MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance waterund17
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 153.07213560 (ANTIGONE) 155.53552890 (BARON) 154.38398760 (COUENNE) 157.09444440 (GUROBI) 154.84014420 (LINDO) 157.09444320 (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_Ex17.gms |
| Applicationⓘ | Water Network Design |
| Added to libraryⓘ | 15 Aug 2014 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 74 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 48 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 15 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 66 |
| #Linear Constraintsⓘ | 39 |
| #Quadratic Constraintsⓘ | 27 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 332 |
| #Nonlinear Nonzeros in Jacobianⓘ | 180 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 168 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 4 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 12 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 12 |
| Average blocksize in Hessian of Lagrangianⓘ | 12.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 8.0000e+02 |
| Infeasibility of initial pointⓘ | 6.08e+04 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 67 35 3 29 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
* 348 168 180 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;
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;
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;
e1.. objvar - x2 - x3 - x4 - x5 - x6 - x7 - x8 - x9 - x10 - x11 - x12 - x13
- x14 - x15 - x16 =E= 0;
e2.. - x2 - x7 - x12 + x17 - x27 - x32 - x37 - x42 - x47 =E= 0;
e3.. - x3 - x8 - x13 + x18 - x28 - x33 - x38 - x43 - x48 =E= 0;
e4.. - x4 - x9 - x14 + x19 - x29 - x34 - x39 - x44 - x49 =E= 0;
e5.. - x5 - x10 - x15 + x20 - x30 - x35 - x40 - x45 - x50 =E= 0;
e6.. - x6 - x11 - x16 - x31 - x36 - x41 - x46 - x51 =E= -65;
e7.. x17 - x22 - x27 - x28 - x29 - x30 - x31 =E= 0;
e8.. x18 - x23 - x32 - x33 - x34 - x35 - x36 =E= 0;
e9.. x19 - x24 - x37 - x38 - x39 - x40 - x41 =E= 0;
e10.. x20 - x25 - x42 - x43 - x44 - x45 - x46 =E= 0;
e11.. - x26 - x47 - x48 - x49 - x50 - x51 =E= -75;
e12.. x17*x52 - (x27*x64 + x32*x67 + x37*x70 + x42*x73) - 3*x2 - 2*x12
- 150*x47 =E= 0;
e13.. x17*x53 - (x27*x65 + x32*x68 + x37*x71 + x42*x74) - 2*x7 - 4*x12
- 800*x47 =E= 0;
e14.. x17*x54 - (x27*x66 + x32*x69 + x37*x72 + x42*x75) - 2*x2 - 2*x7 - 220*x47
=E= 0;
e15.. x18*x55 - (x28*x64 + x33*x67 + x38*x70 + x43*x73) - 3*x3 - 2*x13
- 150*x48 =E= 0;
e16.. x18*x56 - (x28*x65 + x33*x68 + x38*x71 + x43*x74) - 2*x8 - 4*x13
- 800*x48 =E= 0;
e17.. x18*x57 - (x28*x66 + x33*x69 + x38*x72 + x43*x75) - 2*x3 - 2*x8 - 220*x48
=E= 0;
e18.. x19*x58 - (x29*x64 + x34*x67 + x39*x70 + x44*x73) - 3*x4 - 2*x14
- 150*x49 =E= 0;
e19.. x19*x59 - (x29*x65 + x34*x68 + x39*x71 + x44*x74) - 2*x9 - 4*x14
- 800*x49 =E= 0;
e20.. x19*x60 - (x29*x66 + x34*x69 + x39*x72 + x44*x75) - 2*x4 - 2*x9 - 220*x49
=E= 0;
e21.. x20*x61 - (x30*x64 + x35*x67 + x40*x70 + x45*x73) - 3*x5 - 2*x15
- 150*x50 =E= 0;
e22.. x20*x62 - (x30*x65 + x35*x68 + x40*x71 + x45*x74) - 2*x10 - 4*x15
- 800*x50 =E= 0;
e23.. x20*x63 - (x30*x66 + x35*x69 + x40*x72 + x45*x75) - 2*x5 - 2*x10
- 220*x50 =E= 0;
e24.. -x17*(x64 - x52) =E= -6120;
e25.. -x17*(x65 - x53) =E= -3096;
e26.. -x17*(x66 - x54) =E= -1800;
e27.. -x18*(x67 - x55) =E= -6400;
e28.. -x18*(x68 - x56) =E= -60800;
e29.. -x18*(x69 - x57) =E= -8640;
e30.. -x19*(x70 - x58) =E= -5600;
e31.. -x19*(x71 - x59) =E= -1400;
e32.. -x19*(x72 - x60) =E= -11200;
e33.. -x20*(x73 - x61) =E= -648;
e34.. -x20*(x74 - x62) =E= -408;
e35.. -x20*(x75 - x63) =E= -360;
e36.. x52 =L= 30;
e37.. x53 =L= 37;
e38.. x54 =L= 10;
e39.. x55 =L= 20;
e40.. x56 =L= 300;
e41.. x57 =L= 45;
e42.. x58 =L= 120;
e43.. x59 =L= 20;
e44.. x60 =L= 200;
e45.. x61 =L= 23;
e46.. x62 =L= 43;
e47.. x63 =L= 15;
e48.. x64 =L= 115;
e49.. x65 =L= 80;
e50.. x66 =L= 35;
e51.. x67 =L= 120;
e52.. x68 =L= 1250;
e53.. x69 =L= 180;
e54.. x70 =L= 220;
e55.. x71 =L= 45;
e56.. x72 =L= 400;
e57.. x73 =L= 50;
e58.. x74 =L= 60;
e59.. x75 =L= 30;
e60.. -(x31*x64 + x36*x67 + x41*x70 + x46*x73) - 3*x6 - 2*x16 - 150*x51
=G= -5850;
e61.. -(x31*x65 + x36*x68 + x41*x71 + x46*x74) - 2*x11 - 4*x16 - 800*x51
=G= -26000;
e62.. -(x31*x66 + x36*x69 + x41*x72 + x46*x75) - 2*x6 - 2*x11 - 220*x51
=G= -10400;
e63.. x17 =L= 72;
e64.. x18 =L= 64;
e65.. x19 =L= 56;
e66.. x20 =L= 24;
e67.. x21 =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;
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