MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance windfac

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.2544873 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.2544873 (COUENNE) 0.2544873 (LINDO) 0.2544873 (SCIP) 0. (SHOT)
Referencesⓘ	Michna, Michael and Gdanska, Polytechnika, Winding Factor of Electrical Machines.
Sourceⓘ	MacMINLP model wind-fac.mod, GAMS Model Library model windfac
Applicationⓘ	Winding Factor of Electrical Machines
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MINLP
#Variablesⓘ	14
#Binary Variablesⓘ	0
#Integer Variablesⓘ	3
#Nonlinear Variablesⓘ	13
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	3
Objective Senseⓘ	min
Objective typeⓘ	quadratic
Objective curvatureⓘ	convex
#Nonzeros in Objectiveⓘ	2
#Nonlinear Nonzeros in Objectiveⓘ	2
#Constraintsⓘ	13
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	3
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	1
#General Nonlinear Constraintsⓘ	6
Operands in Gen. Nonlin. Functionsⓘ	div mul sin
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	35
#Nonlinear Nonzeros in Jacobianⓘ	22
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	29
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	7
#Blocks in Hessian of Lagrangianⓘ	5
Minimal blocksize in Hessian of Lagrangianⓘ	1
Maximal blocksize in Hessian of Lagrangianⓘ	8
Average blocksize in Hessian of Lagrangianⓘ	2.6
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	2.5000e-01
Maximal coefficientⓘ	1.2566e+01
Infeasibility of initial pointⓘ	2.85
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         14       14        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         15       12        0        3        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         38       14       24        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,x3,x4,i5,x6,x7,x8,x9,x10,x11,objvar,x13,x14,x15;

Integer Variables  i1,i2,i5;

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


e1..  - 12*i1 + i2 =E= 0;

e2.. -12.566370616/i2 + x3 =E= 0;

e3..  - 0.25*i2 + x4 =E= 0;

e4..  - x4 + i5 =E= -1;

e5.. sin(0.5*x3)*i1*x6 - sin(0.5*i1*x3) =E= 0;

e6.. -sin(1.570796327*i5/x4) + x9 =E= 0;

e7.. -x9*x6 + x15 =E= 0;

e8.. sin(1.5*x3)*i1*x7 - sin(1.5*i1*x3) =E= 0;

e9.. -sin(4.712388981*i5/x4) + x10 =E= 0;

e10.. -x10*x7 + x13 =E= 0;

e11.. sin(2.5*x3)*i1*x8 - sin(2.5*i1*x3) =E= 0;

e12.. -sin(7.853981635*i5/x4) + x11 =E= 0;

e13.. -x11*x8 + x14 =E= 0;

e14.. -(x13*x13 + x14*x14) + objvar =E= 0;

* set non-default bounds
i1.lo = 1; i1.up = 10;
i2.lo = 1; i2.up = 100;
i5.lo = 1; i5.up = 100;
x15.lo = 0.8;

* set non-default levels
i1.l = 1.3;
i2.l = 15.4;
x3.l = 1.5;
x4.l = 1;
i5.l = 2.8;

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;