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Instance genpooling_lee2
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -3849.26542400 (ANTIGONE) -3849.26543300 (BARON) -3849.26683100 (COUENNE) -3849.26546300 (GUROBI) -3849.26542400 (LINDO) -3849.26543600 (SCIP) -6366.48000000 (SHOT) |
| Referencesⓘ | Misener, Ruth and Floudas, C A, Generalized Pooling Problem, 2011. |
| Sourceⓘ | generalizedpooling_lee2.gms from minlp.org model 123 |
| Applicationⓘ | Pooling problem |
| Added to libraryⓘ | 25 Sep 2013 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 53 |
| #Binary Variablesⓘ | 9 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 24 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 41 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 92 |
| #Linear Constraintsⓘ | 62 |
| #Quadratic Constraintsⓘ | 30 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 412 |
| #Nonlinear Nonzeros in Jacobianⓘ | 192 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 72 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 6 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 6 |
| Average blocksize in Hessian of Lagrangianⓘ | 6.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 9.0900e-02 |
| Maximal coefficientⓘ | 6.8600e+02 |
| Infeasibility of initial pointⓘ | 284 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 93 17 0 76 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 54 45 9 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 454 262 192 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,b45,b46,b47,b48,b49,b50,b51,b52,b53
,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;
Binary Variables b45,b46,b47,b48,b49,b50,b51,b52,b53;
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;
e1.. - 6.2*x1 - 9.4*x2 - 7.6*x3 - 10.2*x4 - 1.67*x5 - 2.53*x6 - 2.05*x7
- 2.75*x8 - 3.58*x9 - 5.42*x10 - 4.39*x11 - 5.89*x12 - 4.53*x13
- 6.87*x14 - 5.55*x15 - 7.45*x16 - 2.62*x17 - 3.98*x18 - 3.22*x19
- 4.32*x20 + 10.5*x21 + 11.2*x22 + 12.5*x23 + 10.5*x24 + 11.2*x25
+ 12.5*x26 + 10.5*x27 + 11.2*x28 + 12.5*x29 + 10.5*x30 + 11.2*x31
+ 12.5*x32 - 260*b45 - 70*b46 - 150*b47 - 190*b48 - 110*b49 - 310*b50
- 470*b51 - 380*b52 - 510*b53 + objvar =E= 0;
e2.. - x21 - x24 - x27 - x30 =L= -229;
e3.. - x22 - x25 - x28 - x31 =L= -173;
e4.. - x23 - x26 - x29 - x32 =L= -284;
e5.. x21 + x24 + x27 + x30 =L= 229;
e6.. x22 + x25 + x28 + x31 =L= 173;
e7.. x23 + x26 + x29 + x32 =L= 284;
e8.. x1 + x5 + x9 + x13 + x17 - x21 - x22 - x23 =E= 0;
e9.. x2 + x6 + x10 + x14 + x18 - x24 - x25 - x26 =E= 0;
e10.. x3 + x7 + x11 + x15 + x19 - x27 - x28 - x29 =E= 0;
e11.. x4 + x8 + x12 + x16 + x20 - x30 - x31 - x32 =E= 0;
e12.. -(x33*x21 + x33*x22 + x33*x23) + 0.0909*x1 + 0.5*x5 + 0.32*x9
+ 0.4286*x13 + 0.1299*x17 =E= 0;
e13.. -(x34*x21 + x34*x22 + x34*x23) + 0.5455*x1 + 0.125*x5 + 0.44*x9
+ 0.4286*x13 + 0.3506*x17 =E= 0;
e14.. -(x35*x21 + x35*x22 + x35*x23) + 0.3636*x1 + 0.375*x5 + 0.24*x9
+ 0.1428*x13 + 0.5195*x17 =E= 0;
e15.. -(x36*x24 + x36*x25 + x36*x26) + 0.0909*x2 + 0.5*x6 + 0.32*x10
+ 0.4286*x14 + 0.1299*x18 =E= 0;
e16.. -(x37*x24 + x37*x25 + x37*x26) + 0.5455*x2 + 0.125*x6 + 0.44*x10
+ 0.4286*x14 + 0.3506*x18 =E= 0;
e17.. -(x38*x24 + x38*x25 + x38*x26) + 0.3636*x2 + 0.375*x6 + 0.24*x10
+ 0.1428*x14 + 0.5195*x18 =E= 0;
e18.. -(x39*x27 + x39*x28 + x39*x29) + 0.0909*x3 + 0.5*x7 + 0.32*x11
+ 0.4286*x15 + 0.1299*x19 =E= 0;
e19.. -(x40*x27 + x40*x28 + x40*x29) + 0.5455*x3 + 0.125*x7 + 0.44*x11
+ 0.4286*x15 + 0.3506*x19 =E= 0;
e20.. -(x41*x27 + x41*x28 + x41*x29) + 0.3636*x3 + 0.375*x7 + 0.24*x11
+ 0.1428*x15 + 0.5195*x19 =E= 0;
e21.. -(x42*x30 + x42*x31 + x42*x32) + 0.0909*x4 + 0.5*x8 + 0.32*x12
+ 0.4286*x16 + 0.1299*x20 =E= 0;
e22.. -(x43*x30 + x43*x31 + x43*x32) + 0.5455*x4 + 0.125*x8 + 0.44*x12
+ 0.4286*x16 + 0.3506*x20 =E= 0;
e23.. -(x44*x30 + x44*x31 + x44*x32) + 0.3636*x4 + 0.375*x8 + 0.24*x12
+ 0.1428*x16 + 0.5195*x20 =E= 0;
e24.. 0.13*x21 - (x33*x21 + x36*x24 + x39*x27 + x42*x30) + 0.13*x24 + 0.13*x27
+ 0.13*x30 =L= 0;
e25.. 0.38*x21 - (x34*x21 + x37*x24 + x40*x27 + x43*x30) + 0.38*x24 + 0.38*x27
+ 0.38*x30 =L= 0;
e26.. 0.49*x21 - (x35*x21 + x38*x24 + x41*x27 + x44*x30) + 0.49*x24 + 0.49*x27
+ 0.49*x30 =L= 0;
e27.. 0.27*x22 - (x33*x22 + x36*x25 + x39*x28 + x42*x31) + 0.27*x25 + 0.27*x28
+ 0.27*x31 =L= 0;
e28.. 0.43*x22 - (x34*x22 + x37*x25 + x40*x28 + x43*x31) + 0.43*x25 + 0.43*x28
+ 0.43*x31 =L= 0;
e29.. 0.3*x22 - (x35*x22 + x38*x25 + x41*x28 + x44*x31) + 0.3*x25 + 0.3*x28 +
0.3*x31 =L= 0;
e30.. 0.45*x23 - (x33*x23 + x36*x26 + x39*x29 + x42*x32) + 0.45*x26 + 0.45*x29
+ 0.45*x32 =L= 0;
e31.. 0.2*x23 - (x34*x23 + x37*x26 + x40*x29 + x43*x32) + 0.2*x26 + 0.2*x29 +
0.2*x32 =L= 0;
e32.. 0.35*x23 - (x35*x23 + x38*x26 + x41*x29 + x44*x32) + 0.35*x26 + 0.35*x29
+ 0.35*x32 =L= 0;
e33.. x33*x21 + x36*x24 + x39*x27 + x42*x30 - 0.13*x21 - 0.13*x24 - 0.13*x27 -
0.13*x30 =L= 0;
e34.. x34*x21 + x37*x24 + x40*x27 + x43*x30 - 0.38*x21 - 0.38*x24 - 0.38*x27 -
0.38*x30 =L= 0;
e35.. x35*x21 + x38*x24 + x41*x27 + x44*x30 - 0.49*x21 - 0.49*x24 - 0.49*x27 -
0.49*x30 =L= 0;
e36.. x33*x22 + x36*x25 + x39*x28 + x42*x31 - 0.27*x22 - 0.27*x25 - 0.27*x28 -
0.27*x31 =L= 0;
e37.. x34*x22 + x37*x25 + x40*x28 + x43*x31 - 0.43*x22 - 0.43*x25 - 0.43*x28 -
0.43*x31 =L= 0;
e38.. x35*x22 + x38*x25 + x41*x28 + x44*x31 - 0.3*x22 - 0.3*x25 - 0.3*x28 - 0.3
*x31 =L= 0;
e39.. x33*x23 + x36*x26 + x39*x29 + x42*x32 - 0.45*x23 - 0.45*x26 - 0.45*x29 -
0.45*x32 =L= 0;
e40.. x34*x23 + x37*x26 + x40*x29 + x43*x32 - 0.2*x23 - 0.2*x26 - 0.2*x29 - 0.2
*x32 =L= 0;
e41.. x35*x23 + x38*x26 + x41*x29 + x44*x32 - 0.35*x23 - 0.35*x26 - 0.35*x29 -
0.35*x32 =L= 0;
e42.. x1 - 686*b50 =L= 0;
e43.. x2 - 686*b51 =L= 0;
e44.. x3 - 686*b52 =L= 0;
e45.. x4 - 686*b53 =L= 0;
e46.. x5 - 686*b50 =L= 0;
e47.. x6 - 686*b51 =L= 0;
e48.. x7 - 686*b52 =L= 0;
e49.. x8 - 686*b53 =L= 0;
e50.. x9 - 686*b50 =L= 0;
e51.. x10 - 686*b51 =L= 0;
e52.. x11 - 686*b52 =L= 0;
e53.. x12 - 686*b53 =L= 0;
e54.. x13 - 686*b50 =L= 0;
e55.. x14 - 686*b51 =L= 0;
e56.. x15 - 686*b52 =L= 0;
e57.. x16 - 686*b53 =L= 0;
e58.. x17 - 686*b50 =L= 0;
e59.. x18 - 686*b51 =L= 0;
e60.. x19 - 686*b52 =L= 0;
e61.. x20 - 686*b53 =L= 0;
e62.. x1 - 686*b45 =L= 0;
e63.. x2 - 686*b45 =L= 0;
e64.. x3 - 686*b45 =L= 0;
e65.. x4 - 686*b45 =L= 0;
e66.. x5 - 686*b46 =L= 0;
e67.. x6 - 686*b46 =L= 0;
e68.. x7 - 686*b46 =L= 0;
e69.. x8 - 686*b46 =L= 0;
e70.. x9 - 686*b47 =L= 0;
e71.. x10 - 686*b47 =L= 0;
e72.. x11 - 686*b47 =L= 0;
e73.. x12 - 686*b47 =L= 0;
e74.. x13 - 686*b48 =L= 0;
e75.. x14 - 686*b48 =L= 0;
e76.. x15 - 686*b48 =L= 0;
e77.. x16 - 686*b48 =L= 0;
e78.. x17 - 686*b49 =L= 0;
e79.. x18 - 686*b49 =L= 0;
e80.. x19 - 686*b49 =L= 0;
e81.. x20 - 686*b49 =L= 0;
e82.. x21 - 229*b50 =L= 0;
e83.. x22 - 173*b50 =L= 0;
e84.. x23 - 284*b50 =L= 0;
e85.. x24 - 229*b51 =L= 0;
e86.. x25 - 173*b51 =L= 0;
e87.. x26 - 284*b51 =L= 0;
e88.. x27 - 229*b52 =L= 0;
e89.. x28 - 173*b52 =L= 0;
e90.. x29 - 284*b52 =L= 0;
e91.. x30 - 229*b53 =L= 0;
e92.. x31 - 173*b53 =L= 0;
e93.. x32 - 284*b53 =L= 0;
* set non-default bounds
x1.up = 686;
x2.up = 686;
x3.up = 686;
x4.up = 686;
x5.up = 686;
x6.up = 686;
x7.up = 686;
x8.up = 686;
x9.up = 686;
x10.up = 686;
x11.up = 686;
x12.up = 686;
x13.up = 686;
x14.up = 686;
x15.up = 686;
x16.up = 686;
x17.up = 686;
x18.up = 686;
x19.up = 686;
x20.up = 686;
x21.up = 229;
x22.up = 173;
x23.up = 284;
x24.up = 229;
x25.up = 173;
x26.up = 284;
x27.up = 229;
x28.up = 173;
x29.up = 284;
x30.up = 229;
x31.up = 173;
x32.up = 284;
x33.lo = 0.0909; x33.up = 0.5;
x34.lo = 0.125; x34.up = 0.5455;
x35.lo = 0.1428; x35.up = 0.5195;
x36.lo = 0.0909; x36.up = 0.5;
x37.lo = 0.125; x37.up = 0.5455;
x38.lo = 0.1428; x38.up = 0.5195;
x39.lo = 0.0909; x39.up = 0.5;
x40.lo = 0.125; x40.up = 0.5455;
x41.lo = 0.1428; x41.up = 0.5195;
x42.lo = 0.0909; x42.up = 0.5;
x43.lo = 0.125; x43.up = 0.5455;
x44.lo = 0.1428; x44.up = 0.5195;
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