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Instance waterund08

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
164.48977470 p1 ( gdx sol )
(infeas: 3e-11)
Other points (infeas > 1e-08)  
Dual Bounds
164.48977450 (ANTIGONE)
164.48975950 (BARON)
164.48407390 (COUENNE)
164.48977370 (GUROBI)
164.48977470 (LINDO)
164.48940210 (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_Ex08.gms
Application Water Network Design
Added to library 15 Aug 2014
Problem type QCP
#Variables 90
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 70
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 15
#Nonlinear Nonzeros in Objective 0
#Constraints 95
#Linear Constraints 55
#Quadratic Constraints 40
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 460
#Nonlinear Nonzeros in Jacobian 300
#Nonzeros in (Upper-Left) Hessian of Lagrangian 280
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 5
Minimal blocksize in Hessian of Lagrangian 14
Maximal blocksize in Hessian of Lagrangian 14
Average blocksize in Hessian of Lagrangian 14.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e+00
Maximal coefficient 5.0000e+00
Infeasibility of initial point 1.9e+05
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
*         96       51        0       45        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         91       91        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        476      176      300        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,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91;

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,x78,x79,x80,x81,x82,x83,x84,x85
          ,x86,x87,x88,x89,x90,x91;

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;


e1..    objvar - x2 - x3 - x4 - x5 - x6 - x7 - x8 - x9 - x10 - x11 - x12 - x13
      - x14 - x15 - x16 =E= 0;

e2..  - x2 - x7 - x12 + x17 - x27 - x32 - x37 - x42 - x47 =E= 0;

e3..  - x3 - x8 - x13 + x18 - x28 - x33 - x38 - x43 - x48 =E= 0;

e4..  - x4 - x9 - x14 + x19 - x29 - x34 - x39 - x44 - x49 =E= 0;

e5..  - x5 - x10 - x15 + x20 - x30 - x35 - x40 - x45 - x50 =E= 0;

e6..  - x6 - x11 - x16 + x21 - x31 - x36 - x41 - x46 - x51 =E= 0;

e7..    x17 - x22 - x27 - x28 - x29 - x30 - x31 =E= 0;

e8..    x18 - x23 - x32 - x33 - x34 - x35 - x36 =E= 0;

e9..    x19 - x24 - x37 - x38 - x39 - x40 - x41 =E= 0;

e10..    x20 - x25 - x42 - x43 - x44 - x45 - x46 =E= 0;

e11..    x21 - x26 - x47 - x48 - x49 - x50 - x51 =E= 0;

e12.. x17*x52 - (x27*x72 + x32*x76 + x37*x80 + x42*x84 + x47*x88) - 5*x2 =E= 0;

e13.. x17*x53 - (x27*x73 + x32*x77 + x37*x81 + x42*x85 + x47*x89) - 2*x7
       - 4*x12 =E= 0;

e14.. x17*x54 - (x27*x74 + x32*x78 + x37*x82 + x42*x86 + x47*x90) - 3*x7 =E= 0;

e15.. x17*x55 - (x27*x75 + x32*x79 + x37*x83 + x42*x87 + x47*x91) - 2*x2 - 2*x7
       - 3*x12 =E= 0;

e16.. x18*x56 - (x28*x72 + x33*x76 + x38*x80 + x43*x84 + x48*x88) - 5*x3 =E= 0;

e17.. x18*x57 - (x28*x73 + x33*x77 + x38*x81 + x43*x85 + x48*x89) - 2*x8
       - 4*x13 =E= 0;

e18.. x18*x58 - (x28*x74 + x33*x78 + x38*x82 + x43*x86 + x48*x90) - 3*x8 =E= 0;

e19.. x18*x59 - (x28*x75 + x33*x79 + x38*x83 + x43*x87 + x48*x91) - 2*x3 - 2*x8
       - 3*x13 =E= 0;

e20.. x19*x60 - (x29*x72 + x34*x76 + x39*x80 + x44*x84 + x49*x88) - 5*x4 =E= 0;

e21.. x19*x61 - (x29*x73 + x34*x77 + x39*x81 + x44*x85 + x49*x89) - 2*x9
       - 4*x14 =E= 0;

e22.. x19*x62 - (x29*x74 + x34*x78 + x39*x82 + x44*x86 + x49*x90) - 3*x9 =E= 0;

e23.. x19*x63 - (x29*x75 + x34*x79 + x39*x83 + x44*x87 + x49*x91) - 2*x4 - 2*x9
       - 3*x14 =E= 0;

e24.. x20*x64 - (x30*x72 + x35*x76 + x40*x80 + x45*x84 + x50*x88) - 5*x5 =E= 0;

e25.. x20*x65 - (x30*x73 + x35*x77 + x40*x81 + x45*x85 + x50*x89) - 2*x10
       - 4*x15 =E= 0;

e26.. x20*x66 - (x30*x74 + x35*x78 + x40*x82 + x45*x86 + x50*x90) - 3*x10 =E= 0
      ;

e27.. x20*x67 - (x30*x75 + x35*x79 + x40*x83 + x45*x87 + x50*x91) - 2*x5
       - 2*x10 - 3*x15 =E= 0;

e28.. x21*x68 - (x31*x72 + x36*x76 + x41*x80 + x46*x84 + x51*x88) - 5*x6 =E= 0;

e29.. x21*x69 - (x31*x73 + x36*x77 + x41*x81 + x46*x85 + x51*x89) - 2*x11
       - 4*x16 =E= 0;

e30.. x21*x70 - (x31*x74 + x36*x78 + x41*x82 + x46*x86 + x51*x90) - 3*x11 =E= 0
      ;

e31.. x21*x71 - (x31*x75 + x36*x79 + x41*x83 + x46*x87 + x51*x91) - 2*x6
       - 2*x11 - 3*x16 =E= 0;

e32.. -x17*(x72 - x52) =E= -1080;

e33.. -x17*(x73 - x53) =E= -28296;

e34.. -x17*(x74 - x54) =E= -2520;

e35.. -x17*(x75 - x55) =E= -2016;

e36.. -x18*(x76 - x56) =E= -3400;

e37.. -x18*(x77 - x57) =E= -32300;

e38.. -x18*(x78 - x58) =E= -4590;

e39.. -x18*(x79 - x59) =E= -1122;

e40.. -x19*(x80 - x60) =E= -5600;

e41.. -x19*(x81 - x61) =E= -1400;

e42.. -x19*(x82 - x62) =E= -11200;

e43.. -x19*(x83 - x63) =E= -2408;

e44.. -x20*(x84 - x64) =E= -3348;

e45.. -x20*(x85 - x65) =E= -2108;

e46.. -x20*(x86 - x66) =E= -1860;

e47.. -x20*(x87 - x67) =E= -1364;

e48.. -x21*(x88 - x68) =E= -1500;

e49.. -x21*(x89 - x69) =E= -190000;

e50.. -x21*(x90 - x70) =E= -1500;

e51.. -x21*(x91 - x71) =E= -4425;

e52..    x52 =L= 0;

e53..    x53 =L= 7;

e54..    x54 =L= 0;

e55..    x55 =L= 12;

e56..    x56 =L= 20;

e57..    x57 =L= 300;

e58..    x58 =L= 45;

e59..    x59 =L= 34;

e60..    x60 =L= 120;

e61..    x61 =L= 20;

e62..    x62 =L= 200;

e63..    x63 =L= 56;

e64..    x64 =L= 23;

e65..    x65 =L= 43;

e66..    x66 =L= 15;

e67..    x67 =L= 123;

e68..    x68 =L= 90;

e69..    x69 =L= 400;

e70..    x70 =L= 60;

e71..    x71 =L= 57;

e72..    x72 =L= 15;

e73..    x73 =L= 400;

e74..    x74 =L= 35;

e75..    x75 =L= 40;

e76..    x76 =L= 120;

e77..    x77 =L= 1250;

e78..    x78 =L= 180;

e79..    x79 =L= 67;

e80..    x80 =L= 220;

e81..    x81 =L= 45;

e82..    x82 =L= 400;

e83..    x83 =L= 99;

e84..    x84 =L= 50;

e85..    x85 =L= 60;

e86..    x86 =L= 30;

e87..    x87 =L= 134;

e88..    x88 =L= 150;

e89..    x89 =L= 8000;

e90..    x90 =L= 120;

e91..    x91 =L= 234;

e92..    x17 =L= 72;

e93..    x18 =L= 34;

e94..    x19 =L= 56;

e95..    x20 =L= 124;

e96..    x21 =L= 25;

* 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;
x62.up = 100000;
x63.up = 100000;
x64.up = 100000;
x65.up = 100000;
x66.up = 100000;
x67.up = 100000;
x68.up = 100000;
x69.up = 100000;
x70.up = 100000;
x71.up = 100000;
x72.up = 100000;
x73.up = 100000;
x74.up = 100000;
x75.up = 100000;
x76.up = 100000;
x77.up = 100000;
x78.up = 100000;
x79.up = 100000;
x80.up = 100000;
x81.up = 100000;
x82.up = 100000;
x83.up = 100000;
x84.up = 100000;
x85.up = 100000;
x86.up = 100000;
x87.up = 100000;
x88.up = 100000;
x89.up = 100000;
x90.up = 100000;
x91.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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