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Instance: flay05m

Determine the optimal length and width of a number of rectangular patches of land with fixed area, such that the perimeter of the set of patches is minimized.
Formats ams gms mod nl osil
Primal Bounds
64.49806199 p1 ( gdx sol )
(infeas: 1e-14)
Dual Bounds
59.99467900 (ALPHAECP)
64.49805097 (ANTIGONE)
64.49805581 (BARON)
64.49806199 (BONMIN)
64.49803085 (COUENNE)
50.88643441 (LINDO)
64.49803920 (SCIP)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source FLay05M.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBNLP
#Variables 62
#Binary Variables 40
#Integer Variables 0
#Nonlinear Variables 5
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 2
#Nonlinear Nonzeros in Objective 0
#Constraints 65
#Linear Constraints 60
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 5
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 240
#Nonlinear Nonzeros in Jacobian 5
#Nonzeros in (Upper-Left) Hessian of Lagrangian 5
#Nonzeros in Diagonal of Hessian of Lagrangian 5
#Blocks in Hessian of Lagrangian 5
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 74
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
*         66       11       10       45        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         63       23       40        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        243      238        5        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
          ,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x21,x22;

Binary Variables  b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36,b37
          ,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53,b54
          ,b55,b56,b57,b58,b59,b60,b61,b62;

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,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66;


e1..  - 2*x21 - 2*x22 + objvar =E= 0;

e2..  - x1 - x11 + x21 =G= 0;

e3..  - x2 - x12 + x21 =G= 0;

e4..  - x3 - x13 + x21 =G= 0;

e5..  - x4 - x14 + x21 =G= 0;

e6..  - x5 - x15 + x21 =G= 0;

e7..  - x6 - x16 + x22 =G= 0;

e8..  - x7 - x17 + x22 =G= 0;

e9..  - x8 - x18 + x22 =G= 0;

e10..  - x9 - x19 + x22 =G= 0;

e11..  - x10 - x20 + x22 =G= 0;

e12.. 40/x16 - x11 =L= 0;

e13.. 50/x17 - x12 =L= 0;

e14.. 60/x18 - x13 =L= 0;

e15.. 35/x19 - x14 =L= 0;

e16.. 75/x20 - x15 =L= 0;

e17..    x1 - x2 + x11 + 69*b23 =L= 69;

e18..    x1 - x3 + x11 + 69*b24 =L= 69;

e19..    x1 - x4 + x11 + 69*b25 =L= 69;

e20..    x1 - x5 + x11 + 69*b26 =L= 69;

e21..    x2 - x3 + x12 + 79*b27 =L= 79;

e22..    x2 - x4 + x12 + 79*b28 =L= 79;

e23..    x2 - x5 + x12 + 79*b29 =L= 79;

e24..    x3 - x4 + x13 + 89*b30 =L= 89;

e25..    x3 - x5 + x13 + 89*b31 =L= 89;

e26..    x4 - x5 + x14 + 64*b32 =L= 64;

e27..  - x1 + x2 + x12 + 79*b33 =L= 79;

e28..  - x1 + x3 + x13 + 89*b34 =L= 89;

e29..  - x1 + x4 + x14 + 64*b35 =L= 64;

e30..  - x1 + x5 + x15 + 104*b36 =L= 104;

e31..  - x2 + x3 + x13 + 89*b37 =L= 89;

e32..  - x2 + x4 + x14 + 64*b38 =L= 64;

e33..  - x2 + x5 + x15 + 104*b39 =L= 104;

e34..  - x3 + x4 + x14 + 64*b40 =L= 64;

e35..  - x3 + x5 + x15 + 104*b41 =L= 104;

e36..  - x4 + x5 + x15 + 104*b42 =L= 104;

e37..    x6 - x7 + x16 + 69*b43 =L= 69;

e38..    x6 - x8 + x16 + 69*b44 =L= 69;

e39..    x6 - x9 + x16 + 69*b45 =L= 69;

e40..    x6 - x10 + x16 + 69*b46 =L= 69;

e41..    x7 - x8 + x17 + 79*b47 =L= 79;

e42..    x7 - x9 + x17 + 79*b48 =L= 79;

e43..    x7 - x10 + x17 + 79*b49 =L= 79;

e44..    x8 - x9 + x18 + 89*b50 =L= 89;

e45..    x8 - x10 + x18 + 89*b51 =L= 89;

e46..    x9 - x10 + x19 + 64*b52 =L= 64;

e47..  - x6 + x7 + x17 + 79*b53 =L= 79;

e48..  - x6 + x8 + x18 + 89*b54 =L= 89;

e49..  - x6 + x9 + x19 + 64*b55 =L= 64;

e50..  - x6 + x10 + x20 + 104*b56 =L= 104;

e51..  - x7 + x8 + x18 + 89*b57 =L= 89;

e52..  - x7 + x9 + x19 + 64*b58 =L= 64;

e53..  - x7 + x10 + x20 + 104*b59 =L= 104;

e54..  - x8 + x9 + x19 + 64*b60 =L= 64;

e55..  - x8 + x10 + x20 + 104*b61 =L= 104;

e56..  - x9 + x10 + x20 + 104*b62 =L= 104;

e57..    b23 + b33 + b43 + b53 =E= 1;

e58..    b24 + b34 + b44 + b54 =E= 1;

e59..    b25 + b35 + b45 + b55 =E= 1;

e60..    b26 + b36 + b46 + b56 =E= 1;

e61..    b27 + b37 + b47 + b57 =E= 1;

e62..    b28 + b38 + b48 + b58 =E= 1;

e63..    b29 + b39 + b49 + b59 =E= 1;

e64..    b30 + b40 + b50 + b60 =E= 1;

e65..    b31 + b41 + b51 + b61 =E= 1;

e66..    b32 + b42 + b52 + b62 =E= 1;

* set non-default bounds
x1.up = 29;
x2.up = 29;
x3.up = 29;
x4.up = 29;
x5.up = 29;
x6.up = 29;
x7.up = 29;
x8.up = 29;
x9.up = 29;
x10.up = 29;
x11.lo = 1; x11.up = 40;
x12.lo = 1; x12.up = 50;
x13.lo = 1; x13.up = 60;
x14.lo = 1; x14.up = 35;
x15.lo = 1; x15.up = 75;
x16.lo = 1; x16.up = 40;
x17.lo = 1; x17.up = 50;
x18.lo = 1; x18.up = 60;
x19.lo = 1; x19.up = 35;
x20.lo = 1; x20.up = 75;
x21.up = 30;
x22.up = 30;

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;


Last updated: 2018-09-14 Git hash: ac5a5314
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