MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance wastewater14m1

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
513.00086810 p1 ( gdx sol )
(infeas: 2e-13)
Other points (infeas > 1e-08)  
Dual Bounds
475.03216820 (ANTIGONE)
513.00086760 (BARON)
384.88194780 (COUENNE)
513.00086810 (GUROBI)
339.86496110 (LINDO)
512.94957130 (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_Ex14_M1.gms
Application Waste Water Treatment
Added to library 15 Aug 2014
Problem type QCP
#Variables 74
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 55
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 5
#Nonlinear Nonzeros in Objective 0
#Constraints 46
#Linear Constraints 34
#Quadratic Constraints 12
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 315
#Nonlinear Nonzeros in Jacobian 140
#Nonzeros in (Upper-Left) Hessian of Lagrangian 140
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 10
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 8
Average blocksize in Hessian of Lagrangian 5.5
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-01
Maximal coefficient 2.0000e+02
Infeasibility of initial point 120
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
*         47       35        0       12        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         75       75        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        321      181      140        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,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;

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;


e1..  - x70 - x71 - x72 - x73 - x74 + objvar =E= 0;

e2..  - x46 - x54 - x55 - x56 - x57 - x58 =E= -50;

e3..  - x47 - x59 - x60 - x61 - x62 - x63 =E= -120;

e4..  - x48 - x64 - x65 - x66 - x67 - x68 =E= -70;

e5..  - x21 - x26 - x31 - x36 - x41 - x54 - x59 - x64 + x70 =E= 0;

e6..  - x22 - x27 - x32 - x37 - x42 - x55 - x60 - x65 + x71 =E= 0;

e7..  - x23 - x28 - x33 - x38 - x43 - x56 - x61 - x66 + x72 =E= 0;

e8..  - x24 - x29 - x34 - x39 - x44 - x57 - x62 - x67 + x73 =E= 0;

e9..  - x25 - x30 - x35 - x40 - x45 - x58 - x63 - x68 + x74 =E= 0;

e10..  - x21 - x22 - x23 - x24 - x25 - x49 + x70 =E= 0;

e11..  - x26 - x27 - x28 - x29 - x30 - x50 + x71 =E= 0;

e12..  - x31 - x32 - x33 - x34 - x35 - x51 + x72 =E= 0;

e13..  - x36 - x37 - x38 - x39 - x40 - x52 + x73 =E= 0;

e14..  - x41 - x42 - x43 - x44 - x45 - x53 + x74 =E= 0;

e15..  - x46 - x47 - x48 - x49 - x50 - x51 - x52 - x53 + x69 =E= 0;

e16.. x21*x11 + x26*x13 + x31*x15 + x36*x17 + x41*x19 - x70*x1 + 10*x54
       + 110*x59 + 100*x64 =E= 0;

e17.. x21*x12 + x26*x14 + x31*x16 + x36*x18 + x41*x20 - x70*x2 + 200*x54
       + 140*x59 + 25*x64 =E= 0;

e18.. x22*x11 + x27*x13 + x32*x15 + x37*x17 + x42*x19 - x71*x3 + 10*x55
       + 110*x60 + 100*x65 =E= 0;

e19.. x22*x12 + x27*x14 + x32*x16 + x37*x18 + x42*x20 - x71*x4 + 200*x55
       + 140*x60 + 25*x65 =E= 0;

e20.. x23*x11 + x28*x13 + x33*x15 + x38*x17 + x43*x19 - x72*x5 + 10*x56
       + 110*x61 + 100*x66 =E= 0;

e21.. x23*x12 + x28*x14 + x33*x16 + x38*x18 + x43*x20 - x72*x6 + 200*x56
       + 140*x61 + 25*x66 =E= 0;

e22.. x24*x11 + x29*x13 + x34*x15 + x39*x17 + x44*x19 - x73*x7 + 10*x57
       + 110*x62 + 100*x67 =E= 0;

e23.. x24*x12 + x29*x14 + x34*x16 + x39*x18 + x44*x20 - x73*x8 + 200*x57
       + 140*x62 + 25*x67 =E= 0;

e24.. x25*x11 + x30*x13 + x35*x15 + x40*x17 + x45*x19 - x74*x9 + 10*x58
       + 110*x63 + 100*x68 =E= 0;

e25.. x25*x12 + x30*x14 + x35*x16 + x40*x18 + x45*x20 - x74*x10 + 200*x58
       + 140*x63 + 25*x68 =E= 0;

e26..    x1 =L= 145;

e27..    x2 =L= 400;

e28..    x3 =L= 110;

e29..    x4 =L= 90;

e30..    x5 =L= 90;

e31..    x6 =L= 100;

e32..    x7 =L= 200;

e33..    x8 =L= 90;

e34..    x9 =L= 50;

e35..    x10 =L= 80;

e36..  - 0.1*x1 + x11 =E= 0;

e37..  - x2 + x12 =E= 0;

e38..  - 0.3*x3 + x13 =E= 0;

e39..  - 0.1*x4 + x14 =E= 0;

e40..  - x5 + x15 =E= 0;

e41..  - 0.2*x6 + x16 =E= 0;

e42..  - 0.5*x7 + x17 =E= 0;

e43..  - x8 + x18 =E= 0;

e44..  - 0.35*x9 + x19 =E= 0;

e45..  - 0.4*x10 + x20 =E= 0;

e46.. x49*x11 + x50*x13 + x51*x15 + x52*x17 + x53*x19 + 10*x46 + 110*x47
       + 100*x48 - 10*x69 =L= 0;

e47.. x49*x12 + x50*x14 + x51*x16 + x52*x18 + x53*x20 + 200*x46 + 140*x47
       + 25*x48 - 5*x69 =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;

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
Imprint / Privacy Policy / License: CC-BY 4.0