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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: fuel

Formats ams gms lp mod nl osil pip
Primal Bounds
8566.11896200 p1 ( gdx sol )
(infeas: 5e-13)
Dual Bounds
8566.11896200 (ANTIGONE)
8566.11896200 (BARON)
8566.11896200 (COUENNE)
8566.11896200 (LINDO)
8566.11896200 (SCIP)
References Wood, A J and Wollenberg, B F, Example Problem 4e. In Wood, A J and Wollenberg, B F, Power Generation, Operation and Control, John Wiley and Sons, 1984, 85-88.
Source GAMS Model Library model fuel
Application Unit Commitment
Added to library 01 May 2001
Problem type MBQCQP
#Variables 15
#Binary Variables 3
#Integer Variables 0
#Nonlinear Variables 6
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 3
#Nonlinear Nonzeros in Objective 3
#Constraints 15
#Linear Constraints 12
#Quadratic Constraints 3
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 35
#Nonlinear Nonzeros in Jacobian 3
#Nonzeros in (Upper-Left) Hessian of Lagrangian 6
#Nonzeros in Diagonal of Hessian of Lagrangian 6
#Blocks in Hessian of Lagrangian 6
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
Infeasibility of initial point 3500
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         16        7        6        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         16       13        3        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         39       33        6        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,objvar;

Positive Variables  x10,x11,x12,x13,x14;

Binary Variables  b1,b2,b3;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16;


e1.. -(0.0025*sqr(x7) + 6*x7 + 0.0025*sqr(x8) + 6*x8 + 0.0025*sqr(x9) + 6*x9)
      + objvar =E= 900;

e2..  - 100*b1 + x4 =G= 0;

e3..  - 100*b2 + x5 =G= 0;

e4..  - 100*b3 + x6 =G= 0;

e5..  - 500*b1 + x4 =L= 0;

e6..  - 500*b2 + x5 =L= 0;

e7..  - 500*b3 + x6 =L= 0;

e8..    x10 + x13 =E= 3500;

e9..    x11 - x13 + x14 =E= 500;

e10..    x12 - x14 + x15 =E= 500;

e11..    x4 + x7 =G= 400;

e12..    x5 + x8 =G= 900;

e13..    x6 + x9 =G= 700;

e14.. -(0.005*sqr(x4) + x4) - 50*b1 + x10 =E= 0;

e15.. -(0.005*sqr(x5) + x5) - 50*b2 + x11 =E= 0;

e16.. -(0.005*sqr(x6) + x6) - 50*b3 + x12 =E= 0;

* set non-default bounds
x7.lo = 50; x7.up = 700;
x8.lo = 50; x8.up = 700;
x9.lo = 50; x9.up = 700;
x13.up = 4000;
x14.up = 4000;
x15.lo = 2000; x15.up = 4000;

* set non-default levels
x4.l = 100;
x5.l = 100;
x6.l = 100;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2018-09-14 Git hash: ac5a5314
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