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Instance wastewater15m2

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
2446.42857100 p1 ( gdx sol )
(infeas: 7e-12)
Other points (infeas > 1e-08)  
Dual Bounds
2446.42856900 (ANTIGONE)
2446.42856900 (BARON)
1237.89352100 (COUENNE)
2446.42857100 (GUROBI)
1715.35037200 (LINDO)
2446.42857100 (SCIP)
References Castro, Pedro M, Matos, Henrique A, and Novais, Augusto Q, An efficient heuristic procedure for the optimal design of wastewater treatment systems, Resources, Conservation and Recycling, 50:2, 2007, 158-185.
Castro, Pedro M, Teles, João P, and Novais, Augusto Q, Linear program-based algorithm for the optimal design of wastewater treatment systems, Clean Technologies and Environmental Policy, 11:1, 2009, 83-93.
Source ANTIGONE test library model Other_MIQCQP/castro_etal_2007_wts_Ex15_M2.gms
Application Waste Water Treatment
Added to library 15 Aug 2014
Problem type QCP
#Variables 133
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 24
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 0
#Constraints 151
#Linear Constraints 103
#Quadratic Constraints 48
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 547
#Nonlinear Nonzeros in Jacobian 96
#Nonzeros in (Upper-Left) Hessian of Lagrangian 96
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 8
Maximal blocksize in Hessian of Lagrangian 8
Average blocksize in Hessian of Lagrangian 8.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-01
Maximal coefficient 9.0000e+04
Infeasibility of initial point 9e+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
*        152      140        0       12        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        134      134        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        551      455       96        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,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,x123,x124,x125,x126,x127,x128,x129
          ,x130,x131,x132,x133,objvar;

Positive Variables  x1,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,x123,x124,x125,x126,x127
          ,x128,x129,x130,x131,x132,x133;

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,e97,e98,e99,e100,e101,e102,e103
          ,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
          ,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
          ,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152;


e1..  - x26 - x27 - x28 + objvar =E= 0;

e2..  - x10 - x16 - x17 - x18 =E= -150;

e3..  - x11 - x19 - x20 - x21 =E= -70;

e4..  - x12 - x22 - x23 - x24 =E= -900;

e5..  - x1 - x4 - x7 - x16 - x19 - x22 + x26 =E= 0;

e6..  - x2 - x5 - x8 - x17 - x20 - x23 + x27 =E= 0;

e7..  - x3 - x6 - x9 - x18 - x21 - x24 + x28 =E= 0;

e8..  - x1 - x2 - x3 - x13 + x26 =E= 0;

e9..  - x4 - x5 - x6 - x14 + x27 =E= 0;

e10..  - x7 - x8 - x9 - x15 + x28 =E= 0;

e11..  - x10 - x11 - x12 - x13 - x14 - x15 + x25 =E= 0;

e12..  - x56 - x74 - x77 - x80 =E= -1500;

e13..  - x57 - x75 - x78 - x81 =E= -30000;

e14..  - x58 - x76 - x79 - x82 =E= -52500;

e15..  - x59 - x83 - x86 - x89 =E= -7700;

e16..  - x60 - x84 - x87 - x90 =E= -9800;

e17..  - x61 - x85 - x88 - x91 =E= -7000;

e18..  - x62 - x92 - x95 - x98 =E= -90000;

e19..  - x63 - x93 - x96 - x99 =E= -22500;

e20..  - x64 - x94 - x97 - x100 =E= -81000;

e21..  - x74 + 1500*x125 =E= 0;

e22..  - x75 + 30000*x125 =E= 0;

e23..  - x76 + 52500*x125 =E= 0;

e24..  - x77 + 1500*x126 =E= 0;

e25..  - x78 + 30000*x126 =E= 0;

e26..  - x79 + 52500*x126 =E= 0;

e27..  - x80 + 1500*x127 =E= 0;

e28..  - x81 + 30000*x127 =E= 0;

e29..  - x82 + 52500*x127 =E= 0;

e30..  - x83 + 7700*x128 =E= 0;

e31..  - x84 + 9800*x128 =E= 0;

e32..  - x85 + 7000*x128 =E= 0;

e33..  - x86 + 7700*x129 =E= 0;

e34..  - x87 + 9800*x129 =E= 0;

e35..  - x88 + 7000*x129 =E= 0;

e36..  - x89 + 7700*x130 =E= 0;

e37..  - x90 + 9800*x130 =E= 0;

e38..  - x91 + 7000*x130 =E= 0;

e39..  - x92 + 90000*x131 =E= 0;

e40..  - x93 + 22500*x131 =E= 0;

e41..  - x94 + 81000*x131 =E= 0;

e42..  - x95 + 90000*x132 =E= 0;

e43..  - x96 + 22500*x132 =E= 0;

e44..  - x97 + 81000*x132 =E= 0;

e45..  - x98 + 90000*x133 =E= 0;

e46..  - x99 + 22500*x133 =E= 0;

e47..  - x100 + 81000*x133 =E= 0;

e48..  - x56 + 1500*x119 =E= 0;

e49..  - x57 + 30000*x119 =E= 0;

e50..  - x58 + 52500*x119 =E= 0;

e51..  - x59 + 7700*x120 =E= 0;

e52..  - x60 + 9800*x120 =E= 0;

e53..  - x61 + 7000*x120 =E= 0;

e54..  - x62 + 90000*x121 =E= 0;

e55..  - x63 + 22500*x121 =E= 0;

e56..  - x64 + 81000*x121 =E= 0;

e57..  - x16 + 150*x125 =E= 0;

e58..  - x17 + 150*x126 =E= 0;

e59..  - x18 + 150*x127 =E= 0;

e60..  - x19 + 70*x128 =E= 0;

e61..  - x20 + 70*x129 =E= 0;

e62..  - x21 + 70*x130 =E= 0;

e63..  - x22 + 900*x131 =E= 0;

e64..  - x23 + 900*x132 =E= 0;

e65..  - x24 + 900*x133 =E= 0;

e66..  - x10 + 150*x119 =E= 0;

e67..  - x11 + 70*x120 =E= 0;

e68..  - x12 + 900*x121 =E= 0;

e69..    x119 + x125 + x126 + x127 =E= 1;

e70..    x120 + x128 + x129 + x130 =E= 1;

e71..    x121 + x131 + x132 + x133 =E= 1;

e72..  - 145*x26 + x29 + x38 + x47 + x74 + x83 + x92 =L= 0;

e73..  - 400*x26 + x30 + x39 + x48 + x75 + x84 + x93 =L= 0;

e74..  - 200*x26 + x31 + x40 + x49 + x76 + x85 + x94 =L= 0;

e75..  - 110*x27 + x32 + x41 + x50 + x77 + x86 + x95 =L= 0;

e76..  - 90*x27 + x33 + x42 + x51 + x78 + x87 + x96 =L= 0;

e77..  - 120*x27 + x34 + x43 + x52 + x79 + x88 + x97 =L= 0;

e78..  - 90*x28 + x35 + x44 + x53 + x80 + x89 + x98 =L= 0;

e79..  - 100*x28 + x36 + x45 + x54 + x81 + x90 + x99 =L= 0;

e80..  - 300*x28 + x37 + x46 + x55 + x82 + x91 + x100 =L= 0;

e81..    0.1*x29 + 0.1*x38 + 0.1*x47 + 0.1*x74 + 0.1*x83 + 0.1*x92 - x101 =E= 0
      ;

e82..    x30 + x39 + x48 + x75 + x84 + x93 - x102 =E= 0;

e83..    0.3*x31 + 0.3*x40 + 0.3*x49 + 0.3*x76 + 0.3*x85 + 0.3*x94 - x103 =E= 0
      ;

e84..    0.3*x32 + 0.3*x41 + 0.3*x50 + 0.3*x77 + 0.3*x86 + 0.3*x95 - x104 =E= 0
      ;

e85..    0.1*x33 + 0.1*x42 + 0.1*x51 + 0.1*x78 + 0.1*x87 + 0.1*x96 - x105 =E= 0
      ;

e86..    0.6*x34 + 0.6*x43 + 0.6*x52 + 0.6*x79 + 0.6*x88 + 0.6*x97 - x106 =E= 0
      ;

e87..    x35 + x44 + x53 + x80 + x89 + x98 - x107 =E= 0;

e88..    0.2*x36 + 0.2*x45 + 0.2*x54 + 0.2*x81 + 0.2*x90 + 0.2*x99 - x108 =E= 0
      ;

e89..    x37 + x46 + x55 + x82 + x91 + x100 - x109 =E= 0;

e90..  - x29 - x32 - x35 - x65 + x101 =E= 0;

e91..  - x30 - x33 - x36 - x66 + x102 =E= 0;

e92..  - x31 - x34 - x37 - x67 + x103 =E= 0;

e93..  - x38 - x41 - x44 - x68 + x104 =E= 0;

e94..  - x39 - x42 - x45 - x69 + x105 =E= 0;

e95..  - x40 - x43 - x46 - x70 + x106 =E= 0;

e96..  - x47 - x50 - x53 - x71 + x107 =E= 0;

e97..  - x48 - x51 - x54 - x72 + x108 =E= 0;

e98..  - x49 - x52 - x55 - x73 + x109 =E= 0;

e99.. x101*x110 - x29 =E= 0;

e100.. x102*x110 - x30 =E= 0;

e101.. x103*x110 - x31 =E= 0;

e102.. x101*x111 - x32 =E= 0;

e103.. x102*x111 - x33 =E= 0;

e104.. x103*x111 - x34 =E= 0;

e105.. x101*x112 - x35 =E= 0;

e106.. x102*x112 - x36 =E= 0;

e107.. x103*x112 - x37 =E= 0;

e108.. x104*x113 - x38 =E= 0;

e109.. x105*x113 - x39 =E= 0;

e110.. x106*x113 - x40 =E= 0;

e111.. x104*x114 - x41 =E= 0;

e112.. x105*x114 - x42 =E= 0;

e113.. x106*x114 - x43 =E= 0;

e114.. x104*x115 - x44 =E= 0;

e115.. x105*x115 - x45 =E= 0;

e116.. x106*x115 - x46 =E= 0;

e117.. x107*x116 - x47 =E= 0;

e118.. x108*x116 - x48 =E= 0;

e119.. x109*x116 - x49 =E= 0;

e120.. x107*x117 - x50 =E= 0;

e121.. x108*x117 - x51 =E= 0;

e122.. x109*x117 - x52 =E= 0;

e123.. x107*x118 - x53 =E= 0;

e124.. x108*x118 - x54 =E= 0;

e125.. x109*x118 - x55 =E= 0;

e126.. x101*x122 - x65 =E= 0;

e127.. x102*x122 - x66 =E= 0;

e128.. x103*x122 - x67 =E= 0;

e129.. x104*x123 - x68 =E= 0;

e130.. x105*x123 - x69 =E= 0;

e131.. x106*x123 - x70 =E= 0;

e132.. x107*x124 - x71 =E= 0;

e133.. x108*x124 - x72 =E= 0;

e134.. x109*x124 - x73 =E= 0;

e135.. x26*x110 - x1 =E= 0;

e136.. x26*x111 - x2 =E= 0;

e137.. x26*x112 - x3 =E= 0;

e138.. x27*x113 - x4 =E= 0;

e139.. x27*x114 - x5 =E= 0;

e140.. x27*x115 - x6 =E= 0;

e141.. x28*x116 - x7 =E= 0;

e142.. x28*x117 - x8 =E= 0;

e143.. x28*x118 - x9 =E= 0;

e144.. x26*x122 - x13 =E= 0;

e145.. x27*x123 - x14 =E= 0;

e146.. x28*x124 - x15 =E= 0;

e147..    x110 + x111 + x112 + x122 =E= 1;

e148..    x113 + x114 + x115 + x123 =E= 1;

e149..    x116 + x117 + x118 + x124 =E= 1;

e150..  - 10*x25 + x56 + x59 + x62 + x65 + x68 + x71 =L= 0;

e151..  - 15*x25 + x57 + x60 + x63 + x66 + x69 + x72 =L= 0;

e152..  - 20*x25 + x58 + x61 + x64 + x67 + x70 + x73 =L= 0;

* set non-default bounds
x1.up = 1000000;
x2.up = 1000000;
x3.up = 1000000;
x4.up = 1000000;
x5.up = 1000000;
x6.up = 1000000;
x7.up = 1000000;
x8.up = 1000000;
x9.up = 1000000;
x10.up = 1000000;
x11.up = 1000000;
x12.up = 1000000;
x13.up = 1000000;
x14.up = 1000000;
x15.up = 1000000;
x16.up = 1000000;
x17.up = 1000000;
x18.up = 1000000;
x19.up = 1000000;
x20.up = 1000000;
x21.up = 1000000;
x22.up = 1000000;
x23.up = 1000000;
x24.up = 1000000;
x25.up = 1000000;
x26.up = 1000000;
x27.up = 1000000;
x28.up = 1000000;
x29.up = 1000000;
x30.up = 1000000;
x31.up = 1000000;
x32.up = 1000000;
x33.up = 1000000;
x34.up = 1000000;
x35.up = 1000000;
x36.up = 1000000;
x37.up = 1000000;
x38.up = 1000000;
x39.up = 1000000;
x40.up = 1000000;
x41.up = 1000000;
x42.up = 1000000;
x43.up = 1000000;
x44.up = 1000000;
x45.up = 1000000;
x46.up = 1000000;
x47.up = 1000000;
x48.up = 1000000;
x49.up = 1000000;
x50.up = 1000000;
x51.up = 1000000;
x52.up = 1000000;
x53.up = 1000000;
x54.up = 1000000;
x55.up = 1000000;
x56.up = 1000000;
x57.up = 1000000;
x58.up = 1000000;
x59.up = 1000000;
x60.up = 1000000;
x61.up = 1000000;
x62.up = 1000000;
x63.up = 1000000;
x64.up = 1000000;
x65.up = 1000000;
x66.up = 1000000;
x67.up = 1000000;
x68.up = 1000000;
x69.up = 1000000;
x70.up = 1000000;
x71.up = 1000000;
x72.up = 1000000;
x73.up = 1000000;
x74.up = 1000000;
x75.up = 1000000;
x76.up = 1000000;
x77.up = 1000000;
x78.up = 1000000;
x79.up = 1000000;
x80.up = 1000000;
x81.up = 1000000;
x82.up = 1000000;
x83.up = 1000000;
x84.up = 1000000;
x85.up = 1000000;
x86.up = 1000000;
x87.up = 1000000;
x88.up = 1000000;
x89.up = 1000000;
x90.up = 1000000;
x91.up = 1000000;
x92.up = 1000000;
x93.up = 1000000;
x94.up = 1000000;
x95.up = 1000000;
x96.up = 1000000;
x97.up = 1000000;
x98.up = 1000000;
x99.up = 1000000;
x100.up = 1000000;
x101.up = 1000000;
x102.up = 1000000;
x103.up = 1000000;
x104.up = 1000000;
x105.up = 1000000;
x106.up = 1000000;
x107.up = 1000000;
x108.up = 1000000;
x109.up = 1000000;
x110.up = 1000000;
x111.up = 1000000;
x112.up = 1000000;
x113.up = 1000000;
x114.up = 1000000;
x115.up = 1000000;
x116.up = 1000000;
x117.up = 1000000;
x118.up = 1000000;
x119.up = 1000000;
x120.up = 1000000;
x121.up = 1000000;
x122.up = 1000000;
x123.up = 1000000;
x124.up = 1000000;
x125.up = 1000000;
x126.up = 1000000;
x127.up = 1000000;
x128.up = 1000000;
x129.up = 1000000;
x130.up = 1000000;
x131.up = 1000000;
x132.up = 1000000;
x133.up = 1000000;

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: 2022-04-26 Git hash: de668763
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