MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance waterund11
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 104.88614690 (ANTIGONE) 104.87565840 (BARON) 103.86755570 (COUENNE) 104.88611910 (GUROBI) 104.06776960 (LINDO) 104.88607060 (SCIP) 45.00000000 (SHOT) |
| 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_Ex11.gms |
| Applicationⓘ | Water Network Design |
| Added to libraryⓘ | 15 Aug 2014 |
| Problem typeⓘ | QCP |
| #Variablesⓘ | 64 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 39 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 16 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 64 |
| #Linear Constraintsⓘ | 36 |
| #Quadratic Constraintsⓘ | 28 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 310 |
| #Nonlinear Nonzeros in Jacobianⓘ | 156 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 144 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 3 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 13 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 13 |
| Average blocksize in Hessian of Lagrangianⓘ | 13.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 9.0400e+02 |
| Infeasibility of initial pointⓘ | 3.398e+04 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 65 33 4 28 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 65 65 0 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 327 171 156 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;
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;
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;
e1.. objvar - x2 - x3 - x4 - x5 - x6 - x7 - x8 - x9 - x10 - x11 - x12 - x13
- x14 - x15 - x16 - x17 =E= 0;
e2.. - x2 - x6 - x10 - x14 + x18 - x26 - x30 - x34 - x38 =E= 0;
e3.. - x3 - x7 - x11 - x15 + x19 - x27 - x31 - x35 - x39 =E= 0;
e4.. - x4 - x8 - x12 - x16 + x20 - x28 - x32 - x36 - x40 =E= 0;
e5.. - x5 - x9 - x13 - x17 - x29 - x33 - x37 - x41 =E= -95;
e6.. x18 - x22 - x26 - x27 - x28 - x29 =E= 0;
e7.. x19 - x23 - x30 - x31 - x32 - x33 =E= 0;
e8.. x20 - x24 - x34 - x35 - x36 - x37 =E= 0;
e9.. - x25 - x38 - x39 - x40 - x41 =E= -50;
e10.. x18*x42 - (x26*x54 + x30*x58 + x34*x62) - 2*x2 - 3*x6 - 4*x10 - 623*x38
=E= 0;
e11.. x18*x43 - (x26*x55 + x30*x59 + x34*x63) - 2*x6 - 5*x10 - 2*x14 - 904*x38
=E= 0;
e12.. x18*x44 - (x26*x56 + x30*x60 + x34*x64) - 6*x2 - 2*x10 - x14 - 846*x38
=E= 0;
e13.. x18*x45 - (x26*x57 + x30*x61 + x34*x65) - 5*x2 - 3*x6 - x10 - 3*x14
- 611*x38 =E= 0;
e14.. x19*x46 - (x27*x54 + x31*x58 + x35*x62) - 2*x3 - 3*x7 - 4*x11 - 623*x39
=E= 0;
e15.. x19*x47 - (x27*x55 + x31*x59 + x35*x63) - 2*x7 - 5*x11 - 2*x15 - 904*x39
=E= 0;
e16.. x19*x48 - (x27*x56 + x31*x60 + x35*x64) - 6*x3 - 2*x11 - x15 - 846*x39
=E= 0;
e17.. x19*x49 - (x27*x57 + x31*x61 + x35*x65) - 5*x3 - 3*x7 - x11 - 3*x15
- 611*x39 =E= 0;
e18.. x20*x50 - (x28*x54 + x32*x58 + x36*x62) - 2*x4 - 3*x8 - 4*x12 - 623*x40
=E= 0;
e19.. x20*x51 - (x28*x55 + x32*x59 + x36*x63) - 2*x8 - 5*x12 - 2*x16 - 904*x40
=E= 0;
e20.. x20*x52 - (x28*x56 + x32*x60 + x36*x64) - 6*x4 - 2*x12 - x16 - 846*x40
=E= 0;
e21.. x20*x53 - (x28*x57 + x32*x61 + x36*x65) - 5*x4 - 3*x8 - x12 - 3*x16
- 611*x40 =E= 0;
e22.. -x18*(x54 - x42) =E= -18598;
e23.. -x18*(x55 - x43) =E= -3672;
e24.. -x18*(x56 - x44) =E= -7582;
e25.. -x18*(x57 - x45) =E= -11662;
e26.. -x19*(x58 - x46) =E= -1776;
e27.. -x19*(x59 - x47) =E= -576;
e28.. -x19*(x60 - x48) =E= -4236;
e29.. -x19*(x61 - x49) =E= -2724;
e30.. -x20*(x62 - x50) =E= -5130;
e31.. -x20*(x63 - x51) =E= -14310;
e32.. -x20*(x64 - x52) =E= -1035;
e33.. -x20*(x65 - x53) =E= -33975;
e34.. x42 =L= 326;
e35.. x43 =L= 842;
e36.. x44 =L= 733;
e37.. x45 =L= 214;
e38.. x46 =L= 751;
e39.. x47 =L= 963;
e40.. x48 =L= 337;
e41.. x49 =L= 762;
e42.. x50 =L= 837;
e43.. x51 =L= 695;
e44.. x52 =L= 991;
e45.. x53 =L= 180;
e46.. x54 =L= 873;
e47.. x55 =L= 950;
e48.. x56 =L= 956;
e49.. x57 =L= 557;
e50.. x58 =L= 899;
e51.. x59 =L= 1011;
e52.. x60 =L= 690;
e53.. x61 =L= 989;
e54.. x62 =L= 951;
e55.. x63 =L= 1013;
e56.. x64 =L= 1014;
e57.. x65 =L= 935;
e58.. -(x29*x54 + x33*x58 + x37*x62) - 2*x5 - 3*x9 - 4*x13 - 623*x41 =G= -13015
;
e59.. -(x29*x55 + x33*x59 + x37*x63) - 2*x9 - 5*x13 - 2*x17 - 904*x41
=G= -69160;
e60.. -(x29*x56 + x33*x60 + x37*x64) - 6*x5 - 2*x13 - x17 - 846*x41 =G= -65265;
e61.. -(x29*x57 + x33*x61 + x37*x65) - 5*x5 - 3*x9 - x13 - 3*x17 - 611*x41
=G= -48260;
e62.. x18 =L= 34;
e63.. x19 =L= 12;
e64.. x20 =L= 45;
e65.. 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;
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