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Instance: kall_circles_c6b

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
Primal Bounds
2.79127021 p1 ( gdx sol )
(infeas: 4e-10)
1.97359970 p2 ( gdx sol )
(infeas: 9e-16)
Dual Bounds
1.97359684 (ANTIGONE)
1.97359616 (BARON)
1.97355113 (COUENNE)
1.97359969 (LINDO)
1.97359680 (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_circles_c6b
Application Geometry
Added to library 15 Aug 2014
Problem type QCP
#Variables 18
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 16
#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 54
#Linear Constraints 32
#Quadratic Constraints 22
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 149
#Nonlinear Nonzeros in Jacobian 86
#Nonzeros in (Upper-Left) Hessian of Lagrangian 100
#Nonzeros in Diagonal of Hessian of Lagrangian 14
#Blocks in Hessian of Lagrangian 3
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 7
Average blocksize in Hessian of Lagrangian 5.333333
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 6.447
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
*         54        2       21       31        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         18       18        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        149       63       86        0
*
*  Solve m using NLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,objvar;

Positive Variables  x16,x17;

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,e47,e48,e49,e50,e51,e52,e53
          ,e54;


e1..  - x1 + objvar =E= -7.25707902979242;

e2.. -x16*x17 + 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.. (x2 - x14)*(x2 - x14) + (x3 - x15)*(x3 - x15) =G= 1.96;

e9.. (x4 - x6)*(x4 - x6) + (x5 - x7)*(x5 - x7) =G= 1;

e10.. (x4 - x8)*(x4 - x8) + (x5 - x9)*(x5 - x9) =G= 1;

e11.. (x4 - x10)*(x4 - x10) + (x5 - x11)*(x5 - x11) =G= 1;

e12.. (x4 - x12)*(x4 - x12) + (x5 - x13)*(x5 - x13) =G= 1;

e13.. (x4 - x14)*(x4 - x14) + (x5 - x15)*(x5 - x15) =G= 1.96;

e14.. (x6 - x8)*(x6 - x8) + (x7 - x9)*(x7 - x9) =G= 1;

e15.. (x6 - x10)*(x6 - x10) + (x7 - x11)*(x7 - x11) =G= 1;

e16.. (x6 - x12)*(x6 - x12) + (x7 - x13)*(x7 - x13) =G= 1;

e17.. (x6 - x14)*(x6 - x14) + (x7 - x15)*(x7 - x15) =G= 1.96;

e18.. (x8 - x10)*(x8 - x10) + (x9 - x11)*(x9 - x11) =G= 1;

e19.. (x8 - x12)*(x8 - x12) + (x9 - x13)*(x9 - x13) =G= 1;

e20.. (x8 - x14)*(x8 - x14) + (x9 - x15)*(x9 - x15) =G= 1.96;

e21.. (x10 - x12)*(x10 - x12) + (x11 - x13)*(x11 - x13) =G= 1;

e22.. (x10 - x14)*(x10 - x14) + (x11 - x15)*(x11 - x15) =G= 1.96;

e23.. (x12 - x14)*(x12 - x14) + (x13 - x15)*(x13 - x15) =G= 1.96;

e24..    x2 - x16 =L= -0.5;

e25..    x3 - x17 =L= -0.5;

e26..    x4 - x16 =L= -0.5;

e27..    x5 - x17 =L= -0.5;

e28..    x6 - x16 =L= -0.5;

e29..    x7 - x17 =L= -0.5;

e30..    x8 - x16 =L= -0.5;

e31..    x9 - x17 =L= -0.5;

e32..    x10 - x16 =L= -0.5;

e33..    x11 - x17 =L= -0.5;

e34..    x12 - x16 =L= -0.5;

e35..    x13 - x17 =L= -0.5;

e36..    x14 - x16 =L= -0.9;

e37..    x15 - x17 =L= -0.9;

e38..    x2 =L= 4;

e39..    x3 =L= 1.45;

e40..    x2 - x4 =L= 0;

e41..    x2 - x6 =L= 0;

e42..    x2 - x8 =L= 0;

e43..    x2 - x10 =L= 0;

e44..    x2 - x12 =L= 0;

e45..    x4 - x6 =L= 0;

e46..    x4 - x8 =L= 0;

e47..    x4 - x10 =L= 0;

e48..    x4 - x12 =L= 0;

e49..    x6 - x8 =L= 0;

e50..    x6 - x10 =L= 0;

e51..    x6 - x12 =L= 0;

e52..    x8 - x10 =L= 0;

e53..    x8 - x12 =L= 0;

e54..    x10 - x12 =L= 0;

* set non-default bounds
x1.lo = 0.81; x1.up = 23.2;
x2.lo = 0.5; x2.up = 7.5;
x3.lo = 0.5; x3.up = 2.4;
x4.lo = 0.5; x4.up = 7.5;
x5.lo = 0.5; x5.up = 2.4;
x6.lo = 0.5; x6.up = 7.5;
x7.lo = 0.5; x7.up = 2.4;
x8.lo = 0.5; x8.up = 7.5;
x9.lo = 0.5; x9.up = 2.4;
x10.lo = 0.5; x10.up = 7.5;
x11.lo = 0.5; x11.up = 2.4;
x12.lo = 0.5; x12.up = 7.5;
x13.lo = 0.5; x13.up = 2.4;
x14.lo = 0.9; x14.up = 7.1;
x15.lo = 0.9; x15.up = 2;
x16.up = 8;
x17.up = 2.9;
objvar.lo = 0; objvar.up = 23.2;

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: 2018-09-14 Git hash: ac5a5314
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