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Instance pooling_rt2stp
STP formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -4391.82589700 (ANTIGONE) -4391.82589800 (BARON) -4391.82589400 (COUENNE) -4391.82594000 (GUROBI) -4391.82589300 (LINDO) -4391.82600500 (SCIP) |
| Referencesⓘ | Audet, Charles, Hansen, Pierre, Jaumard, Brigitte, and Savard, Gilles, A branch and cut algorithm for nonconvex quadratically constrained quadratic programming, Mathematical Programming, 87:1, 2000, 131-152. Alfaki, Mohammed and Haugland, Dag, Strong formulations for the pooling problem, Journal of Global Optimization, 56:3, 2013, 897-916. |
| Sourceⓘ | RT2.gms from Standard Pooling Problem Instances |
| Applicationⓘ | Pooling problem |
| Added to libraryⓘ | 12 Sep 2017 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 46 |
| #Binary Variablesⓘ | 0 |
| #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ⓘ | 22 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 72 |
| #Linear Constraintsⓘ | 36 |
| #Quadratic Constraintsⓘ | 36 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 337 |
| #Nonlinear Nonzeros in Jacobianⓘ | 72 |
| #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ⓘ | 1.0000e-02 |
| Maximal coefficientⓘ | 1.8080e+02 |
| Infeasibility of initial pointⓘ | 5 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 73 41 3 29 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 47 47 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 360 288 72 0
*
* Solve m using NLP minimizing objvar;
Variables objvar,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;
Positive Variables 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;
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;
e1.. objvar + 180.8*x4 + 128*x7 + 88*x8 - 110*x11 + 140.8*x30 + 180.8*x31
+ 100.8*x32 + 140.8*x33 + 180.8*x34 + 100.8*x35 + 128*x36 + 168*x37
+ 88*x38 + 128*x39 + 168*x40 + 88*x41 - 110*x42 - 70*x43 - 150*x44
- 110*x45 - 70*x46 - 150*x47 =E= 0;
e2.. x4 + x30 + x31 + x32 + x33 + x34 + x35 =L= 60.98;
e3.. x7 + x8 + x36 + x37 + x38 + x39 + x40 + x41 =L= 161.29;
e4.. x11 + x42 + x43 + x44 + x45 + x46 + x47 =L= 5;
e5.. x30 + x31 + x32 + x36 + x37 + x38 + x42 + x43 + x44 =L= 12.5;
e6.. x33 + x34 + x35 + x39 + x40 + x41 + x45 + x46 + x47 =L= 17.5;
e7.. x7 + x11 + x30 + x33 + x36 + x39 + x42 + x45 =G= 5;
e8.. x4 + x31 + x34 + x37 + x40 + x43 + x46 =G= 5;
e9.. x8 + x32 + x35 + x38 + x41 + x44 + x47 =G= 5;
e10.. x7 + x11 + x30 + x33 + x36 + x39 + x42 + x45 =L= 300;
e11.. x4 + x31 + x34 + x37 + x40 + x43 + x46 =L= 300;
e12.. x8 + x32 + x35 + x38 + x41 + x44 + x47 =L= 300;
e13.. - 0.17*x7 - 0.04*x11 + 0.0299999999999999*x30 + 0.0299999999999999*x33
- 0.17*x36 - 0.17*x39 - 0.04*x42 - 0.04*x45 =L= 0;
e14.. - 3*x7 - 3*x11 - 3*x36 - 3*x39 - 3*x42 - 3*x45 =L= 0;
e15.. - 26.1*x7 - 14.8*x30 - 14.8*x33 - 26.1*x36 - 26.1*x39 =L= 0;
e16.. - 15.2*x7 - 8.2*x30 - 8.2*x33 - 15.2*x36 - 15.2*x39 =L= 0;
e17.. 0.12*x7 - 0.01*x11 - 0.08*x30 - 0.08*x33 + 0.12*x36 + 0.12*x39
- 0.01*x42 - 0.01*x45 =L= 0;
e18.. 7.09999999999999*x7 - 19*x11 - 4.2*x30 - 4.2*x33
+ 7.09999999999999*x36 + 7.09999999999999*x39 - 19*x42 - 19*x45 =L= 0;
e19.. 1.5*x7 - 13.7*x11 - 5.5*x30 - 5.5*x33 + 1.5*x36 + 1.5*x39 - 13.7*x42
- 13.7*x45 =L= 0;
e20.. 0.0299999999999999*x4 + 0.0299999999999999*x31
+ 0.0299999999999999*x34 - 0.17*x37 - 0.17*x40 - 0.04*x43 - 0.04*x46
=L= 0;
e21.. 2.1*x4 + 2.1*x31 + 2.1*x34 - 0.9*x37 - 0.9*x40 - 0.9*x43 - 0.9*x46
=L= 0;
e22.. - 14.8*x4 - 14.8*x31 - 14.8*x34 - 26.1*x37 - 26.1*x40 =L= 0;
e23.. - 8.2*x4 - 8.2*x31 - 8.2*x34 - 15.2*x37 - 15.2*x40 =L= 0;
e24.. - 0.08*x4 - 0.08*x31 - 0.08*x34 + 0.12*x37 + 0.12*x40 - 0.01*x43
- 0.01*x46 =L= 0;
e25.. - 3.2*x4 - 3.2*x31 - 3.2*x34 + 8.09999999999999*x37
+ 8.09999999999999*x40 - 18*x43 - 18*x46 =L= 0;
e26.. - 2.5*x4 - 2.5*x31 - 2.5*x34 + 4.5*x37 + 4.5*x40 - 10.7*x43 - 10.7*x46
=L= 0;
e27.. - 0.17*x8 + 0.0299999999999999*x32 + 0.0299999999999999*x35 - 0.17*x38
- 0.17*x41 - 0.04*x44 - 0.04*x47 =L= 0;
e28.. - 3*x8 - 3*x38 - 3*x41 - 3*x44 - 3*x47 =L= 0;
e29.. - 26.1*x8 - 14.8*x32 - 14.8*x35 - 26.1*x38 - 26.1*x41 =L= 0;
e30.. - 15.2*x8 - 8.2*x32 - 8.2*x35 - 15.2*x38 - 15.2*x41 =L= 0;
e31.. 0.12*x8 - 0.08*x32 - 0.08*x35 + 0.12*x38 + 0.12*x41 - 0.01*x44
- 0.01*x47 =L= 0;
e32.. 3.09999999999999*x8 - 8.2*x32 - 8.2*x35 + 3.09999999999999*x38
+ 3.09999999999999*x41 - 23*x44 - 23*x47 =L= 0;
e33.. - 7*x32 - 7*x35 - 15.2*x44 - 15.2*x47 =L= 0;
e34.. x18 + x20 + x22 =E= 1;
e35.. x19 + x21 + x23 =E= 1;
e36.. x24 + x25 + x26 =E= 1;
e37.. x27 + x28 + x29 =E= 1;
e38.. -x18*x12 + x30 =E= 0;
e39.. -x18*x13 + x31 =E= 0;
e40.. -x18*x14 + x32 =E= 0;
e41.. -x19*x15 + x33 =E= 0;
e42.. -x19*x16 + x34 =E= 0;
e43.. -x19*x17 + x35 =E= 0;
e44.. -x20*x12 + x36 =E= 0;
e45.. -x20*x13 + x37 =E= 0;
e46.. -x20*x14 + x38 =E= 0;
e47.. -x21*x15 + x39 =E= 0;
e48.. -x21*x16 + x40 =E= 0;
e49.. -x21*x17 + x41 =E= 0;
e50.. -x22*x12 + x42 =E= 0;
e51.. -x22*x13 + x43 =E= 0;
e52.. -x22*x14 + x44 =E= 0;
e53.. -x23*x15 + x45 =E= 0;
e54.. -x23*x16 + x46 =E= 0;
e55.. -x23*x17 + x47 =E= 0;
e56.. -x24*x2 + x30 =E= 0;
e57.. -x25*x2 + x31 =E= 0;
e58.. -x26*x2 + x32 =E= 0;
e59.. -x27*x3 + x33 =E= 0;
e60.. -x28*x3 + x34 =E= 0;
e61.. -x29*x3 + x35 =E= 0;
e62.. -x24*x5 + x36 =E= 0;
e63.. -x25*x5 + x37 =E= 0;
e64.. -x26*x5 + x38 =E= 0;
e65.. -x27*x6 + x39 =E= 0;
e66.. -x28*x6 + x40 =E= 0;
e67.. -x29*x6 + x41 =E= 0;
e68.. -x24*x9 + x42 =E= 0;
e69.. -x25*x9 + x43 =E= 0;
e70.. -x26*x9 + x44 =E= 0;
e71.. -x27*x10 + x45 =E= 0;
e72.. -x28*x10 + x46 =E= 0;
e73.. -x29*x10 + x47 =E= 0;
* set non-default bounds
x2.up = 12.5;
x3.up = 17.5;
x4.up = 60.98;
x5.up = 12.5;
x6.up = 17.5;
x7.up = 161.29;
x8.up = 161.29;
x9.up = 5;
x10.up = 5;
x11.up = 5;
x12.up = 12.5;
x13.up = 12.5;
x14.up = 12.5;
x15.up = 17.5;
x16.up = 17.5;
x17.up = 17.5;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.up = 1;
x29.up = 1;
x30.up = 12.5;
x31.up = 12.5;
x32.up = 12.5;
x33.up = 17.5;
x34.up = 17.5;
x35.up = 17.5;
x36.up = 12.5;
x37.up = 12.5;
x38.up = 12.5;
x39.up = 17.5;
x40.up = 17.5;
x41.up = 17.5;
x42.up = 5;
x43.up = 5;
x44.up = 5;
x45.up = 5;
x46.up = 5;
x47.up = 5;
Model m / all /;
m.limrow=0; m.limcol=0;
m.tolproj=0.0;
$if NOT '%gams.u1%' == '' $include '%gams.u1%'
$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;
Last updated: 2024-08-26 Git hash: 6cc1607f