00000000 (LINDO)
-40.00000000 (SCIP)
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_2pm_77_777.dimacs
Application Graph Partitioning
Added to library 26 Feb 2014
Problem type BQP
#Variables 147
#Binary Variables 147
#Integer Variables 0
#Nonlinear Variables 147
#Nonlinear Binary Variables 147
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature indefinite
#Nonzeros in Objective 147
#Nonlinear Nonzeros in Objective 147
#Constraints 49
#Linear Constraints 49
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 147
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 588
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 49
Maximal blocksize in Hessian of Lagrangian 49
Average blocksize in Hessian of Lagrangian 49.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1
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
*         50       50        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        148        1      147        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        295      148      147        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,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,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;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50;


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..    b61 + b62 + b63 =E= 1;

e22..    b64 + b65 + b66 =E= 1;

e23..    b67 + b68 + b69 =E= 1;

e24..    b70 + b71 + b72 =E= 1;

e25..    b73 + b74 + b75 =E= 1;

e26..    b76 + b77 + b78 =E= 1;

e27..    b79 + b80 + b81 =E= 1;

e28..    b82 + b83 + b84 =E= 1;

e29..    b85 + b86 + b87 =E= 1;

e30..    b88 + b89 + b90 =E= 1;

e31..    b91 + b92 + b93 =E= 1;

e32..    b94 + b95 + b96 =E= 1;

e33..    b97 + b98 + b99 =E= 1;

e34..    b100 + b101 + b102 =E= 1;

e35..    b103 + b104 + b105 =E= 1;

e36..    b106 + b107 + b108 =E= 1;

e37..    b109 + b110 + b111 =E= 1;

e38..    b112 + b113 + b114 =E= 1;

e39..    b115 + b116 + b117 =E= 1;

e40..    b118 + b119 + b120 =E= 1;

e41..    b121 + b122 + b123 =E= 1;

e42..    b124 + b125 + b126 =E= 1;

e43..    b127 + b128 + b129 =E= 1;

e44..    b130 + b131 + b132 =E= 1;

e45..    b133 + b134 + b135 =E= 1;

e46..    b136 + b137 + b138 =E= 1;

e47..    b139 + b140 + b141 =E= 1;

e48..    b142 + b143 + b144 =E= 1;

e49..    b145 + b146 + b147 =E= 1;

e50.. b1*b4 - b1*b19 + b1*b22 - b1*b127 + b2*b5 - b2*b20 + b2*b23 - b2*b128 + 
      b3*b6 - b3*b21 + b3*b24 - b3*b129 - b4*b7 + b4*b25 + b4*b130 - b5*b8 + b5
      *b26 + b5*b131 - b6*b9 + b6*b27 + b6*b132 - b7*b10 - b7*b28 - b7*b133 - 
      b8*b11 - b8*b29 - b8*b134 - b9*b12 - b9*b30 - b9*b135 - b10*b13 + b10*b31
       + b10*b136 - b11*b14 + b11*b32 + b11*b137 - b12*b15 + b12*b33 + b12*b138
       + b13*b16 - b13*b34 + b13*b139 + b14*b17 - b14*b35 + b14*b140 + b15*b18
       - b15*b36 + b15*b141 + b16*b19 + b16*b37 - b16*b142 + b17*b20 + b17*b38
       - b17*b143 + b18*b21 + b18*b39 - b18*b144 + b19*b40 + b19*b145 + b20*b41
       + b20*b146 + b21*b42 + b21*b147 + b22*b25 + b22*b40 - b22*b43 + b23*b26
       + b23*b41 - b23*b44 + b24*b27 + b24*b42 - b24*b45 - b25*b28 - b25*b46 - 
      b26*b29 - b26*b47 - b27*b30 - b27*b48 + b28*b31 + b28*b49 + b29*b32 + b29
      *b50 + b30*b33 + b30*b51 + b31*b34 + b31*b52 + b32*b35 + b32*b53 + b33*
      b36 + b33*b54 + b34*b37 - b34*b55 + b35*b38 - b35*b56 + b36*b39 - b36*b57
       - b37*b40 + b37*b58 - b38*b41 + b38*b59 - b39*b42 + b39*b60 - b40*b61 - 
      b41*b62 - b42*b63 - b43*b46 - b43*b61 - b43*b64 - b44*b47 - b44*b62 - b44
      *b65 - b45*b48 - b45*b63 - b45*b66 - b46*b49 + b46*b67 - b47*b50 + b47*
      b68 - b48*b51 + b48*b69 - b49*b52 + b49*b70 - b50*b53 + b50*b71 - b51*b54
       + b51*b72 - b52*b55 + b52*b73 - b53*b56 + b53*b74 - b54*b57 + b54*b75 - 
      b55*b58 - b55*b76 - b56*b59 - b56*b77 - b57*b60 - b57*b78 + b58*b61 - b58
      *b79 + b59*b62 - b59*b80 + b60*b63 - b60*b81 + b61*b82 + b62*b83 + b63*
      b84 - b64*b67 + b64*b82 + b64*b85 - b65*b68 + b65*b83 + b65*b86 - b66*b69
       + b66*b84 + b66*b87 - b67*b70 - b67*b88 - b68*b71 - b68*b89 - b69*b72 - 
      b69*b90 + b70*b73 + b70*b91 + b71*b74 + b71*b92 + b72*b75 + b72*b93 + b73
      *b76 - b73*b94 + b74*b77 - b74*b95 + b75*b78 - b75*b96 - b76*b79 + b76*
      b97 - b77*b80 + b77*b98 - b78*b81 + b78*b99 + b79*b82 + b79*b100 + b80*
      b83 + b80*b101 + b81*b84 + b81*b102 - b82*b103 - b83*b104 - b84*b105 + 
      b85*b88 - b85*b103 + b85*b106 + b86*b89 - b86*b104 + b86*b107 + b87*b90
       - b87*b105 + b87*b108 - b88*b91 - b88*b109 - b89*b92 - b89*b110 - b90*
      b93 - b90*b111 + b91*b94 + b91*b112 + b92*b95 + b92*b113 + b93*b96 + b93*
      b114 - b94*b97 - b94*b115 - b95*b98 - b95*b116 - b96*b99 - b96*b117 - b97
      *b100 - b97*b118 - b98*b101 - b98*b119 - b99*b102 - b99*b120 - b100*b103
       - b100*b121 - b101*b104 - b101*b122 - b102*b105 - b102*b123 - b103*b124
       - b104*b125 - b105*b126 - b106*b109 - b106*b124 + b106*b127 - b107*b110
       - b107*b125 + b107*b128 - b108*b111 - b108*b126 + b108*b129 - b109*b112
       - b109*b130 - b110*b113 - b110*b131 - b111*b114 - b111*b132 + b112*b115
       + b112*b133 + b113*b116 + b113*b134 + b114*b117 + b114*b135 + b115*b118
       - b115*b136 + b116*b119 - b116*b137 + b117*b120 - b117*b138 - b118*b121
       + b118*b139 - b119*b122 + b119*b140 - b120*b123 + b120*b141 + b121*b124
       + b121*b142 + b122*b125 + b122*b143 + b123*b126 + b123*b144 - b124*b145
       - b125*b146 - b126*b147 - b127*b130 + b127*b145 - b128*b131 + b128*b146
       - b129*b132 + b129*b147 + b130*b133 + b131*b134 + b132*b135 - b133*b136
       - b134*b137 - b135*b138 + b136*b139 + b137*b140 + b138*b141 + b139*b142
       + b140*b143 + b141*b144 + b142*b145 + b143*b146 + b144*b147 - 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: 2018-09-14 Git hash: ac5a5314
Imprint / Privacy Policy