MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance kall_congruentcircles_c63

A set of circles are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions.
The objective is to minimize the area of the design rectangles.
The design plates are subject to lower and upper bounds of their widths and lengths.
The objects are free of any orientation restrictions.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
1.28761102 p1 ( gdx sol )
(infeas: 3e-10)
Other points (infeas > 1e-08)  
Dual Bounds
1.28761085 (ANTIGONE)
1.28761101 (BARON)
1.28761102 (COUENNE)
1.28760805 (GUROBI)
1.28761102 (LINDO)
1.28761039 (SCIP)
References Kallrath, Josef, Cutting circles and polygons from area-minimizing rectangles, Journal of Global Optimization, 43:2-3, 2009, 299-328.
Source ANTIGONE test library model Other_MIQCQP/kall_congruentcircles_c63
Application Geometry
Added to library 15 Aug 2014
Problem type QCP
#Variables 16
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 14
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 46
#Linear Constraints 30
#Quadratic Constraints 16
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 121
#Nonlinear Nonzeros in Jacobian 62
#Nonzeros in (Upper-Left) Hessian of Lagrangian 74
#Nonzeros in Diagonal of Hessian of Lagrangian 12
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 6
Average blocksize in Hessian of Lagrangian 4.666667
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e+00
Maximal coefficient 1.0000e+00
Infeasibility of initial point 4.462
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
*         46        2       15       29        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         16       16        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        121       59       62        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,objvar;

Positive Variables  x14,x15;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46;


e1..  - x1 + objvar =E= -4.71238898038469;

e2.. -x14*x15 + x1 =E= 0;

e3.. (x2 - x4)*(x2 - x4) + (x3 - x5)*(x3 - x5) =G= 1;

e4.. (x2 - x6)*(x2 - x6) + (x3 - x7)*(x3 - x7) =G= 1;

e5.. (x2 - x8)*(x2 - x8) + (x3 - x9)*(x3 - x9) =G= 1;

e6.. (x2 - x10)*(x2 - x10) + (x3 - x11)*(x3 - x11) =G= 1;

e7.. (x2 - x12)*(x2 - x12) + (x3 - x13)*(x3 - x13) =G= 1;

e8.. (x4 - x6)*(x4 - x6) + (x5 - x7)*(x5 - x7) =G= 1;

e9.. (x4 - x8)*(x4 - x8) + (x5 - x9)*(x5 - x9) =G= 1;

e10.. (x4 - x10)*(x4 - x10) + (x5 - x11)*(x5 - x11) =G= 1;

e11.. (x4 - x12)*(x4 - x12) + (x5 - x13)*(x5 - x13) =G= 1;

e12.. (x6 - x8)*(x6 - x8) + (x7 - x9)*(x7 - x9) =G= 1;

e13.. (x6 - x10)*(x6 - x10) + (x7 - x11)*(x7 - x11) =G= 1;

e14.. (x6 - x12)*(x6 - x12) + (x7 - x13)*(x7 - x13) =G= 1;

e15.. (x8 - x10)*(x8 - x10) + (x9 - x11)*(x9 - x11) =G= 1;

e16.. (x8 - x12)*(x8 - x12) + (x9 - x13)*(x9 - x13) =G= 1;

e17.. (x10 - x12)*(x10 - x12) + (x11 - x13)*(x11 - x13) =G= 1;

e18..    x2 - x14 =L= -0.5;

e19..    x3 - x15 =L= -0.5;

e20..    x4 - x14 =L= -0.5;

e21..    x5 - x15 =L= -0.5;

e22..    x6 - x14 =L= -0.5;

e23..    x7 - x15 =L= -0.5;

e24..    x8 - x14 =L= -0.5;

e25..    x9 - x15 =L= -0.5;

e26..    x10 - x14 =L= -0.5;

e27..    x11 - x15 =L= -0.5;

e28..    x12 - x14 =L= -0.5;

e29..    x13 - x15 =L= -0.5;

e30..    x2 =L= 4;

e31..    x3 =L= 0.95;

e32..    x2 - x4 =L= 0;

e33..    x2 - x6 =L= 0;

e34..    x2 - x8 =L= 0;

e35..    x2 - x10 =L= 0;

e36..    x2 - x12 =L= 0;

e37..    x4 - x6 =L= 0;

e38..    x4 - x8 =L= 0;

e39..    x4 - x10 =L= 0;

e40..    x4 - x12 =L= 0;

e41..    x6 - x8 =L= 0;

e42..    x6 - x10 =L= 0;

e43..    x6 - x12 =L= 0;

e44..    x8 - x10 =L= 0;

e45..    x8 - x12 =L= 0;

e46..    x10 - x12 =L= 0;

* set non-default bounds
x1.lo = 0.25; x1.up = 15.2;
x2.lo = 0.5; x2.up = 7.5;
x3.lo = 0.5; x3.up = 1.4;
x4.lo = 0.5; x4.up = 7.5;
x5.lo = 0.5; x5.up = 1.4;
x6.lo = 0.5; x6.up = 7.5;
x7.lo = 0.5; x7.up = 1.4;
x8.lo = 0.5; x8.up = 7.5;
x9.lo = 0.5; x9.up = 1.4;
x10.lo = 0.5; x10.up = 7.5;
x11.lo = 0.5; x11.up = 1.4;
x12.lo = 0.5; x12.up = 7.5;
x13.lo = 0.5; x13.up = 1.4;
x14.up = 8;
x15.up = 1.9;
objvar.lo = 0; objvar.up = 15.2;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


Last updated: 2024-03-25 Git hash: 1dae024f
Imprint / Privacy Policy / License: CC-BY 4.0