MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance gear4

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	1.64342847 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	1.64342847 (ANTIGONE) 1.64342847 (BARON) 1.64342847 (COUENNE) 1.64342847 (LINDO) 1.64342847 (SCIP) 0. (SHOT)
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ⓘ	modified GAMS Model Library model gear, modified MacMINLP model geartrain.mod
Applicationⓘ	Gear Train Design
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MINLP
#Variablesⓘ	6
#Binary Variablesⓘ	0
#Integer Variablesⓘ	4
#Nonlinear Variablesⓘ	4
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	4
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	1
#Linear Constraintsⓘ	0
#Quadratic Constraintsⓘ	0
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	1
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	6
#Nonlinear Nonzeros in Jacobianⓘ	4
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	14
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#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
Minimal coefficientⓘ	1.0000e+00
Maximal coefficientⓘ	1.0000e+06
Infeasibility of initial pointⓘ	8.557e+05
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          2        2        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*          7        3        0        4        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*          9        5        4        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,objvar,x6,x7;

Positive Variables  x6,x7;

Integer Variables  i1,i2,i3,i4;

Equations  e1,e2;


e1.. -1000000*i1*i2/(i3*i4) - x6 + x7 =E= -144279.32477276;

e2..    objvar - x6 - x7 =E= 0;

* set non-default bounds
i1.lo = 12; i1.up = 60;
i2.lo = 12; i2.up = 60;
i3.lo = 12; i3.up = 60;
i4.lo = 12; i4.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;