MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
Home // Instances // Documentation // Download // Statistics
Instance wastewater15m1
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 2446.42856900 (ANTIGONE) 2446.42856900 (BARON) 1967.99125200 (COUENNE) 2446.42856900 (GUROBI) 1559.59800800 (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_M1.gms |
| Applicationⓘ | Waste Water Treatment |
| Added to libraryⓘ | 15 Aug 2014 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 46 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 33 |
| #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ⓘ | 40 |
| #Linear Constraintsⓘ | 28 |
| #Quadratic Constraintsⓘ | 12 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 211 |
| #Nonlinear Nonzeros in Jacobianⓘ | 90 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 90 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 6 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 4 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 7 |
| 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ⓘ | 3.5000e+02 |
| Infeasibility of initial pointⓘ | 900 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 41 29 0 12 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 47 47 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 215 125 90 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,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;
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;
e1.. - x44 - x45 - x46 + objvar =E= 0;
e2.. - x28 - x34 - x35 - x36 =E= -150;
e3.. - x29 - x37 - x38 - x39 =E= -70;
e4.. - x30 - x40 - x41 - x42 =E= -900;
e5.. - x19 - x22 - x25 - x34 - x37 - x40 + x44 =E= 0;
e6.. - x20 - x23 - x26 - x35 - x38 - x41 + x45 =E= 0;
e7.. - x21 - x24 - x27 - x36 - x39 - x42 + x46 =E= 0;
e8.. - x19 - x20 - x21 - x31 + x44 =E= 0;
e9.. - x22 - x23 - x24 - x32 + x45 =E= 0;
e10.. - x25 - x26 - x27 - x33 + x46 =E= 0;
e11.. - x28 - x29 - x30 - x31 - x32 - x33 + x43 =E= 0;
e12.. x19*x10 + x22*x13 + x25*x16 - x44*x1 + 10*x34 + 110*x37 + 100*x40 =E= 0;
e13.. x19*x11 + x22*x14 + x25*x17 - x44*x2 + 200*x34 + 140*x37 + 25*x40 =E= 0;
e14.. x19*x12 + x22*x15 + x25*x18 - x44*x3 + 350*x34 + 100*x37 + 90*x40 =E= 0;
e15.. x20*x10 + x23*x13 + x26*x16 - x45*x4 + 10*x35 + 110*x38 + 100*x41 =E= 0;
e16.. x20*x11 + x23*x14 + x26*x17 - x45*x5 + 200*x35 + 140*x38 + 25*x41 =E= 0;
e17.. x20*x12 + x23*x15 + x26*x18 - x45*x6 + 350*x35 + 100*x38 + 90*x41 =E= 0;
e18.. x21*x10 + x24*x13 + x27*x16 - x46*x7 + 10*x36 + 110*x39 + 100*x42 =E= 0;
e19.. x21*x11 + x24*x14 + x27*x17 - x46*x8 + 200*x36 + 140*x39 + 25*x42 =E= 0;
e20.. x21*x12 + x24*x15 + x27*x18 - x46*x9 + 350*x36 + 100*x39 + 90*x42 =E= 0;
e21.. x1 =L= 145;
e22.. x2 =L= 400;
e23.. x3 =L= 200;
e24.. x4 =L= 110;
e25.. x5 =L= 90;
e26.. x6 =L= 120;
e27.. x7 =L= 90;
e28.. x8 =L= 100;
e29.. x9 =L= 300;
e30.. - 0.1*x1 + x10 =E= 0;
e31.. - x2 + x11 =E= 0;
e32.. - 0.3*x3 + x12 =E= 0;
e33.. - 0.3*x4 + x13 =E= 0;
e34.. - 0.1*x5 + x14 =E= 0;
e35.. - 0.6*x6 + x15 =E= 0;
e36.. - x7 + x16 =E= 0;
e37.. - 0.2*x8 + x17 =E= 0;
e38.. - x9 + x18 =E= 0;
e39.. x31*x10 + x32*x13 + x33*x16 + 10*x28 + 110*x29 + 100*x30 - 10*x43 =L= 0;
e40.. x31*x11 + x32*x14 + x33*x17 + 200*x28 + 140*x29 + 25*x30 - 15*x43 =L= 0;
e41.. x31*x12 + x32*x15 + x33*x18 + 350*x28 + 100*x29 + 90*x30 - 20*x43 =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;
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: 2025-08-07 Git hash: e62cedfc