MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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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 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;