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Instance pooling_rt2pq

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)
-4391.82589300 p1 ( gdx sol )
(infeas: 1e-14)
Other points (infeas > 1e-08)  
Dual Bounds
-4391.82593000 (ANTIGONE)
-4391.82590200 (BARON)
-4391.82681600 (COUENNE)
-4391.82595600 (GUROBI)
-4391.82589300 (LINDO)
-4391.82600300 (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 34
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 12
#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 52
#Linear Constraints 34
#Quadratic Constraints 18
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 277
#Nonlinear Nonzeros in Jacobian 36
#Nonzeros in (Upper-Left) Hessian of Lagrangian 36
#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 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 of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         53       21        3       29        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         35       35        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        300      264       36        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;

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;

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 + 180.8*x8 + 128*x9 + 88*x10 - 110*x11 + 140.8*x18 + 180.8*x19
      + 100.8*x20 + 140.8*x21 + 180.8*x22 + 100.8*x23 + 128*x24 + 168*x25
      + 88*x26 + 128*x27 + 168*x28 + 88*x29 - 110*x30 - 70*x31 - 150*x32
      - 110*x33 - 70*x34 - 150*x35 =E= 0;

e2..    x8 + x18 + x19 + x20 + x21 + x22 + x23 =L= 60.98;

e3..    x9 + x10 + x24 + x25 + x26 + x27 + x28 + x29 =L= 161.29;

e4..    x11 + x30 + x31 + x32 + x33 + x34 + x35 =L= 5;

e5..    x18 + x19 + x20 + x24 + x25 + x26 + x30 + x31 + x32 =L= 12.5;

e6..    x21 + x22 + x23 + x27 + x28 + x29 + x33 + x34 + x35 =L= 17.5;

e7..    x9 + x11 + x18 + x21 + x24 + x27 + x30 + x33 =G= 5;

e8..    x8 + x19 + x22 + x25 + x28 + x31 + x34 =G= 5;

e9..    x10 + x20 + x23 + x26 + x29 + x32 + x35 =G= 5;

e10..    x9 + x11 + x18 + x21 + x24 + x27 + x30 + x33 =L= 300;

e11..    x8 + x19 + x22 + x25 + x28 + x31 + x34 =L= 300;

e12..    x10 + x20 + x23 + x26 + x29 + x32 + x35 =L= 300;

e13..  - 0.17*x9 - 0.04*x11 + 0.0299999999999999*x18 + 0.0299999999999999*x21
       - 0.17*x24 - 0.17*x27 - 0.04*x30 - 0.04*x33 =L= 0;

e14..  - 3*x9 - 3*x11 - 3*x24 - 3*x27 - 3*x30 - 3*x33 =L= 0;

e15..  - 26.1*x9 - 14.8*x18 - 14.8*x21 - 26.1*x24 - 26.1*x27 =L= 0;

e16..  - 15.2*x9 - 8.2*x18 - 8.2*x21 - 15.2*x24 - 15.2*x27 =L= 0;

e17..    0.12*x9 - 0.01*x11 - 0.08*x18 - 0.08*x21 + 0.12*x24 + 0.12*x27
       - 0.01*x30 - 0.01*x33 =L= 0;

e18..    7.09999999999999*x9 - 19*x11 - 4.2*x18 - 4.2*x21
       + 7.09999999999999*x24 + 7.09999999999999*x27 - 19*x30 - 19*x33 =L= 0;

e19..    1.5*x9 - 13.7*x11 - 5.5*x18 - 5.5*x21 + 1.5*x24 + 1.5*x27 - 13.7*x30
       - 13.7*x33 =L= 0;

e20..    0.0299999999999999*x8 + 0.0299999999999999*x19
       + 0.0299999999999999*x22 - 0.17*x25 - 0.17*x28 - 0.04*x31 - 0.04*x34
       =L= 0;

e21..    2.1*x8 + 2.1*x19 + 2.1*x22 - 0.9*x25 - 0.9*x28 - 0.9*x31 - 0.9*x34
       =L= 0;

e22..  - 14.8*x8 - 14.8*x19 - 14.8*x22 - 26.1*x25 - 26.1*x28 =L= 0;

e23..  - 8.2*x8 - 8.2*x19 - 8.2*x22 - 15.2*x25 - 15.2*x28 =L= 0;

e24..  - 0.08*x8 - 0.08*x19 - 0.08*x22 + 0.12*x25 + 0.12*x28 - 0.01*x31
       - 0.01*x34 =L= 0;

e25..  - 3.2*x8 - 3.2*x19 - 3.2*x22 + 8.09999999999999*x25
       + 8.09999999999999*x28 - 18*x31 - 18*x34 =L= 0;

e26..  - 2.5*x8 - 2.5*x19 - 2.5*x22 + 4.5*x25 + 4.5*x28 - 10.7*x31 - 10.7*x34
       =L= 0;

e27..  - 0.17*x10 + 0.0299999999999999*x20 + 0.0299999999999999*x23 - 0.17*x26
       - 0.17*x29 - 0.04*x32 - 0.04*x35 =L= 0;

e28..  - 3*x10 - 3*x26 - 3*x29 - 3*x32 - 3*x35 =L= 0;

e29..  - 26.1*x10 - 14.8*x20 - 14.8*x23 - 26.1*x26 - 26.1*x29 =L= 0;

e30..  - 15.2*x10 - 8.2*x20 - 8.2*x23 - 15.2*x26 - 15.2*x29 =L= 0;

e31..    0.12*x10 - 0.08*x20 - 0.08*x23 + 0.12*x26 + 0.12*x29 - 0.01*x32
       - 0.01*x35 =L= 0;

e32..    3.09999999999999*x10 - 8.2*x20 - 8.2*x23 + 3.09999999999999*x26
       + 3.09999999999999*x29 - 23*x32 - 23*x35 =L= 0;

e33..  - 7*x20 - 7*x23 - 15.2*x32 - 15.2*x35 =L= 0;

e34..    x2 + x4 + x6 =E= 1;

e35..    x3 + x5 + x7 =E= 1;

e36.. -x2*x12 + x18 =E= 0;

e37.. -x2*x13 + x19 =E= 0;

e38.. -x2*x14 + x20 =E= 0;

e39.. -x3*x15 + x21 =E= 0;

e40.. -x3*x16 + x22 =E= 0;

e41.. -x3*x17 + x23 =E= 0;

e42.. -x4*x12 + x24 =E= 0;

e43.. -x4*x13 + x25 =E= 0;

e44.. -x4*x14 + x26 =E= 0;

e45.. -x5*x15 + x27 =E= 0;

e46.. -x5*x16 + x28 =E= 0;

e47.. -x5*x17 + x29 =E= 0;

e48.. -x6*x12 + x30 =E= 0;

e49.. -x6*x13 + x31 =E= 0;

e50.. -x6*x14 + x32 =E= 0;

e51.. -x7*x15 + x33 =E= 0;

e52.. -x7*x16 + x34 =E= 0;

e53.. -x7*x17 + x35 =E= 0;

* set non-default bounds
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 60.98;
x9.up = 161.29;
x10.up = 161.29;
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 = 12.5;
x19.up = 12.5;
x20.up = 12.5;
x21.up = 17.5;
x22.up = 17.5;
x23.up = 17.5;
x24.up = 12.5;
x25.up = 12.5;
x26.up = 12.5;
x27.up = 17.5;
x28.up = 17.5;
x29.up = 17.5;
x30.up = 5;
x31.up = 5;
x32.up = 5;
x33.up = 5;
x34.up = 5;
x35.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: 2022-08-11 Git hash: f176bd52
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