MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: graphpart_3g-0344-0344

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
-5267631.00000000 p1 ( gdx sol )
(infeas: 0)
-5301516.00000000 p2 ( gdx sol )
(infeas: 0)
Dual Bounds
-5301516.00500000 (ANTIGONE)
-5301516.00000000 (BARON)
-5301516.00000000 (COUENNE)
-5301516.00000000 (LINDO)
-5301516.00000000 (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_3g_344_344.dimacs
Application Graph Partitioning
Added to library 26 Feb 2014
Problem type BQP
#Variables 144
#Binary Variables 144
#Integer Variables 0
#Nonlinear Variables 144
#Nonlinear Binary Variables 144
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature indefinite
#Nonzeros in Objective 144
#Nonlinear Nonzeros in Objective 144
#Constraints 48
#Linear Constraints 48
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 144
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 864
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 48
Maximal blocksize in Hessian of Lagrangian 48
Average blocksize in Hessian of Lagrangian 48.0
#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
*         49       49        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        145        1      144        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        289      145      144        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,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;

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;


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.. 37177*b1*b10 - 123362*b1*b4 + 135068*b1*b13 - 10174*b1*b25 + 112363*b1*
      b37 - 174059*b1*b109 - 123362*b2*b5 + 37177*b2*b11 + 135068*b2*b14 - 
      10174*b2*b26 + 112363*b2*b38 - 174059*b2*b110 - 123362*b3*b6 + 37177*b3*
      b12 + 135068*b3*b15 - 10174*b3*b27 + 112363*b3*b39 - 174059*b3*b111 + 
      1496*b4*b7 - 86083*b4*b16 + 116754*b4*b28 - 135325*b4*b40 - 78283*b4*b112
       + 1496*b5*b8 - 86083*b5*b17 + 116754*b5*b29 - 135325*b5*b41 - 78283*b5*
      b113 + 1496*b6*b9 - 86083*b6*b18 + 116754*b6*b30 - 135325*b6*b42 - 78283*
      b6*b114 + 167165*b7*b10 + 48311*b7*b19 + 168758*b7*b31 - 19619*b7*b43 + 
      43825*b7*b115 + 167165*b8*b11 + 48311*b8*b20 + 168758*b8*b32 - 19619*b8*
      b44 + 43825*b8*b116 + 167165*b9*b12 + 48311*b9*b21 + 168758*b9*b33 - 
      19619*b9*b45 + 43825*b9*b117 + 40689*b10*b22 + 27673*b10*b34 + 20805*b10*
      b46 + 45651*b10*b118 + 40689*b11*b23 + 27673*b11*b35 + 20805*b11*b47 + 
      45651*b11*b119 + 40689*b12*b24 + 27673*b12*b36 + 20805*b12*b48 + 45651*
      b12*b120 - 109255*b13*b16 - 119367*b13*b22 + 20179*b13*b25 - 25440*b13*
      b49 + 248492*b13*b121 - 109255*b14*b17 - 119367*b14*b23 + 20179*b14*b26
       - 25440*b14*b50 + 248492*b14*b122 - 109255*b15*b18 - 119367*b15*b24 + 
      20179*b15*b27 - 25440*b15*b51 + 248492*b15*b123 + 46814*b16*b19 + 51470*
      b16*b28 + 80578*b16*b52 + 3701*b16*b124 + 46814*b17*b20 + 51470*b17*b29
       + 80578*b17*b53 + 3701*b17*b125 + 46814*b18*b21 + 51470*b18*b30 + 80578*
      b18*b54 + 3701*b18*b126 + 80772*b19*b22 + 147754*b19*b31 + 175164*b19*b55
       - 1841*b19*b127 + 80772*b20*b23 + 147754*b20*b32 + 175164*b20*b56 - 1841
      *b20*b128 + 80772*b21*b24 + 147754*b21*b33 + 175164*b21*b57 - 1841*b21*
      b129 + 55808*b22*b34 - 217714*b22*b58 + 103147*b22*b130 + 55808*b23*b35
       - 217714*b23*b59 + 103147*b23*b131 + 55808*b24*b36 - 217714*b24*b60 + 
      103147*b24*b132 - 61931*b25*b28 - 88108*b25*b34 - 130441*b25*b61 + 3699*
      b25*b133 - 61931*b26*b29 - 88108*b26*b35 - 130441*b26*b62 + 3699*b26*b134
       - 61931*b27*b30 - 88108*b27*b36 - 130441*b27*b63 + 3699*b27*b135 + 
      100468*b28*b31 - 77669*b28*b64 - 186268*b28*b136 + 100468*b29*b32 - 77669
      *b29*b65 - 186268*b29*b137 + 100468*b30*b33 - 77669*b30*b66 - 186268*b30*
      b138 - 128480*b31*b34 - 110381*b31*b67 - 157818*b31*b139 - 128480*b32*b35
       - 110381*b32*b68 - 157818*b32*b140 - 128480*b33*b36 - 110381*b33*b69 - 
      157818*b33*b141 + 25177*b34*b70 - 66379*b34*b142 + 25177*b35*b71 - 66379*
      b35*b143 + 25177*b36*b72 - 66379*b36*b144 + 50456*b37*b40 + 26576*b37*b46
       - 45705*b37*b49 + 79590*b37*b61 - 3381*b37*b73 + 50456*b38*b41 + 26576*
      b38*b47 - 45705*b38*b50 + 79590*b38*b62 - 3381*b38*b74 + 50456*b39*b42 + 
      26576*b39*b48 - 45705*b39*b51 + 79590*b39*b63 - 3381*b39*b75 - 114651*b40
      *b43 - 105547*b40*b52 - 92459*b40*b64 - 85605*b40*b76 - 114651*b41*b44 - 
      105547*b41*b53 - 92459*b41*b65 - 85605*b41*b77 - 114651*b42*b45 - 105547*
      b42*b54 - 92459*b42*b66 - 85605*b42*b78 + 60686*b43*b46 + 35436*b43*b55
       + 36881*b43*b67 + 63966*b43*b79 + 60686*b44*b47 + 35436*b44*b56 + 36881*
      b44*b68 + 63966*b44*b80 + 60686*b45*b48 + 35436*b45*b57 + 36881*b45*b69
       + 63966*b45*b81 + 98324*b46*b58 - 142437*b46*b70 - 113425*b46*b82 + 
      98324*b47*b59 - 142437*b47*b71 - 113425*b47*b83 + 98324*b48*b60 - 142437*
      b48*b72 - 113425*b48*b84 - 182685*b49*b52 - 72416*b49*b58 - 17870*b49*b61
       + 98276*b49*b85 - 182685*b50*b53 - 72416*b50*b59 - 17870*b50*b62 + 98276
      *b50*b86 - 182685*b51*b54 - 72416*b51*b60 - 17870*b51*b63 + 98276*b51*b87
       - 273533*b52*b55 - 241208*b52*b64 - 49346*b52*b88 - 273533*b53*b56 - 
      241208*b53*b65 - 49346*b53*b89 - 273533*b54*b57 - 241208*b54*b66 - 49346*
      b54*b90 - 64316*b55*b58 - 135240*b55*b67 - 180528*b55*b91 - 64316*b56*b59
       - 135240*b56*b68 - 180528*b56*b92 - 64316*b57*b60 - 135240*b57*b69 - 
      180528*b57*b93 + 91874*b58*b70 - 3696*b58*b94 + 91874*b59*b71 - 3696*b59*
      b95 + 91874*b60*b72 - 3696*b60*b96 - 40119*b61*b64 + 122867*b61*b70 - 
      61997*b61*b97 - 40119*b62*b65 + 122867*b62*b71 - 61997*b62*b98 - 40119*
      b63*b66 + 122867*b63*b72 - 61997*b63*b99 - 37348*b64*b67 + 175208*b64*
      b100 - 37348*b65*b68 + 175208*b65*b101 - 37348*b66*b69 + 175208*b66*b102
       - 22393*b67*b70 - 14921*b67*b103 - 22393*b68*b71 - 14921*b68*b104 - 
      22393*b69*b72 - 14921*b69*b105 - 601*b70*b106 - 601*b71*b107 - 601*b72*
      b108 - 76681*b73*b76 + 12689*b73*b82 + 208440*b73*b85 - 27358*b73*b97 - 
      73618*b73*b109 - 76681*b74*b77 + 12689*b74*b83 + 208440*b74*b86 - 27358*
      b74*b98 - 73618*b74*b110 - 76681*b75*b78 + 12689*b75*b84 + 208440*b75*b87
       - 27358*b75*b99 - 73618*b75*b111 + 21498*b76*b79 + 46551*b76*b88 + 
      150817*b76*b100 - 15190*b76*b112 + 21498*b77*b80 + 46551*b77*b89 + 150817
      *b77*b101 - 15190*b77*b113 + 21498*b78*b81 + 46551*b78*b90 + 150817*b78*
      b102 - 15190*b78*b114 + 28754*b79*b82 - 106952*b79*b91 - 65156*b79*b103
       + 70131*b79*b115 + 28754*b80*b83 - 106952*b80*b92 - 65156*b80*b104 + 
      70131*b80*b116 + 28754*b81*b84 - 106952*b81*b93 - 65156*b81*b105 + 70131*
      b81*b117 + 32192*b82*b94 - 81667*b82*b106 - 72237*b82*b118 + 32192*b83*
      b95 - 81667*b83*b107 - 72237*b83*b119 + 32192*b84*b96 - 81667*b84*b108 - 
      72237*b84*b120 + 28857*b85*b88 - 21532*b85*b94 + 34081*b85*b97 + 217807*
      b85*b121 + 28857*b86*b89 - 21532*b86*b95 + 34081*b86*b98 + 217807*b86*
      b122 + 28857*b87*b90 - 21532*b87*b96 + 34081*b87*b99 + 217807*b87*b123 - 
      14063*b88*b91 - 32891*b88*b100 + 150197*b88*b124 - 14063*b89*b92 - 32891*
      b89*b101 + 150197*b89*b125 - 14063*b90*b93 - 32891*b90*b102 + 150197*b90*
      b126 - 8558*b91*b94 - 186729*b91*b103 + 15271*b91*b127 - 8558*b92*b95 - 
      186729*b92*b104 + 15271*b92*b128 - 8558*b93*b96 - 186729*b93*b105 + 15271
      *b93*b129 + 99216*b94*b106 + 17426*b94*b130 + 99216*b95*b107 + 17426*b95*
      b131 + 99216*b96*b108 + 17426*b96*b132 - 84666*b97*b100 + 6362*b97*b106
       - 50758*b97*b133 - 84666*b98*b101 + 6362*b98*b107 - 50758*b98*b134 - 
      84666*b99*b102 + 6362*b99*b108 - 50758*b99*b135 - 69658*b100*b103 - 
      124701*b100*b136 - 69658*b101*b104 - 124701*b101*b137 - 69658*b102*b105
       - 124701*b102*b138 - 51670*b103*b106 - 271413*b103*b139 - 51670*b104*
      b107 - 271413*b104*b140 - 51670*b105*b108 - 271413*b105*b141 + 32359*b106
      *b142 + 32359*b107*b143 + 32359*b108*b144 + 26315*b109*b112 - 173269*b109
      *b118 - 81930*b109*b121 + 77066*b109*b133 + 26315*b110*b113 - 173269*b110
      *b119 - 81930*b110*b122 + 77066*b110*b134 + 26315*b111*b114 - 173269*b111
      *b120 - 81930*b111*b123 + 77066*b111*b135 + 185719*b112*b115 + 48690*b112
      *b124 - 73445*b112*b136 + 185719*b113*b116 + 48690*b113*b125 - 73445*b113
      *b137 + 185719*b114*b117 + 48690*b114*b126 - 73445*b114*b138 - 69569*b115
      *b118 + 128748*b115*b127 + 72205*b115*b139 - 69569*b116*b119 + 128748*
      b116*b128 + 72205*b116*b140 - 69569*b117*b120 + 128748*b117*b129 + 72205*
      b117*b141 + 18784*b118*b130 + 123614*b118*b142 + 18784*b119*b131 + 123614
      *b119*b143 + 18784*b120*b132 + 123614*b120*b144 - 202564*b121*b124 + 
      48234*b121*b130 + 50091*b121*b133 - 202564*b122*b125 + 48234*b122*b131 + 
      50091*b122*b134 - 202564*b123*b126 + 48234*b123*b132 + 50091*b123*b135 + 
      96700*b124*b127 + 9225*b124*b136 + 96700*b125*b128 + 9225*b125*b137 + 
      96700*b126*b129 + 9225*b126*b138 + 109964*b127*b130 + 113810*b127*b139 + 
      109964*b128*b131 + 113810*b128*b140 + 109964*b129*b132 + 113810*b129*b141
       - 118476*b130*b142 - 118476*b131*b143 - 118476*b132*b144 - 36835*b133*
      b136 + 9987*b133*b142 - 36835*b134*b137 + 9987*b134*b143 - 36835*b135*
      b138 + 9987*b135*b144 + 10830*b136*b139 + 10830*b137*b140 + 10830*b138*
      b141 - 32179*b139*b142 - 32179*b140*b143 - 32179*b141*b144 - 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
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