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Instance pooling_adhya2stp
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ⓘ | -549.80305380 (ANTIGONE) -549.80305080 (BARON) -549.80305910 (GUROBI) -549.80305020 (LINDO) -549.80306280 (SCIP) |
| Referencesⓘ | Adhya, Nilanjan, Tawarmalani, Mohit, and Sahinidis, Nikolaos V., A Lagrangian Approach to the Pooling Problem, Industrial & Engineering Chemistry Research, 38:5, 1999, 1956-1972. Alfaki, Mohammed and Haugland, Dag, Strong formulations for the pooling problem, Journal of Global Optimization, 56:3, 2013, 897-916. |
| Sourceⓘ | Adhya2.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ⓘ | 26 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 19 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 79 |
| #Linear Constraintsⓘ | 39 |
| #Quadratic Constraintsⓘ | 40 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 303 |
| #Nonlinear Nonzeros in Jacobianⓘ | 80 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 80 |
| #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ⓘ | 7 |
| Average blocksize in Hessian of Lagrangianⓘ | 6.5 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-01 |
| Maximal coefficientⓘ | 2.3000e+01 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 80 45 0 35 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
* 323 243 80 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,e74,e75,e76,e77,e78,e79,e80;
e1.. objvar + 9*x28 + 18*x29 + 8*x30 + 3*x31 + 13*x32 + 22*x33 + 12*x34
+ 7*x35 + 14*x36 + 23*x37 + 13*x38 + 8*x39 + 6*x40 + 15*x41 + 5*x42
+ 11*x44 + 20*x45 + 10*x46 + 5*x47 =E= 0;
e2.. x28 + x29 + x30 + x31 =L= 75;
e3.. x32 + x33 + x34 + x35 =L= 75;
e4.. x36 + x37 + x38 + x39 =L= 75;
e5.. x40 + x41 + x42 + x43 =L= 75;
e6.. x44 + x45 + x46 + x47 =L= 75;
e7.. x28 + x29 + x30 + x31 + x32 + x33 + x34 + x35 =L= 75;
e8.. x36 + x37 + x38 + x39 + x40 + x41 + x42 + x43 + x44 + x45 + x46 + x47
=L= 75;
e9.. x28 + x32 + x36 + x40 + x44 =L= 10;
e10.. x29 + x33 + x37 + x41 + x45 =L= 25;
e11.. x30 + x34 + x38 + x42 + x46 =L= 30;
e12.. x31 + x35 + x39 + x43 + x47 =L= 10;
e13.. - 2*x28 + x32 + x36 - 2*x44 =L= 0;
e14.. 3*x28 - 2*x32 + 2.5*x36 - 0.3*x44 =L= 0;
e15.. 0.75*x28 - 0.25*x32 - 0.25*x36 - 0.25*x40 + 0.75*x44 =L= 0;
e16.. - 0.25*x28 + 1.25*x32 + 0.15*x36 + 0.25*x40 + 0.85*x44 =L= 0;
e17.. - x28 - 2*x32 + x36 - 3*x40 - 3*x44 =L= 0;
e18.. 4*x28 - x32 + 5*x36 - x40 + 2*x44 =L= 0;
e19.. - 3*x29 - x41 - 3*x45 =L= 0;
e20.. 3.5*x29 - 1.5*x33 + 3*x37 + 0.5*x41 + 0.2*x45 =L= 0;
e21.. 0.5*x29 - 0.5*x33 - 0.5*x37 - 0.5*x41 + 0.5*x45 =L= 0;
e22.. - x29 + 0.5*x33 - 0.6*x37 - 0.5*x41 + 0.1*x45 =L= 0;
e23.. - 2*x29 - 3*x33 - 4*x41 - 4*x45 =L= 0;
e24.. 3*x29 - 2*x33 + 4*x37 - 2*x41 + x45 =L= 0;
e25.. - 0.5*x30 + 2.5*x34 + 2.5*x38 + 1.5*x42 - 0.5*x46 =L= 0;
e26.. 0.5*x30 - 4.5*x34 - 2.5*x42 - 2.8*x46 =L= 0;
e27.. 0.1*x30 - 0.9*x34 - 0.9*x38 - 0.9*x42 + 0.1*x46 =L= 0;
e28.. - 0.3*x30 + 1.2*x34 + 0.1*x38 + 0.2*x42 + 0.8*x46 =L= 0;
e29.. - 2*x30 - 3*x34 - 4*x42 - 4*x46 =L= 0;
e30.. 3*x30 - 2*x34 + 4*x38 - 2*x42 + x46 =L= 0;
e31.. - 2*x31 + x35 + x39 - 2*x47 =L= 0;
e32.. 2*x31 - 3*x35 + 1.5*x39 - x43 - 1.3*x47 =L= 0;
e33.. - x35 - x39 - x43 =L= 0;
e34.. - 1.3*x31 + 0.2*x35 - 0.9*x39 - 0.8*x43 - 0.2*x47 =L= 0;
e35.. - 3*x31 - 4*x35 - x39 - 5*x43 - 5*x47 =L= 0;
e36.. 3*x31 - 2*x35 + 4*x39 - 2*x43 + x47 =L= 0;
e37.. x15 + x16 =E= 1;
e38.. x17 + x18 + x19 =E= 1;
e39.. x20 + x21 + x22 + x23 =E= 1;
e40.. x24 + x25 + x26 + x27 =E= 1;
e41.. -x15*x7 + x28 =E= 0;
e42.. -x15*x8 + x29 =E= 0;
e43.. -x15*x9 + x30 =E= 0;
e44.. -x15*x10 + x31 =E= 0;
e45.. -x16*x7 + x32 =E= 0;
e46.. -x16*x8 + x33 =E= 0;
e47.. -x16*x9 + x34 =E= 0;
e48.. -x16*x10 + x35 =E= 0;
e49.. -x17*x11 + x36 =E= 0;
e50.. -x17*x12 + x37 =E= 0;
e51.. -x17*x13 + x38 =E= 0;
e52.. -x17*x14 + x39 =E= 0;
e53.. -x18*x11 + x40 =E= 0;
e54.. -x18*x12 + x41 =E= 0;
e55.. -x18*x13 + x42 =E= 0;
e56.. -x18*x14 + x43 =E= 0;
e57.. -x19*x11 + x44 =E= 0;
e58.. -x19*x12 + x45 =E= 0;
e59.. -x19*x13 + x46 =E= 0;
e60.. -x19*x14 + x47 =E= 0;
e61.. -x20*x2 + x28 =E= 0;
e62.. -x21*x2 + x29 =E= 0;
e63.. -x22*x2 + x30 =E= 0;
e64.. -x23*x2 + x31 =E= 0;
e65.. -x20*x3 + x32 =E= 0;
e66.. -x21*x3 + x33 =E= 0;
e67.. -x22*x3 + x34 =E= 0;
e68.. -x23*x3 + x35 =E= 0;
e69.. -x24*x4 + x36 =E= 0;
e70.. -x25*x4 + x37 =E= 0;
e71.. -x26*x4 + x38 =E= 0;
e72.. -x27*x4 + x39 =E= 0;
e73.. -x24*x5 + x40 =E= 0;
e74.. -x25*x5 + x41 =E= 0;
e75.. -x26*x5 + x42 =E= 0;
e76.. -x27*x5 + x43 =E= 0;
e77.. -x24*x6 + x44 =E= 0;
e78.. -x25*x6 + x45 =E= 0;
e79.. -x26*x6 + x46 =E= 0;
e80.. -x27*x6 + x47 =E= 0;
* set non-default bounds
x2.up = 75;
x3.up = 75;
x4.up = 75;
x5.up = 75;
x6.up = 75;
x7.up = 10;
x8.up = 25;
x9.up = 30;
x10.up = 10;
x11.up = 10;
x12.up = 25;
x13.up = 30;
x14.up = 10;
x15.up = 1;
x16.up = 1;
x17.up = 1;
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 = 10;
x29.up = 25;
x30.up = 30;
x31.up = 10;
x32.up = 10;
x33.up = 25;
x34.up = 30;
x35.up = 10;
x36.up = 10;
x37.up = 25;
x38.up = 30;
x39.up = 10;
x40.up = 10;
x41.up = 25;
x42.up = 30;
x43.up = 10;
x44.up = 10;
x45.up = 25;
x46.up = 30;
x47.up = 10;
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