MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance gear2

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.00000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	-0.00000000 (ANTIGONE) -0.00000000 (BARON) 0.00000000 (COUENNE) 0.00000000 (LINDO) 0.00000000 (SCIP) 0.00000000 (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ⓘ	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ⓘ	signomial
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ⓘ
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
Minimal coefficientⓘ	1.4428e-01
Maximal coefficientⓘ	3.2000e+01
Infeasibility of initial pointⓘ	12
Sparsity Jacobianⓘ
Sparsity 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;