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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: gear2

Formats ams gms mod nl osil
Primal Bounds
0.00000000 p1 ( gdx sol )
(infeas: 0)
Dual Bounds
-0.00000000 (ANTIGONE)
-0.00000000 (BARON)
0.00000000 (COUENNE)
0.00000000 (LINDO)
0.00000000 (SCIP)
References Deb, Kalyanmoy and Goyal, Mayank, Optimizing Engineering Designs Using a Combined Genetic Search. In Bäck, Thomas, Ed, Proceedings of the Seventh International Conference on Genetic Algorithms, 1997, 521-528.
Source GAMS Model Library model gear, modified MacMINLP model geartrain.mod
Application Gear Train Design
Added to library 01 May 2001
Problem type MBNLP
#Variables 28
#Binary Variables 24
#Integer Variables 0
#Nonlinear Variables 4
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature nonconcave
#Nonzeros in Objective 4
#Nonlinear Nonzeros in Objective 4
#Constraints 4
#Linear Constraints 4
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions mul div sqr
Constraints curvature linear
#Nonzeros in Jacobian 28
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 16
#Nonzeros in Diagonal of Hessian of Lagrangian 4
#Blocks in Hessian of Lagrangian 1
Minimal blocksize in Hessian of Lagrangian 4
Maximal blocksize in Hessian of Lagrangian 4
Average blocksize in Hessian of Lagrangian 4.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 12
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
*          5        5        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         29        5       24        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         33       29        4        0
*
*  Solve m using MINLP minimizing objvar;


Variables  objvar,x2,x3,x4,x5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18
          ,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29;

Binary Variables  b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21
          ,b22,b23,b24,b25,b26,b27,b28,b29;

Equations  e1,e2,e3,e4,e5;


e1.. -sqr(0.14427932477276 - x2*x3/(x4*x5)) + objvar =E= 0;

e2..    x2 - b6 - 2*b7 - 4*b8 - 8*b9 - 16*b10 - 32*b11 =E= 0;

e3..    x3 - b12 - 2*b13 - 4*b14 - 8*b15 - 16*b16 - 32*b17 =E= 0;

e4..    x4 - b18 - 2*b19 - 4*b20 - 8*b21 - 16*b22 - 32*b23 =E= 0;

e5..    x5 - b24 - 2*b25 - 4*b26 - 8*b27 - 16*b28 - 32*b29 =E= 0;

* set non-default bounds
x2.lo = 12; x2.up = 60;
x3.lo = 12; x3.up = 60;
x4.lo = 12; x4.up = 60;
x5.lo = 12; x5.up = 60;

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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