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Instance waterund18

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
238.73333330 p1 ( gdx sol )
(infeas: 5e-13)
Other points (infeas > 1e-08)  
Dual Bounds
237.14317200 (ANTIGONE)
237.08510780 (BARON)
236.84070550 (COUENNE)
238.66375020 (GUROBI)
236.95696980 (LINDO)
238.65264270 (SCIP)
References Castro, Pedro M and Teles, João P, Comparison of global optimization algorithms for the design of water-using networks, Computers and Chemical Engineering, 52, 2013, 249-261.
Teles, João P, Castro, Pedro M, and Novais, Augusto Q, LP-based solution strategies for the optimal design of industrial water networks with multiple contaminants, Chemical Engineering Science, 63:2, 2008, 376-394.
Teles, João P, Castro, Pedro M, and Matos, Henrique A, Global optimization of water networks design using multiparametric disaggregation, Computers and Chemical Engineering 40, 2012, 132-147.
Source ANTIGONE test library model Other_MIQCQP/teles_etal_2009_WUN_Ex18.gms
Application Water Network Design
Added to library 15 Aug 2014
Problem type QCP
#Variables 60
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 39
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 12
#Nonlinear Nonzeros in Objective 0
#Constraints 64
#Linear Constraints 36
#Quadratic Constraints 28
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 274
#Nonlinear Nonzeros in Jacobian 156
#Nonzeros in (Upper-Left) Hessian of Lagrangian 144
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 13
Maximal blocksize in Hessian of Lagrangian 13
Average blocksize in Hessian of Lagrangian 13.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e+00
Maximal coefficient 2.5000e+02
Infeasibility of initial point 1.23e+04
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
*         65       33        4       28        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         61       61        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        287      131      156        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;

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;

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;


e1..    objvar - x2 - x3 - x4 - x5 - x6 - x7 - x8 - x9 - x10 - x11 - x12 - x13
      =E= 0;

e2..  - x2 - x6 - x10 + x14 - x22 - x26 - x30 - x34 =E= 0;

e3..  - x3 - x7 - x11 + x15 - x23 - x27 - x31 - x35 =E= 0;

e4..  - x4 - x8 - x12 + x16 - x24 - x28 - x32 - x36 =E= 0;

e5..  - x5 - x9 - x13 - x25 - x29 - x33 - x37 =E= -170;

e6..    x14 - x18 - x22 - x23 - x24 - x25 =E= 0;

e7..    x15 - x19 - x26 - x27 - x28 - x29 =E= 0;

e8..    x16 - x20 - x30 - x31 - x32 - x33 =E= 0;

e9..  - x21 - x34 - x35 - x36 - x37 =E= -140;

e10.. x14*x38 - (x22*x50 + x26*x54 + x30*x58) - 2*x6 - 250*x34 =E= 0;

e11.. x14*x39 - (x22*x51 + x26*x55 + x30*x59) - 3*x2 - x6 - 180*x34 =E= 0;

e12.. x14*x40 - (x22*x52 + x26*x56 + x30*x60) - x10 - 90*x34 =E= 0;

e13.. x14*x41 - (x22*x53 + x26*x57 + x30*x61) - 3*x10 - 90*x34 =E= 0;

e14.. x15*x42 - (x23*x50 + x27*x54 + x31*x58) - 2*x7 - 250*x35 =E= 0;

e15.. x15*x43 - (x23*x51 + x27*x55 + x31*x59) - 3*x3 - x7 - 180*x35 =E= 0;

e16.. x15*x44 - (x23*x52 + x27*x56 + x31*x60) - x11 - 90*x35 =E= 0;

e17.. x15*x45 - (x23*x53 + x27*x57 + x31*x61) - 3*x11 - 90*x35 =E= 0;

e18.. x16*x46 - (x24*x50 + x28*x54 + x32*x58) - 2*x8 - 250*x36 =E= 0;

e19.. x16*x47 - (x24*x51 + x28*x55 + x32*x59) - 3*x4 - x8 - 180*x36 =E= 0;

e20.. x16*x48 - (x24*x52 + x28*x56 + x32*x60) - x12 - 90*x36 =E= 0;

e21.. x16*x49 - (x24*x53 + x28*x57 + x32*x61) - 3*x12 - 90*x36 =E= 0;

e22.. -x14*(x50 - x38) =E= -3690;

e23.. -x14*(x51 - x39) =E= -3690;

e24.. -x14*(x52 - x40) =E= -1230;

e25.. -x14*(x53 - x41) =E= -3690;

e26.. -x15*(x54 - x42) =E= -940;

e27.. -x15*(x55 - x43) =E= -2350;

e28.. -x15*(x56 - x44) =E= -1175;

e29.. -x15*(x57 - x45) =E= -1880;

e30.. -x16*(x58 - x46) =E= -12300;

e31.. -x16*(x59 - x47) =E= -12300;

e32.. -x16*(x60 - x48) =E= -6150;

e33.. -x16*(x61 - x49) =E= -4920;

e34..    x38 =L= 20;

e35..    x39 =L= 30;

e36..    x40 =L= 20;

e37..    x41 =L= 10;

e38..    x42 =L= 50;

e39..    x43 =L= 20;

e40..    x44 =L= 20;

e41..    x45 =L= 20;

e42..    x46 =L= 100;

e43..    x47 =L= 150;

e44..    x48 =L= 30;

e45..    x49 =L= 20;

e46..    x50 =L= 50;

e47..    x51 =L= 60;

e48..    x52 =L= 30;

e49..    x53 =L= 40;

e50..    x54 =L= 70;

e51..    x55 =L= 70;

e52..    x56 =L= 45;

e53..    x57 =L= 60;

e54..    x58 =L= 200;

e55..    x59 =L= 250;

e56..    x60 =L= 80;

e57..    x61 =L= 60;

e58.. -(x25*x50 + x29*x54 + x33*x58) - 2*x9 - 250*x37 =G= -34000;

e59.. -(x25*x51 + x29*x55 + x33*x59) - 3*x5 - x9 - 180*x37 =G= -13600;

e60.. -(x25*x52 + x29*x56 + x33*x60) - x13 - 90*x37 =G= -3400;

e61.. -(x25*x53 + x29*x57 + x33*x61) - 3*x13 - 90*x37 =G= -10200;

e62..    x14 =L= 123;

e63..    x15 =L= 47;

e64..    x16 =L= 123;

e65..    x17 =L= 0;

* set non-default bounds
x2.up = 100000;
x3.up = 100000;
x4.up = 100000;
x5.up = 100000;
x6.up = 100000;
x7.up = 100000;
x8.up = 100000;
x9.up = 100000;
x10.up = 100000;
x11.up = 100000;
x12.up = 100000;
x13.up = 100000;
x14.up = 100000;
x15.up = 100000;
x16.up = 100000;
x17.up = 100000;
x18.up = 100000;
x19.up = 100000;
x20.up = 100000;
x21.up = 100000;
x22.up = 100000;
x23.up = 100000;
x24.up = 100000;
x25.up = 100000;
x26.up = 100000;
x27.up = 100000;
x28.up = 100000;
x29.up = 100000;
x30.up = 100000;
x31.up = 100000;
x32.up = 100000;
x33.up = 100000;
x34.up = 100000;
x35.up = 100000;
x36.up = 100000;
x37.up = 100000;
x38.up = 100000;
x39.up = 100000;
x40.up = 100000;
x41.up = 100000;
x42.up = 100000;
x43.up = 100000;
x44.up = 100000;
x45.up = 100000;
x46.up = 100000;
x47.up = 100000;
x48.up = 100000;
x49.up = 100000;
x50.up = 100000;
x51.up = 100000;
x52.up = 100000;
x53.up = 100000;
x54.up = 100000;
x55.up = 100000;
x56.up = 100000;
x57.up = 100000;
x58.up = 100000;
x59.up = 100000;
x60.up = 100000;
x61.up = 100000;

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: 2022-05-24 Git hash: 1198c186
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