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Instance waterund25

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
415.47404790 p1 ( gdx sol )
(infeas: 3e-11)
410.63539290 p2 ( gdx sol )
(infeas: 1e-11)
Other points (infeas > 1e-08)  
Dual Bounds
395.14352860 (ANTIGONE)
381.64063260 (BARON)
375.06207940 (COUENNE)
400.22497160 (GUROBI)
388.71356520 (LINDO)
407.49487730 (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_Ex25.gms
Application Water Network Design
Added to library 15 Aug 2014
Problem type QCP
#Variables 121
#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 28
#Nonlinear Nonzeros in Objective 0
#Constraints 87
#Linear Constraints 51
#Quadratic Constraints 36
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 591
#Nonlinear Nonzeros in Jacobian 285
#Nonzeros in (Upper-Left) Hessian of Lagrangian 270
#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 1.0520e+03
Infeasibility of initial point 1.182e+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
*         88       45        6       37        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        122      122        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        620      335      285        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,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
          ,x116,x117,x118,x119,x120,x121,x122;

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,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101
          ,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114
          ,x115,x116,x117,x118,x119,x120,x121,x122;

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;


e1..    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 =E= 0;

e2..  - x2 - x9 - x16 - x23 + x30 - x44 - x51 - x58 - x65 - x72 - x79 - x86
      =E= 0;

e3..  - x3 - x10 - x17 - x24 + x31 - x45 - x52 - x59 - x66 - x73 - x80 - x87
      =E= 0;

e4..  - x4 - x11 - x18 - x25 + x32 - x46 - x53 - x60 - x67 - x74 - x81 - x88
      =E= 0;

e5..  - x5 - x12 - x19 - x26 + x33 - x47 - x54 - x61 - x68 - x75 - x82 - x89
      =E= 0;

e6..  - x6 - x13 - x20 - x27 + x34 - x48 - x55 - x62 - x69 - x76 - x83 - x90
      =E= 0;

e7..  - x7 - x14 - x21 - x28 - x49 - x56 - x63 - x70 - x77 - x84 - x91 =E= -95;

e8..  - x8 - x15 - x22 - x29 - x50 - x57 - x64 - x71 - x78 - x85 - x92 =E= -50;

e9..    x30 - x37 - x44 - x45 - x46 - x47 - x48 - x49 - x50 =E= 0;

e10..    x31 - x38 - x51 - x52 - x53 - x54 - x55 - x56 - x57 =E= 0;

e11..    x32 - x39 - x58 - x59 - x60 - x61 - x62 - x63 - x64 =E= 0;

e12..    x33 - x40 - x65 - x66 - x67 - x68 - x69 - x70 - x71 =E= 0;

e13..    x34 - x41 - x72 - x73 - x74 - x75 - x76 - x77 - x78 =E= 0;

e14..  - x42 - x79 - x80 - x81 - x82 - x83 - x84 - x85 =E= -55;

e15..  - x43 - x86 - x87 - x88 - x89 - x90 - x91 - x92 =E= -80;

e16.. x30*x93 - (x44*x108 + x51*x111 + x58*x114 + x65*x117 + x72*x120) - 4*x2
       - 7*x9 - 7*x16 - 6*x23 - 809*x79 - 1052*x86 =E= 0;

e17.. x30*x94 - (x44*x109 + x51*x112 + x58*x115 + x65*x118 + x72*x121) - 5*x2
       - 8*x9 - 3*x16 - 4*x23 - 899*x79 - 229*x86 =E= 0;

e18.. x30*x95 - (x44*x110 + x51*x113 + x58*x116 + x65*x119 + x72*x122) - 9*x2
       - x9 - x16 - 9*x23 - 985*x79 - 783*x86 =E= 0;

e19.. x31*x96 - (x45*x108 + x52*x111 + x59*x114 + x66*x117 + x73*x120) - 4*x3
       - 7*x10 - 7*x17 - 6*x24 - 809*x80 - 1052*x87 =E= 0;

e20.. x31*x97 - (x45*x109 + x52*x112 + x59*x115 + x66*x118 + x73*x121) - 5*x3
       - 8*x10 - 3*x17 - 4*x24 - 899*x80 - 229*x87 =E= 0;

e21.. x31*x98 - (x45*x110 + x52*x113 + x59*x116 + x66*x119 + x73*x122) - 9*x3
       - x10 - x17 - 9*x24 - 985*x80 - 783*x87 =E= 0;

e22.. x32*x99 - (x46*x108 + x53*x111 + x60*x114 + x67*x117 + x74*x120) - 4*x4
       - 7*x11 - 7*x18 - 6*x25 - 809*x81 - 1052*x88 =E= 0;

e23.. x32*x100 - (x46*x109 + x53*x112 + x60*x115 + x67*x118 + x74*x121) - 5*x4
       - 8*x11 - 3*x18 - 4*x25 - 899*x81 - 229*x88 =E= 0;

e24.. x32*x101 - (x46*x110 + x53*x113 + x60*x116 + x67*x119 + x74*x122) - 9*x4
       - x11 - x18 - 9*x25 - 985*x81 - 783*x88 =E= 0;

e25.. x33*x102 - (x47*x108 + x54*x111 + x61*x114 + x68*x117 + x75*x120) - 4*x5
       - 7*x12 - 7*x19 - 6*x26 - 809*x82 - 1052*x89 =E= 0;

e26.. x33*x103 - (x47*x109 + x54*x112 + x61*x115 + x68*x118 + x75*x121) - 5*x5
       - 8*x12 - 3*x19 - 4*x26 - 899*x82 - 229*x89 =E= 0;

e27.. x33*x104 - (x47*x110 + x54*x113 + x61*x116 + x68*x119 + x75*x122) - 9*x5
       - x12 - x19 - 9*x26 - 985*x82 - 783*x89 =E= 0;

e28.. x34*x105 - (x48*x108 + x55*x111 + x62*x114 + x69*x117 + x76*x120) - 4*x6
       - 7*x13 - 7*x20 - 6*x27 - 809*x83 - 1052*x90 =E= 0;

e29.. x34*x106 - (x48*x109 + x55*x112 + x62*x115 + x69*x118 + x76*x121) - 5*x6
       - 8*x13 - 3*x20 - 4*x27 - 899*x83 - 229*x90 =E= 0;

e30.. x34*x107 - (x48*x110 + x55*x113 + x62*x116 + x69*x119 + x76*x122) - 9*x6
       - x13 - x20 - 9*x27 - 985*x83 - 783*x90 =E= 0;

e31.. -x30*(x108 - x93) =E= -702;

e32.. -x30*(x109 - x94) =E= -3294;

e33.. -x30*(x110 - x95) =E= -918;

e34.. -x31*(x111 - x96) =E= -102138;

e35.. -x31*(x112 - x97) =E= -32364;

e36.. -x31*(x113 - x98) =E= -2088;

e37.. -x32*(x114 - x99) =E= -118198;

e38.. -x32*(x115 - x100) =E= -36838;

e39.. -x32*(x116 - x101) =E= -113678;

e40.. -x33*(x117 - x102) =E= -8568;

e41.. -x33*(x118 - x103) =E= -44948;

e42.. -x33*(x119 - x104) =E= -19788;

e43.. -x34*(x120 - x105) =E= -82600;

e44.. -x34*(x121 - x106) =E= -4100;

e45.. -x34*(x122 - x107) =E= -90400;

e46..    x93 =L= 857;

e47..    x94 =L= 479;

e48..    x95 =L= 781;

e49..    x96 =L= 71;

e50..    x97 =L= 990;

e51..    x98 =L= 998;

e52..    x99 =L= 650;

e53..    x100 =L= 759;

e54..    x101 =L= 54;

e55..    x102 =L= 905;

e56..    x103 =L= 120;

e57..    x104 =L= 452;

e58..    x105 =L= 366;

e59..    x106 =L= 169;

e60..    x107 =L= 169;

e61..    x108 =L= 870;

e62..    x109 =L= 540;

e63..    x110 =L= 798;

e64..    x111 =L= 658;

e65..    x112 =L= 1176;

e66..    x113 =L= 1010;

e67..    x114 =L= 1173;

e68..    x115 =L= 922;

e69..    x116 =L= 557;

e70..    x117 =L= 1031;

e71..    x118 =L= 781;

e72..    x119 =L= 743;

e73..    x120 =L= 1192;

e74..    x121 =L= 210;

e75..    x122 =L= 1073;

e76.. -(x49*x108 + x56*x111 + x63*x114 + x70*x117 + x77*x120) - 4*x7 - 7*x14
       - 7*x21 - 6*x28 - 809*x84 - 1052*x91 =G= -22990;

e77.. -(x49*x109 + x56*x112 + x63*x115 + x70*x118 + x77*x121) - 5*x7 - 8*x14
       - 3*x21 - 4*x28 - 899*x84 - 229*x91 =G= -61940;

e78.. -(x49*x110 + x56*x113 + x63*x116 + x70*x119 + x77*x122) - 9*x7 - x14
       - x21 - 9*x28 - 985*x84 - 783*x91 =G= -8740;

e79.. -(x50*x108 + x57*x111 + x64*x114 + x71*x117 + x78*x120) - 4*x8 - 7*x15
       - 7*x22 - 6*x29 - 809*x85 - 1052*x92 =G= -30900;

e80.. -(x50*x109 + x57*x112 + x64*x115 + x71*x118 + x78*x121) - 5*x8 - 8*x15
       - 3*x22 - 4*x29 - 899*x85 - 229*x92 =G= -6700;

e81.. -(x50*x110 + x57*x113 + x64*x116 + x71*x119 + x78*x122) - 9*x8 - x15
       - x22 - 9*x29 - 985*x85 - 783*x92 =G= -37200;

e82..    x30 =L= 54;

e83..    x31 =L= 174;

e84..    x32 =L= 226;

e85..    x33 =L= 68;

e86..    x34 =L= 100;

e87..    x35 =L= 0;

e88..    x36 =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;
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;
x92.up = 100000;
x93.up = 100000;
x94.up = 100000;
x95.up = 100000;
x96.up = 100000;
x97.up = 100000;
x98.up = 100000;
x99.up = 100000;
x100.up = 100000;
x101.up = 100000;
x102.up = 100000;
x103.up = 100000;
x104.up = 100000;
x105.up = 100000;
x106.up = 100000;
x107.up = 100000;
x108.up = 100000;
x109.up = 100000;
x110.up = 100000;
x111.up = 100000;
x112.up = 100000;
x113.up = 100000;
x114.up = 100000;
x115.up = 100000;
x116.up = 100000;
x117.up = 100000;
x118.up = 100000;
x119.up = 100000;
x120.up = 100000;
x121.up = 100000;
x122.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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