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Instance pooling_foulds2stp
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ⓘ | -1100.00000100 (ANTIGONE) -1100.00000000 (BARON) -1100.00000000 (COUENNE) -1100.00000000 (GUROBI) -1100.00000000 (LINDO) -1100.00000000 (SCIP) |
| Referencesⓘ | Foulds, L. R., Haugland, D., and Jörnsten, K., A bilinear approach to the pooling problem, Optimization, 24:1-2, 1992, 165-180. Alfaki, Mohammed and Haugland, Dag, Strong formulations for the pooling problem, Journal of Global Optimization, 56:3, 2013, 897-916. |
| Sourceⓘ | Foulds2.gms from Standard Pooling Problem Instances |
| Applicationⓘ | Pooling problem |
| Added to libraryⓘ | 12 Sep 2017 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 48 |
| #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ⓘ | 23 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 52 |
| #Linear Constraintsⓘ | 20 |
| #Quadratic Constraintsⓘ | 32 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 192 |
| #Nonlinear Nonzeros in Jacobianⓘ | 64 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 64 |
| #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ⓘ | 5.0000e-01 |
| Maximal coefficientⓘ | 1.2000e+01 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 53 37 0 16 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 49 49 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 216 152 64 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,x48,x49;
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,x48,x49;
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;
e1.. objvar - x4 + 5*x5 - 4*x6 + 2*x7 + 2*x10 + 8*x11 - x12 + 5*x13 + 3*x34
+ 9*x35 + 6*x37 - 7*x38 - x39 - 10*x40 - 4*x41 + 6*x42 + 12*x43 + 3*x44
+ 9*x45 - 4*x46 + 2*x47 - 7*x48 - x49 =E= 0;
e2.. x34 + x35 + x36 + x37 =L= 600;
e3.. x38 + x39 + x40 + x41 =L= 600;
e4.. x4 + x5 + x6 + x7 =L= 600;
e5.. x42 + x43 + x44 + x45 =L= 600;
e6.. x46 + x47 + x48 + x49 =L= 600;
e7.. x10 + x11 + x12 + x13 =L= 600;
e8.. x34 + x35 + x36 + x37 + x38 + x39 + x40 + x41 =L= 600;
e9.. x42 + x43 + x44 + x45 + x46 + x47 + x48 + x49 =L= 600;
e10.. x4 + x10 + x34 + x38 + x42 + x46 =L= 100;
e11.. x5 + x11 + x35 + x39 + x43 + x47 =L= 200;
e12.. x6 + x12 + x36 + x40 + x44 + x48 =L= 100;
e13.. x7 + x13 + x37 + x41 + x45 + x49 =L= 200;
e14.. - 0.5*x4 + 0.5*x34 - 1.5*x38 + x42 - x46 =L= 0;
e15.. 0.5*x5 + x11 + 1.5*x35 - 0.5*x39 + 2*x43 =L= 0;
e16.. - x6 - 0.5*x12 - 2*x40 + 0.5*x44 - 1.5*x48 =L= 0;
e17.. 0.5*x13 + x37 - x41 + 1.5*x45 - 0.5*x49 =L= 0;
e18.. x22 + x23 =E= 1;
e19.. x24 + x25 =E= 1;
e20.. x26 + x27 + x28 + x29 =E= 1;
e21.. x30 + x31 + x32 + x33 =E= 1;
e22.. -x22*x14 + x34 =E= 0;
e23.. -x22*x15 + x35 =E= 0;
e24.. -x22*x16 + x36 =E= 0;
e25.. -x22*x17 + x37 =E= 0;
e26.. -x23*x14 + x38 =E= 0;
e27.. -x23*x15 + x39 =E= 0;
e28.. -x23*x16 + x40 =E= 0;
e29.. -x23*x17 + x41 =E= 0;
e30.. -x24*x18 + x42 =E= 0;
e31.. -x24*x19 + x43 =E= 0;
e32.. -x24*x20 + x44 =E= 0;
e33.. -x24*x21 + x45 =E= 0;
e34.. -x25*x18 + x46 =E= 0;
e35.. -x25*x19 + x47 =E= 0;
e36.. -x25*x20 + x48 =E= 0;
e37.. -x25*x21 + x49 =E= 0;
e38.. -x26*x2 + x34 =E= 0;
e39.. -x27*x2 + x35 =E= 0;
e40.. -x28*x2 + x36 =E= 0;
e41.. -x29*x2 + x37 =E= 0;
e42.. -x26*x3 + x38 =E= 0;
e43.. -x27*x3 + x39 =E= 0;
e44.. -x28*x3 + x40 =E= 0;
e45.. -x29*x3 + x41 =E= 0;
e46.. -x30*x8 + x42 =E= 0;
e47.. -x31*x8 + x43 =E= 0;
e48.. -x32*x8 + x44 =E= 0;
e49.. -x33*x8 + x45 =E= 0;
e50.. -x30*x9 + x46 =E= 0;
e51.. -x31*x9 + x47 =E= 0;
e52.. -x32*x9 + x48 =E= 0;
e53.. -x33*x9 + x49 =E= 0;
* set non-default bounds
x2.up = 600;
x3.up = 600;
x4.up = 100;
x5.up = 200;
x6.up = 100;
x7.up = 200;
x8.up = 600;
x9.up = 600;
x10.up = 100;
x11.up = 200;
x12.up = 100;
x13.up = 200;
x14.up = 100;
x15.up = 200;
x16.up = 100;
x17.up = 200;
x18.up = 100;
x19.up = 200;
x20.up = 100;
x21.up = 200;
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 = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 100;
x35.up = 200;
x36.up = 100;
x37.up = 200;
x38.up = 100;
x39.up = 200;
x40.up = 100;
x41.up = 200;
x42.up = 100;
x43.up = 200;
x44.up = 100;
x45.up = 200;
x46.up = 100;
x47.up = 200;
x48.up = 100;
x49.up = 200;
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: 2025-08-07 Git hash: e62cedfc