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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance wastewater14m1
Formatsⓘ | ams gms lp mod nl osil pip py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
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) 0.00000000 (SHOT) |
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 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: 2024-12-17 Git hash: 8eaceb91