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Instance pooling_adhya4stp
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ⓘ | -877.64574080 (ANTIGONE) -877.64574280 (BARON) -877.64573990 (COUENNE) -877.64574080 (GUROBI) -877.64573990 (LINDO) -877.64574030 (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ⓘ | Adhya4.gms from Standard Pooling Problem Instances |
| Applicationⓘ | Pooling problem |
| Added to libraryⓘ | 12 Sep 2017 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 76 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 36 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 39 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 119 |
| #Linear Constraintsⓘ | 39 |
| #Quadratic Constraintsⓘ | 80 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 521 |
| #Nonlinear Nonzeros in Jacobianⓘ | 160 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 160 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 9 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 9 |
| Average blocksize in Hessian of Lagrangianⓘ | 9.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-01 |
| Maximal coefficientⓘ | 2.7000e+01 |
| Infeasibility of initial pointⓘ | 1 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 120 85 0 35 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 77 77 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 561 401 160 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,x50,x51,x52
,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69
,x70,x71,x72,x73,x74,x75,x76,x77;
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,x50,x51
,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68
,x69,x70,x71,x72,x73,x74,x75,x76,x77;
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;
e1.. objvar - 5*x38 + 10*x39 + 15*x40 - 9*x41 - 5*x42 + 3*x43 + 18*x44
+ 23*x45 - x46 + 3*x47 + 6*x48 + 21*x49 + 26*x50 + 2*x51 + 6*x52 + 5*x53
+ 20*x54 + 25*x55 + x56 + 5*x57 + 4*x58 + 19*x59 + 24*x60 + 4*x62 + 7*x63
+ 22*x64 + 27*x65 + 3*x66 + 7*x67 + 5*x68 + 20*x69 + 25*x70 + x71 + 5*x72
+ 5*x73 + 20*x74 + 25*x75 + x76 + 5*x77 =E= 0;
e2.. x38 + x39 + x40 + x41 + x42 =L= 85;
e3.. x43 + x44 + x45 + x46 + x47 =L= 85;
e4.. x48 + x49 + x50 + x51 + x52 =L= 85;
e5.. x53 + x54 + x55 + x56 + x57 =L= 85;
e6.. x58 + x59 + x60 + x61 + x62 =L= 85;
e7.. x63 + x64 + x65 + x66 + x67 =L= 85;
e8.. x68 + x69 + x70 + x71 + x72 =L= 85;
e9.. x73 + x74 + x75 + x76 + x77 =L= 85;
e10.. x38 + x39 + x40 + x41 + x42 + x43 + x44 + x45 + x46 + x47 + x48 + x49
+ x50 + x51 + x52 + x53 + x54 + x55 + x56 + x57 =L= 85;
e11.. x58 + x59 + x60 + x61 + x62 + x63 + x64 + x65 + x66 + x67 + x68 + x69
+ x70 + x71 + x72 + x73 + x74 + x75 + x76 + x77 =L= 85;
e12.. x38 + x43 + x48 + x53 + x58 + x63 + x68 + x73 =L= 15;
e13.. x39 + x44 + x49 + x54 + x59 + x64 + x69 + x74 =L= 25;
e14.. x40 + x45 + x50 + x55 + x60 + x65 + x70 + x75 =L= 10;
e15.. x41 + x46 + x51 + x56 + x61 + x66 + x71 + x76 =L= 20;
e16.. x42 + x47 + x52 + x57 + x62 + x67 + x72 + x77 =L= 15;
e17.. - 0.7*x38 + 0.2*x43 + 0.3*x53 + 0.4*x58 + 0.3*x68 + 0.2*x73 =L= 0;
e18.. 0.2*x38 + 0.1*x43 + 0.2*x48 - 0.5*x53 + 0.1*x58 - 0.6*x63 - 0.2*x68
- 0.0999999999999999*x73 =L= 0;
e19.. - 0.0999999999999999*x38 + 0.3*x43 + 0.3*x53 + 0.2*x58 + 0.1*x68
- 0.2*x73 =L= 0;
e20.. - 0.7*x38 - 0.0999999999999999*x43 - 0.3*x48 - 0.4*x53 + 0.3*x58
+ 0.3*x63 - 0.2*x68 - 0.0999999999999999*x73 =L= 0;
e21.. - 0.9*x39 - 0.2*x49 + 0.1*x54 + 0.2*x59 - 0.2*x64 + 0.1*x69 =L= 0;
e22.. 0.6*x39 + 0.5*x44 + 0.6*x49 - 0.1*x54 + 0.5*x59 - 0.2*x64 + 0.2*x69
+ 0.3*x74 =L= 0;
e23.. - 0.5*x39 - 0.1*x44 - 0.4*x49 - 0.1*x54 - 0.2*x59 - 0.4*x64 - 0.3*x69
- 0.6*x74 =L= 0;
e24.. - 0.4*x39 + 0.2*x44 - 0.0999999999999999*x54 + 0.6*x59 + 0.6*x64
+ 0.1*x69 + 0.2*x74 =L= 0;
e25.. - 0.8*x40 + 0.0999999999999999*x45 - 0.1*x50 + 0.2*x55 + 0.3*x60
- 0.1*x65 + 0.2*x70 + 0.0999999999999999*x75 =L= 0;
e26.. 0.6*x40 + 0.5*x45 + 0.6*x50 - 0.1*x55 + 0.5*x60 - 0.2*x65 + 0.2*x70
+ 0.3*x75 =L= 0;
e27.. - 0.6*x40 - 0.2*x45 - 0.5*x50 - 0.2*x55 - 0.3*x60 - 0.5*x65 - 0.4*x70
- 0.7*x75 =L= 0;
e28.. - 0.9*x40 - 0.3*x45 - 0.5*x50 - 0.6*x55 + 0.1*x60 + 0.1*x65 - 0.4*x70
- 0.3*x75 =L= 0;
e29.. - 0.7*x41 + 0.2*x46 + 0.3*x56 + 0.4*x61 + 0.3*x71 + 0.2*x76 =L= 0;
e30.. 0.8*x41 + 0.7*x46 + 0.8*x51 + 0.0999999999999999*x56 + 0.7*x61
+ 0.4*x71 + 0.5*x76 =L= 0;
e31.. - 0.4*x41 - 0.3*x51 - 0.0999999999999999*x61 - 0.3*x66 - 0.2*x71
- 0.5*x76 =L= 0;
e32.. - 0.6*x41 - 0.2*x51 - 0.3*x56 + 0.4*x61 + 0.4*x66 - 0.1*x71 =L= 0;
e33.. - 1.1*x42 - 0.2*x47 - 0.4*x52 - 0.1*x57 - 0.4*x67 - 0.1*x72 - 0.2*x77
=L= 0;
e34.. - 0.0999999999999999*x47 - 0.7*x57 - 0.0999999999999999*x62 - 0.8*x67
- 0.4*x72 - 0.3*x77 =L= 0;
e35.. - 0.7*x42 - 0.3*x47 - 0.6*x52 - 0.3*x57 - 0.4*x62 - 0.6*x67 - 0.5*x72
- 0.8*x77 =L= 0;
e36.. - 1.5*x42 - 0.9*x47 - 1.1*x52 - 1.2*x57 - 0.5*x62 - 0.5*x67 - x72
- 0.9*x77 =L= 0;
e37.. x20 + x21 + x22 + x23 =E= 1;
e38.. x24 + x25 + x26 + x27 =E= 1;
e39.. x28 + x29 + x30 + x31 + x32 =E= 1;
e40.. x33 + x34 + x35 + x36 + x37 =E= 1;
e41.. -x20*x10 + x38 =E= 0;
e42.. -x20*x11 + x39 =E= 0;
e43.. -x20*x12 + x40 =E= 0;
e44.. -x20*x13 + x41 =E= 0;
e45.. -x20*x14 + x42 =E= 0;
e46.. -x21*x10 + x43 =E= 0;
e47.. -x21*x11 + x44 =E= 0;
e48.. -x21*x12 + x45 =E= 0;
e49.. -x21*x13 + x46 =E= 0;
e50.. -x21*x14 + x47 =E= 0;
e51.. -x22*x10 + x48 =E= 0;
e52.. -x22*x11 + x49 =E= 0;
e53.. -x22*x12 + x50 =E= 0;
e54.. -x22*x13 + x51 =E= 0;
e55.. -x22*x14 + x52 =E= 0;
e56.. -x23*x10 + x53 =E= 0;
e57.. -x23*x11 + x54 =E= 0;
e58.. -x23*x12 + x55 =E= 0;
e59.. -x23*x13 + x56 =E= 0;
e60.. -x23*x14 + x57 =E= 0;
e61.. -x24*x15 + x58 =E= 0;
e62.. -x24*x16 + x59 =E= 0;
e63.. -x24*x17 + x60 =E= 0;
e64.. -x24*x18 + x61 =E= 0;
e65.. -x24*x19 + x62 =E= 0;
e66.. -x25*x15 + x63 =E= 0;
e67.. -x25*x16 + x64 =E= 0;
e68.. -x25*x17 + x65 =E= 0;
e69.. -x25*x18 + x66 =E= 0;
e70.. -x25*x19 + x67 =E= 0;
e71.. -x26*x15 + x68 =E= 0;
e72.. -x26*x16 + x69 =E= 0;
e73.. -x26*x17 + x70 =E= 0;
e74.. -x26*x18 + x71 =E= 0;
e75.. -x26*x19 + x72 =E= 0;
e76.. -x27*x15 + x73 =E= 0;
e77.. -x27*x16 + x74 =E= 0;
e78.. -x27*x17 + x75 =E= 0;
e79.. -x27*x18 + x76 =E= 0;
e80.. -x27*x19 + x77 =E= 0;
e81.. -x28*x2 + x38 =E= 0;
e82.. -x29*x2 + x39 =E= 0;
e83.. -x30*x2 + x40 =E= 0;
e84.. -x31*x2 + x41 =E= 0;
e85.. -x32*x2 + x42 =E= 0;
e86.. -x28*x3 + x43 =E= 0;
e87.. -x29*x3 + x44 =E= 0;
e88.. -x30*x3 + x45 =E= 0;
e89.. -x31*x3 + x46 =E= 0;
e90.. -x32*x3 + x47 =E= 0;
e91.. -x28*x4 + x48 =E= 0;
e92.. -x29*x4 + x49 =E= 0;
e93.. -x30*x4 + x50 =E= 0;
e94.. -x31*x4 + x51 =E= 0;
e95.. -x32*x4 + x52 =E= 0;
e96.. -x28*x5 + x53 =E= 0;
e97.. -x29*x5 + x54 =E= 0;
e98.. -x30*x5 + x55 =E= 0;
e99.. -x31*x5 + x56 =E= 0;
e100.. -x32*x5 + x57 =E= 0;
e101.. -x33*x6 + x58 =E= 0;
e102.. -x34*x6 + x59 =E= 0;
e103.. -x35*x6 + x60 =E= 0;
e104.. -x36*x6 + x61 =E= 0;
e105.. -x37*x6 + x62 =E= 0;
e106.. -x33*x7 + x63 =E= 0;
e107.. -x34*x7 + x64 =E= 0;
e108.. -x35*x7 + x65 =E= 0;
e109.. -x36*x7 + x66 =E= 0;
e110.. -x37*x7 + x67 =E= 0;
e111.. -x33*x8 + x68 =E= 0;
e112.. -x34*x8 + x69 =E= 0;
e113.. -x35*x8 + x70 =E= 0;
e114.. -x36*x8 + x71 =E= 0;
e115.. -x37*x8 + x72 =E= 0;
e116.. -x33*x9 + x73 =E= 0;
e117.. -x34*x9 + x74 =E= 0;
e118.. -x35*x9 + x75 =E= 0;
e119.. -x36*x9 + x76 =E= 0;
e120.. -x37*x9 + x77 =E= 0;
* set non-default bounds
x2.up = 85;
x3.up = 85;
x4.up = 85;
x5.up = 85;
x6.up = 85;
x7.up = 85;
x8.up = 85;
x9.up = 85;
x10.up = 15;
x11.up = 25;
x12.up = 10;
x13.up = 20;
x14.up = 15;
x15.up = 15;
x16.up = 25;
x17.up = 10;
x18.up = 20;
x19.up = 15;
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 = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1;
x38.up = 15;
x39.up = 25;
x40.up = 10;
x41.up = 20;
x42.up = 15;
x43.up = 15;
x44.up = 25;
x45.up = 10;
x46.up = 20;
x47.up = 15;
x48.up = 15;
x49.up = 25;
x50.up = 10;
x51.up = 20;
x52.up = 15;
x53.up = 15;
x54.up = 25;
x55.up = 10;
x56.up = 20;
x57.up = 15;
x58.up = 15;
x59.up = 25;
x60.up = 10;
x61.up = 20;
x62.up = 15;
x63.up = 15;
x64.up = 25;
x65.up = 10;
x66.up = 20;
x67.up = 15;
x68.up = 15;
x69.up = 25;
x70.up = 10;
x71.up = 20;
x72.up = 15;
x73.up = 15;
x74.up = 25;
x75.up = 10;
x76.up = 20;
x77.up = 15;
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