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Instance pooling_adhya2pq

PQ 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)ⓘ	-549.80305020 p1 ( gdx sol ) (infeas: 5e-12)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-549.80306980 (ANTIGONE) -549.80306560 (BARON) -549.80306500 (GUROBI) -549.80305030 (LINDO) -549.80306360 (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ⓘ	33
#Binary Variablesⓘ	0
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	13
#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ⓘ	57
#Linear Constraintsⓘ	37
#Quadratic Constraintsⓘ	20
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	235
#Nonlinear Nonzeros in Jacobianⓘ	40
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	40
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	2
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
*         58       23        0       35        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         34       34        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        255      215       40        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;

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;

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;


e1..    objvar + 9*x15 + 18*x16 + 8*x17 + 3*x18 + 13*x19 + 22*x20 + 12*x21
      + 7*x22 + 14*x23 + 23*x24 + 13*x25 + 8*x26 + 6*x27 + 15*x28 + 5*x29
      + 11*x31 + 20*x32 + 10*x33 + 5*x34 =E= 0;

e2..    x15 + x16 + x17 + x18 =L= 75;

e3..    x19 + x20 + x21 + x22 =L= 75;

e4..    x23 + x24 + x25 + x26 =L= 75;

e5..    x27 + x28 + x29 + x30 =L= 75;

e6..    x31 + x32 + x33 + x34 =L= 75;

e7..    x15 + x16 + x17 + x18 + x19 + x20 + x21 + x22 =L= 75;

e8..    x23 + x24 + x25 + x26 + x27 + x28 + x29 + x30 + x31 + x32 + x33 + x34
      =L= 75;

e9..    x15 + x19 + x23 + x27 + x31 =L= 10;

e10..    x16 + x20 + x24 + x28 + x32 =L= 25;

e11..    x17 + x21 + x25 + x29 + x33 =L= 30;

e12..    x18 + x22 + x26 + x30 + x34 =L= 10;

e13..  - 2*x15 + x19 + x23 - 2*x31 =L= 0;

e14..    3*x15 - 2*x19 + 2.5*x23 - 0.3*x31 =L= 0;

e15..    0.75*x15 - 0.25*x19 - 0.25*x23 - 0.25*x27 + 0.75*x31 =L= 0;

e16..  - 0.25*x15 + 1.25*x19 + 0.15*x23 + 0.25*x27 + 0.85*x31 =L= 0;

e17..  - x15 - 2*x19 + x23 - 3*x27 - 3*x31 =L= 0;

e18..    4*x15 - x19 + 5*x23 - x27 + 2*x31 =L= 0;

e19..  - 3*x16 - x28 - 3*x32 =L= 0;

e20..    3.5*x16 - 1.5*x20 + 3*x24 + 0.5*x28 + 0.2*x32 =L= 0;

e21..    0.5*x16 - 0.5*x20 - 0.5*x24 - 0.5*x28 + 0.5*x32 =L= 0;

e22..  - x16 + 0.5*x20 - 0.6*x24 - 0.5*x28 + 0.1*x32 =L= 0;

e23..  - 2*x16 - 3*x20 - 4*x28 - 4*x32 =L= 0;

e24..    3*x16 - 2*x20 + 4*x24 - 2*x28 + x32 =L= 0;

e25..  - 0.5*x17 + 2.5*x21 + 2.5*x25 + 1.5*x29 - 0.5*x33 =L= 0;

e26..    0.5*x17 - 4.5*x21 - 2.5*x29 - 2.8*x33 =L= 0;

e27..    0.1*x17 - 0.9*x21 - 0.9*x25 - 0.9*x29 + 0.1*x33 =L= 0;

e28..  - 0.3*x17 + 1.2*x21 + 0.1*x25 + 0.2*x29 + 0.8*x33 =L= 0;

e29..  - 2*x17 - 3*x21 - 4*x29 - 4*x33 =L= 0;

e30..    3*x17 - 2*x21 + 4*x25 - 2*x29 + x33 =L= 0;

e31..  - 2*x18 + x22 + x26 - 2*x34 =L= 0;

e32..    2*x18 - 3*x22 + 1.5*x26 - x30 - 1.3*x34 =L= 0;

e33..  - x22 - x26 - x30 =L= 0;

e34..  - 1.3*x18 + 0.2*x22 - 0.9*x26 - 0.8*x30 - 0.2*x34 =L= 0;

e35..  - 3*x18 - 4*x22 - x26 - 5*x30 - 5*x34 =L= 0;

e36..    3*x18 - 2*x22 + 4*x26 - 2*x30 + x34 =L= 0;

e37..    x2 + x3 =E= 1;

e38..    x4 + x5 + x6 =E= 1;

e39.. -x2*x7 + x15 =E= 0;

e40.. -x2*x8 + x16 =E= 0;

e41.. -x2*x9 + x17 =E= 0;

e42.. -x2*x10 + x18 =E= 0;

e43.. -x3*x7 + x19 =E= 0;

e44.. -x3*x8 + x20 =E= 0;

e45.. -x3*x9 + x21 =E= 0;

e46.. -x3*x10 + x22 =E= 0;

e47.. -x4*x11 + x23 =E= 0;

e48.. -x4*x12 + x24 =E= 0;

e49.. -x4*x13 + x25 =E= 0;

e50.. -x4*x14 + x26 =E= 0;

e51.. -x5*x11 + x27 =E= 0;

e52.. -x5*x12 + x28 =E= 0;

e53.. -x5*x13 + x29 =E= 0;

e54.. -x5*x14 + x30 =E= 0;

e55.. -x6*x11 + x31 =E= 0;

e56.. -x6*x12 + x32 =E= 0;

e57.. -x6*x13 + x33 =E= 0;

e58.. -x6*x14 + x34 =E= 0;

* set non-default bounds
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
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 = 10;
x16.up = 25;
x17.up = 30;
x18.up = 10;
x19.up = 10;
x20.up = 25;
x21.up = 30;
x22.up = 10;
x23.up = 10;
x24.up = 25;
x25.up = 30;
x26.up = 10;
x27.up = 10;
x28.up = 25;
x29.up = 30;
x30.up = 10;
x31.up = 10;
x32.up = 25;
x33.up = 30;
x34.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;