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Instance genpooling_meyer04
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 1086187.13700000 (ANTIGONE) 1086187.13700000 (BARON) 857953.45580000 (COUENNE) 895953.37880000 (GUROBI) 1086187.13700000 (LINDO) 866341.16060000 (SCIP) 102765.89810000 (SHOT) |
| Referencesⓘ | Misener, Ruth and Floudas, C A, Generalized Pooling Problem, 2011. |
| Sourceⓘ | generalizedpooling_meyer4.gms from minlp.org model 123 |
| Applicationⓘ | Pooling problem |
| Added to libraryⓘ | 25 Sep 2013 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 118 |
| #Binary Variablesⓘ | 55 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 28 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 106 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 141 |
| #Linear Constraintsⓘ | 126 |
| #Quadratic Constraintsⓘ | 15 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 633 |
| #Nonlinear Nonzeros in Jacobianⓘ | 156 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 96 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 7 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 7 |
| Average blocksize in Hessian of Lagrangianⓘ | 7.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-02 |
| Maximal coefficientⓘ | 3.6676e+04 |
| Infeasibility of initial pointⓘ | 300.5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 142 17 51 74 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 119 64 55 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 740 584 156 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,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,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
,x35,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51
,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63;
Binary Variables 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;
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,e51,e52,e53
,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142;
e1.. - 75.0708333333333*x1 - 150.141666666667*x2 - 280.264444444444*x3
- 245.231388888889*x4 - 55.0519444444444*x5 - 125.118055555556*x6
- 260.245555555556*x7 - 215.203055555556*x8 - 30.0283333333333*x9
- 115.108611111111*x10 - 240.226666666667*x11 - 220.207777777778*x12
- 55.0519444444444*x13 - 140.132222222222*x14 - 245.231388888889*x15
- 245.231388888889*x16 - 55.0519444444444*x17 - 40.0377777777778*x18
- 150.141666666667*x19 - 150.141666666667*x20 - 40.0377777777778*x21
- 120.113333333333*x22 - 230.217222222222*x23 - 230.217222222222*x24
- 30.0283333333333*x25 - 60.0566666666667*x26 - 175.165277777778*x27
- 165.155833333333*x28 - 1177.97083333333*x29 - 2975.27555555556*x30
- 1263.05111111111*x31 - 1293.07944444444*x32 - 1182.97555555556*x33
- 1313.09833333333*x34 - 1293.07944444444*x35 - 2975.27555555556*x36
- 3025.32277777778*x37 - 2995.29444444444*x38 - 1313.09833333333*x39
- 1233.02277777778*x40 - 1213.00388888889*x41 - 1293.07944444444*x42
- 1202.99444444444*x43 - 1213.00388888889*x44 - 150.141666666667*x45
- 135.1275*x46 - 100.094444444444*x47 - 90.085*x48 - 40.0377777777778*x49
- 70.0661111111111*x50 - 45.0425*x51 - 9345*b64 - 18690*b65 - 34888*b66
- 30527*b67 - 6853*b68 - 15575*b69 - 32396*b70 - 26789*b71 - 3738*b72
- 14329*b73 - 29904*b74 - 27412*b75 - 6853*b76 - 17444*b77 - 30527*b78
- 30527*b79 - 6853*b80 - 4984*b81 - 18690*b82 - 18690*b83 - 4984*b84
- 14952*b85 - 28658*b86 - 28658*b87 - 3738*b88 - 7476*b89 - 21805*b90
- 20559*b91 - 9345*b92 - 9968*b93 - 19936*b94 - 23674*b95 - 9968*b96
- 26166*b97 - 23674*b98 - 9968*b99 - 16198*b100 - 12460*b101 - 26166*b102
- 16198*b103 - 13706*b104 - 23674*b105 - 12460*b106 - 13706*b107
- 18690*b108 - 16821*b109 - 12460*b110 - 11214*b111 - 4984*b112
- 8722*b113 - 5607*b114 - 13972*b115 - 36676*b116 - 13972*b117
- 13972*b118 + objvar =E= 0;
e2.. - x1 - x2 - x3 - x4 - x45 =L= -20;
e3.. - x5 - x6 - x7 - x8 - x46 =L= -50;
e4.. - x9 - x10 - x11 - x12 - x47 =L= -47.5;
e5.. - x13 - x14 - x15 - x16 - x48 =L= -28;
e6.. - x17 - x18 - x19 - x20 - x49 =L= -100;
e7.. - x21 - x22 - x23 - x24 - x50 =L= -30;
e8.. - x25 - x26 - x27 - x28 - x51 =L= -25;
e9.. x1 + x2 + x3 + x4 + x45 =L= 20;
e10.. x5 + x6 + x7 + x8 + x46 =L= 50;
e11.. x9 + x10 + x11 + x12 + x47 =L= 47.5;
e12.. x13 + x14 + x15 + x16 + x48 =L= 28;
e13.. x17 + x18 + x19 + x20 + x49 =L= 100;
e14.. x21 + x22 + x23 + x24 + x50 =L= 30;
e15.. x25 + x26 + x27 + x28 + x51 =L= 25;
e16.. x29 + x33 + x34 + x35 - 300.5*b115 =L= 0;
e17.. x30 + x36 + x37 + x38 - 300.5*b116 =L= 0;
e18.. x31 + x39 + x40 + x41 - 300.5*b117 =L= 0;
e19.. x32 + x42 + x43 + x44 - 300.5*b118 =L= 0;
e20.. - x29 - x30 - x31 - x32 - x45 - x46 - x47 - x48 - x49 - x50 - x51
=L= -300.5;
e21.. x29 + x30 + x31 + x32 + x45 + x46 + x47 + x48 + x49 + x50 + x51
=L= 300.5;
e22.. x1 + x5 + x9 + x13 + x17 + x21 + x25 - x29 - x33 - x34 - x35 + x36
+ x39 + x42 =E= 0;
e23.. x2 + x6 + x10 + x14 + x18 + x22 + x26 - x30 + x33 - x36 - x37 - x38
+ x40 + x43 =E= 0;
e24.. x3 + x7 + x11 + x15 + x19 + x23 + x27 - x31 + x34 + x37 - x39 - x40
- x41 + x44 =E= 0;
e25.. x4 + x8 + x12 + x16 + x20 + x24 + x28 - x32 + x35 + x38 + x41 - x42
- x43 - x44 =E= 0;
e26.. 0.01*(x55*x36 + x58*x39 + x61*x42) - (x52*x29 + x52*x33 + x52*x34 + x52*
x35) + x1 + 8.00000000000001*x5 + 4*x9 + 12*x13 + 5*x17 + 0.5*x21
+ 10*x25 =E= 0;
e27.. 0.1*(x56*x36 + x59*x39 + x62*x42) - (x53*x29 + x53*x33 + x53*x34 + x53*
x35) + 50*x1 + 175*x5 + 8*x9 + 100*x13 + 70*x17 + 10*x21 + 5*x25 =E= 0;
e28.. 0.05*(x57*x36 + x60*x39 + x63*x42) - (x54*x29 + x54*x33 + x54*x34 + x54*
x35) + 25*x1 + 100*x5 + 5*x9 + 20*x13 + 12.5*x17 + 2.5*x21
+ 7.50000000000001*x25 =E= 0;
e29.. x52*x33 + x58*x40 + x61*x43 - (x55*x30 + x55*x36 + x55*x37 + x55*x38)
+ 100*x2 + 800*x6 + 400*x10 + 1200*x14 + 500*x18 + 50*x22 + 1000*x26
=E= 0;
e30.. 0.13*(x53*x33 + x59*x40 + x62*x43) - (x56*x30 + x56*x36 + x56*x37 + x56*
x38) + 65*x2 + 227.5*x6 + 10.4*x10 + 130*x14 + 91*x18 + 13*x22 + 6.5*x26
=E= 0;
e31.. 0.1*(x54*x33 + x60*x40 + x63*x43) - (x57*x30 + x57*x36 + x57*x37 + x57*
x38) + 50*x2 + 200*x6 + 10*x10 + 40*x14 + 25*x18 + 5*x22 + 15*x26 =E= 0;
e32.. 0.9*(x52*x34 + x55*x37 + x61*x44) - (x58*x31 + x58*x39 + x58*x40 + x58*
x41) + 90*x3 + 720*x7 + 360*x11 + 1080*x15 + 450*x19 + 45*x23 + 900*x27
=E= 0;
e33.. 0.01*(x53*x34 + x56*x37 + x62*x44) - (x59*x31 + x59*x39 + x59*x40 + x59*
x41) + 5*x3 + 17.5*x7 + 0.800000000000001*x11 + 10*x15
+ 7.00000000000001*x19 + x23 + 0.5*x27 =E= 0;
e34.. x54*x34 + x57*x37 + x63*x44 - (x60*x31 + x60*x39 + x60*x40 + x60*x41)
+ 500*x3 + 2000*x7 + 100*x11 + 400*x15 + 250*x19 + 50*x23 + 150*x27
=E= 0;
e35.. 0.3*(x52*x35 + x55*x38 + x58*x41) - (x61*x32 + x61*x42 + x61*x43 + x61*
x44) + 30*x4 + 240*x8 + 120*x12 + 360*x16 + 150*x20 + 15*x24 + 300*x28
=E= 0;
e36.. 0.8*(x53*x35 + x56*x38 + x59*x41) - (x62*x32 + x62*x42 + x62*x43 + x62*
x44) + 400*x4 + 1400*x8 + 64*x12 + 800*x16 + 560*x20 + 80*x24 + 40*x28
=E= 0;
e37.. 0.7*(x54*x35 + x57*x38 + x60*x41) - (x63*x32 + x63*x42 + x63*x43 + x63*
x44) + 350*x4 + 1400*x8 + 70*x12 + 280*x16 + 175*x20 + 35*x24 + 105*x28
=E= 0;
e38.. x52*x29 + x55*x30 + x58*x31 + x61*x32 - 5*x29 - 5*x30 - 5*x31 - 5*x32
+ 95*x45 + 795*x46 + 395*x47 + 1195*x48 + 495*x49 + 45*x50 + 995*x51
=L= 0;
e39.. x53*x29 + x56*x30 + x59*x31 + x62*x32 - 5*x29 - 5*x30 - 5*x31 - 5*x32
+ 495*x45 + 1745*x46 + 75*x47 + 995*x48 + 695*x49 + 95*x50 + 45*x51
=L= 0;
e40.. x54*x29 + x57*x30 + x60*x31 + x63*x32 - 10*x29 - 10*x30 - 10*x31 - 10*x32
+ 490*x45 + 1990*x46 + 90*x47 + 390*x48 + 240*x49 + 40*x50 + 140*x51
=L= 0;
e41.. x1 - 0.2*b64 =G= 0;
e42.. x2 - 0.2*b65 =G= 0;
e43.. x3 - 0.2*b66 =G= 0;
e44.. x4 - 0.2*b67 =G= 0;
e45.. x5 - 0.2*b68 =G= 0;
e46.. x6 - 0.2*b69 =G= 0;
e47.. x7 - 0.2*b70 =G= 0;
e48.. x8 - 0.2*b71 =G= 0;
e49.. x9 - 0.2*b72 =G= 0;
e50.. x10 - 0.2*b73 =G= 0;
e51.. x11 - 0.2*b74 =G= 0;
e52.. x12 - 0.2*b75 =G= 0;
e53.. x13 - 0.2*b76 =G= 0;
e54.. x14 - 0.2*b77 =G= 0;
e55.. x15 - 0.2*b78 =G= 0;
e56.. x16 - 0.2*b79 =G= 0;
e57.. x17 - 0.2*b80 =G= 0;
e58.. x18 - 0.2*b81 =G= 0;
e59.. x19 - 0.2*b82 =G= 0;
e60.. x20 - 0.2*b83 =G= 0;
e61.. x21 - 0.2*b84 =G= 0;
e62.. x22 - 0.2*b85 =G= 0;
e63.. x23 - 0.2*b86 =G= 0;
e64.. x24 - 0.2*b87 =G= 0;
e65.. x25 - 0.2*b88 =G= 0;
e66.. x26 - 0.2*b89 =G= 0;
e67.. x27 - 0.2*b90 =G= 0;
e68.. x28 - 0.2*b91 =G= 0;
e69.. x1 - 20*b64 =L= 0;
e70.. x2 - 20*b65 =L= 0;
e71.. x3 - 20*b66 =L= 0;
e72.. x4 - 20*b67 =L= 0;
e73.. x5 - 50*b68 =L= 0;
e74.. x6 - 50*b69 =L= 0;
e75.. x7 - 50*b70 =L= 0;
e76.. x8 - 50*b71 =L= 0;
e77.. x9 - 47.5*b72 =L= 0;
e78.. x10 - 47.5*b73 =L= 0;
e79.. x11 - 47.5*b74 =L= 0;
e80.. x12 - 47.5*b75 =L= 0;
e81.. x13 - 28*b76 =L= 0;
e82.. x14 - 28*b77 =L= 0;
e83.. x15 - 28*b78 =L= 0;
e84.. x16 - 28*b79 =L= 0;
e85.. x17 - 100*b80 =L= 0;
e86.. x18 - 100*b81 =L= 0;
e87.. x19 - 100*b82 =L= 0;
e88.. x20 - 100*b83 =L= 0;
e89.. x21 - 30*b84 =L= 0;
e90.. x22 - 30*b85 =L= 0;
e91.. x23 - 30*b86 =L= 0;
e92.. x24 - 30*b87 =L= 0;
e93.. x25 - 25*b88 =L= 0;
e94.. x26 - 25*b89 =L= 0;
e95.. x27 - 25*b90 =L= 0;
e96.. x28 - 25*b91 =L= 0;
e97.. x29 - 0.2*b92 =G= 0;
e98.. x30 - 0.2*b93 =G= 0;
e99.. x31 - 0.2*b94 =G= 0;
e100.. x32 - 0.2*b95 =G= 0;
e101.. x29 - 300.5*b92 =L= 0;
e102.. x30 - 300.5*b93 =L= 0;
e103.. x31 - 300.5*b94 =L= 0;
e104.. x32 - 300.5*b95 =L= 0;
e105.. x45 - 0.2*b108 =G= 0;
e106.. x46 - 0.2*b109 =G= 0;
e107.. x47 - 0.2*b110 =G= 0;
e108.. x48 - 0.2*b111 =G= 0;
e109.. x49 - 0.2*b112 =G= 0;
e110.. x50 - 0.2*b113 =G= 0;
e111.. x51 - 0.2*b114 =G= 0;
e112.. x45 - 20*b108 =L= 0;
e113.. x46 - 50*b109 =L= 0;
e114.. x47 - 47.5*b110 =L= 0;
e115.. x48 - 28*b111 =L= 0;
e116.. x49 - 100*b112 =L= 0;
e117.. x50 - 30*b113 =L= 0;
e118.. x51 - 25*b114 =L= 0;
e119.. x36 - 0.2*b99 =G= 0;
e120.. x39 - 0.2*b102 =G= 0;
e121.. x42 - 0.2*b105 =G= 0;
e122.. x33 - 0.2*b96 =G= 0;
e123.. x40 - 0.2*b103 =G= 0;
e124.. x43 - 0.2*b106 =G= 0;
e125.. x34 - 0.2*b97 =G= 0;
e126.. x37 - 0.2*b100 =G= 0;
e127.. x44 - 0.2*b107 =G= 0;
e128.. x35 - 0.2*b98 =G= 0;
e129.. x38 - 0.2*b101 =G= 0;
e130.. x41 - 0.2*b104 =G= 0;
e131.. x36 - 300.5*b99 =L= 0;
e132.. x39 - 300.5*b102 =L= 0;
e133.. x42 - 300.5*b105 =L= 0;
e134.. x33 - 300.5*b96 =L= 0;
e135.. x40 - 300.5*b103 =L= 0;
e136.. x43 - 300.5*b106 =L= 0;
e137.. x34 - 300.5*b97 =L= 0;
e138.. x37 - 300.5*b100 =L= 0;
e139.. x44 - 300.5*b107 =L= 0;
e140.. x35 - 300.5*b98 =L= 0;
e141.. x38 - 300.5*b101 =L= 0;
e142.. x41 - 300.5*b104 =L= 0;
* set non-default bounds
x1.up = 20;
x2.up = 20;
x3.up = 20;
x4.up = 20;
x5.up = 50;
x6.up = 50;
x7.up = 50;
x8.up = 50;
x9.up = 47.5;
x10.up = 47.5;
x11.up = 47.5;
x12.up = 47.5;
x13.up = 28;
x14.up = 28;
x15.up = 28;
x16.up = 28;
x17.up = 100;
x18.up = 100;
x19.up = 100;
x20.up = 100;
x21.up = 30;
x22.up = 30;
x23.up = 30;
x24.up = 30;
x25.up = 25;
x26.up = 25;
x27.up = 25;
x28.up = 25;
x29.up = 300.5;
x30.up = 300.5;
x31.up = 300.5;
x32.up = 300.5;
x33.up = 300.5;
x34.up = 300.5;
x35.up = 300.5;
x36.up = 300.5;
x37.up = 300.5;
x38.up = 300.5;
x39.up = 300.5;
x40.up = 300.5;
x41.up = 300.5;
x42.up = 300.5;
x43.up = 300.5;
x44.up = 300.5;
x45.up = 20;
x46.up = 50;
x47.up = 47.5;
x48.up = 28;
x49.up = 100;
x50.up = 30;
x51.up = 25;
x52.up = 12;
x53.up = 175;
x54.up = 100;
x55.up = 1200;
x56.up = 227.5;
x57.up = 200;
x58.up = 1080;
x59.up = 17.5;
x60.up = 2000;
x61.up = 360;
x62.up = 1400;
x63.up = 1400;
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: 2025-08-07 Git hash: e62cedfc