MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance hydro
Formatsⓘ | ams gms lp mod nl osil pip py |
Primal Bounds (infeas ≤ 1e-08)ⓘ | |
Other points (infeas > 1e-08)ⓘ | |
Dual Boundsⓘ | 4366944.10500000 (ANTIGONE) 4366944.15500000 (BARON) 4366944.15900000 (COUENNE) 4366944.15400000 (GUROBI) 4366944.15900000 (LINDO) 4366944.16000000 (SCIP) |
Referencesⓘ | Wood, A J and Wollenberg, B F, Example Problem 7b. Chapter 7 in Wood, A J and Wollenberg, B F, Power Generation, Operation and Control, John Wiley and Sons, 1984, 202. |
Sourceⓘ | GAMS Model Library model hydro |
Applicationⓘ | Hydro Energy System Scheduling |
Added to libraryⓘ | 31 Jul 2001 |
Problem typeⓘ | QCQP |
#Variablesⓘ | 31 |
#Binary Variablesⓘ | 0 |
#Integer Variablesⓘ | 0 |
#Nonlinear Variablesⓘ | 12 |
#Nonlinear Binary Variablesⓘ | 0 |
#Nonlinear Integer Variablesⓘ | 0 |
Objective Senseⓘ | min |
Objective typeⓘ | quadratic |
Objective curvatureⓘ | convex |
#Nonzeros in Objectiveⓘ | 6 |
#Nonlinear Nonzeros in Objectiveⓘ | 6 |
#Constraintsⓘ | 24 |
#Linear Constraintsⓘ | 18 |
#Quadratic Constraintsⓘ | 6 |
#Polynomial Constraintsⓘ | 0 |
#Signomial Constraintsⓘ | 0 |
#General Nonlinear Constraintsⓘ | 0 |
Operands in Gen. Nonlin. Functionsⓘ | |
Constraints curvatureⓘ | indefinite |
#Nonzeros in Jacobianⓘ | 60 |
#Nonlinear Nonzeros in Jacobianⓘ | 6 |
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 12 |
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 12 |
#Blocks in Hessian of Lagrangianⓘ | 12 |
Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
Maximal blocksize in Hessian of Lagrangianⓘ | 1 |
Average blocksize in Hessian of Lagrangianⓘ | 1.0 |
#Semicontinuitiesⓘ | 0 |
#Nonlinear Semicontinuitiesⓘ | 0 |
#SOS type 1ⓘ | 0 |
#SOS type 2ⓘ | 0 |
Minimal coefficientⓘ | 8.0000e-05 |
Maximal coefficientⓘ | 8.2800e+01 |
Infeasibility of initial pointⓘ | 6.4e+04 |
Sparsity Jacobianⓘ | |
Sparsity Hessian of Lagrangianⓘ |
$offlisting * * Equation counts * Total E G L N X C B * 25 19 6 0 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 32 32 0 0 0 0 0 0 * FX 1 * * Nonzero counts * Total const NL DLL * 67 55 12 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,objvar; Positive Variables x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21 ,x22,x23,x24; 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; e1.. -82.8*(0.0016*sqr(x1) + 8*x1 + 0.0016*sqr(x2) + 8*x2 + 0.0016*sqr(x3) + 8* x3 + 0.0016*sqr(x4) + 8*x4 + 0.0016*sqr(x5) + 8*x5 + 0.0016*sqr(x6) + 8*x6 ) + objvar =E= 248400; e2.. x1 + x7 - x13 =G= 1200; e3.. x2 + x8 - x14 =G= 1500; e4.. x3 + x9 - x15 =G= 1100; e5.. x4 + x10 - x16 =G= 1800; e6.. x5 + x11 - x17 =G= 950; e7.. x6 + x12 - x18 =G= 1300; e8.. 12*x19 - x25 + x26 =E= 24000; e9.. 12*x20 - x26 + x27 =E= 24000; e10.. 12*x21 - x27 + x28 =E= 24000; e11.. 12*x22 - x28 + x29 =E= 24000; e12.. 12*x23 - x29 + x30 =E= 24000; e13.. 12*x24 - x30 + x31 =E= 24000; e14.. -8e-5*sqr(x7) + x13 =E= 0; e15.. -8e-5*sqr(x8) + x14 =E= 0; e16.. -8e-5*sqr(x9) + x15 =E= 0; e17.. -8e-5*sqr(x10) + x16 =E= 0; e18.. -8e-5*sqr(x11) + x17 =E= 0; e19.. -8e-5*sqr(x12) + x18 =E= 0; e20.. - 4.97*x7 + x19 =E= 330; e21.. - 4.97*x8 + x20 =E= 330; e22.. - 4.97*x9 + x21 =E= 330; e23.. - 4.97*x10 + x22 =E= 330; e24.. - 4.97*x11 + x23 =E= 330; e25.. - 4.97*x12 + x24 =E= 330; * set non-default bounds x1.lo = 150; x1.up = 1500; x2.lo = 150; x2.up = 1500; x3.lo = 150; x3.up = 1500; x4.lo = 150; x4.up = 1500; x5.lo = 150; x5.up = 1500; x6.lo = 150; x6.up = 1500; x7.up = 1000; x8.up = 1000; x9.up = 1000; x10.up = 1000; x11.up = 1000; x12.up = 1000; x25.fx = 100000; x26.lo = 60000; x26.up = 120000; x27.lo = 60000; x27.up = 120000; x28.lo = 60000; x28.up = 120000; x29.lo = 60000; x29.up = 120000; x30.lo = 60000; x30.up = 120000; x31.lo = 60000; x31.up = 120000; 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: 2024-11-25 Git hash: de62f3e5