MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance spring

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.8462441 p3 ( gdx sol ) (infeas: 1e-08) 0.84624567 p1 ( gdx sol ) (infeas: 3e-15)
Other points (infeas > 1e-08)ⓘ	0.84622067 p2 ( gdx sol ) (infeas: 5e-07)
Dual Boundsⓘ	0.84624567 (ANTIGONE) 0.84624567 (BARON) 0.84624567 (COUENNE) 0.84624567 (LINDO) 0.84624567 (SCIP) 0.04179768 (SHOT)
Referencesⓘ	Sandgren, E, Nonlinear Integer and Discrete Programming in Mechanical Design Optimization, Journal of Mechanical Design, 112:2, 1990, 223-229.
Sourceⓘ	modified MacMINLP model spring.mod, modified GAMS Model Library model spring
Applicationⓘ	Coil Compression String Design
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MINLP
#Variablesⓘ	17
#Binary Variablesⓘ	11
#Integer Variablesⓘ	1
#Nonlinear Variablesⓘ	5
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	1
Objective Senseⓘ	min
Objective typeⓘ	polynomial
Objective curvatureⓘ	indefinite
#Nonzeros in Objectiveⓘ	3
#Nonlinear Nonzeros in Objectiveⓘ	3
#Constraintsⓘ	8
#Linear Constraintsⓘ	3
#Quadratic Constraintsⓘ	1
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	3
#General Nonlinear Constraintsⓘ	1
Operands in Gen. Nonlin. Functionsⓘ	div
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	40
#Nonlinear Nonzeros in Jacobianⓘ	11
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	16
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	2
#Blocks in Hessian of Lagrangianⓘ	1
Minimal blocksize in Hessian of Lagrangianⓘ	5
Maximal blocksize in Hessian of Lagrangianⓘ	5
Average blocksize in Hessian of Lagrangianⓘ	5.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	6.9565e-07
Maximal coefficientⓘ	2.5465e+03
Infeasibility of initial pointⓘ	9.059
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*          9        6        0        3        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         18        6       11        1        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*         44       30       14        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,i4,x5,x6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,objvar;

Binary Variables  b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17;

Integer Variables  i4;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9;


e1.. -(1.570796327 + 0.7853981635*i4)*x1*sqr(x2) + objvar =E= 0;

e2.. -x1/x2 + x5 =E= 0;

e3.. -((-1 + 4*x5)/(-4 + 4*x5) + 0.615/x5) + x6 =E= 0;

e4.. 2546.47908913782*x6*x5/sqr(x2) =L= 189000;

e5.. -6.95652173913044e-7*x5**3*i4/x2 + x3 =E= 0;

e6.. (2.1 + 1.05*i4)*x2 + 1000*x3 =L= 14;

e7..    x1 + x2 =L= 3;

e8..    x2 - 0.207*b7 - 0.225*b8 - 0.244*b9 - 0.263*b10 - 0.283*b11 - 0.307*b12
      - 0.331*b13 - 0.362*b14 - 0.394*b15 - 0.4375*b16 - 0.5*b17 =E= 0;

e9..    b7 + b8 + b9 + b10 + b11 + b12 + b13 + b14 + b15 + b16 + b17 =E= 1;

* set non-default bounds
x1.lo = 0.414;
x2.lo = 0.207;
x3.lo = 0.00178571428571429; x3.up = 0.02;
i4.lo = 1; i4.up = 100;
x5.lo = 1.1;

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;