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Instance slay05m

Determine the optimal placement of a set of units with fixed width and length such that the Euclidean distance between their center point and a predefined "safety point" is minimized.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
22664.67865000 p1 ( gdx sol )
(infeas: 4e-15)
Other points (infeas > 1e-08)  
Dual Bounds
22664.67800000 (ALPHAECP)
22664.67846000 (ANTIGONE)
22664.67865000 (BARON)
22664.67865000 (BONMIN)
22664.67843000 (COUENNE)
22664.67865000 (CPLEX)
22664.67865000 (GUROBI)
22664.67865000 (LINDO)
22664.67865000 (SCIP)
22664.67865000 (SHOT)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source SLay05M.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBQP
#Variables 70
#Binary Variables 40
#Integer Variables 0
#Nonlinear Variables 10
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 30
#Nonlinear Nonzeros in Objective 10
#Constraints 90
#Linear Constraints 90
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 280
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 10
#Nonzeros in Diagonal of Hessian of Lagrangian 10
#Blocks in Hessian of Lagrangian 10
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
Minimal coefficient 1.0000e+00
Maximal coefficient 3.9000e+02
Infeasibility of initial point 2.5
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
*         91       11       40       40        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         71       31       40        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        311      301       10        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,b11,b12,b13,b14,b15,b16,b17,b18,b19
          ,b20,b21,b22,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,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
          ,objvar;

Positive Variables  x51,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64
          ,x65,x66,x67,x68,x69,x70;

Binary Variables  b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22,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;

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,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91;


e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x6)) + 390*(sqr((-10) + x2) + sqr((-15
     ) + x7)) + 240*(sqr((-7) + x3) + sqr((-9) + x8)) + 70*(sqr((-3) + x4) + 
     sqr((-3) + x9)) + 165*(sqr((-20) + x5) + sqr((-17) + x10))) - 300*x51
      - 240*x52 - 210*x53 - 140*x54 - 100*x55 - 150*x56 - 220*x57 - 120*x58
      - 300*x59 - 100*x60 - 300*x61 - 240*x62 - 210*x63 - 140*x64 - 100*x65
      - 150*x66 - 220*x67 - 120*x68 - 300*x69 - 100*x70 + objvar =E= 0;

e2..  - x1 + x2 + x51 =G= 0;

e3..  - x1 + x3 + x52 =G= 0;

e4..  - x1 + x4 + x53 =G= 0;

e5..  - x1 + x5 + x54 =G= 0;

e6..  - x2 + x3 + x55 =G= 0;

e7..  - x2 + x4 + x56 =G= 0;

e8..  - x2 + x5 + x57 =G= 0;

e9..  - x3 + x4 + x58 =G= 0;

e10..  - x3 + x5 + x59 =G= 0;

e11..  - x4 + x5 + x60 =G= 0;

e12..    x1 - x2 + x51 =G= 0;

e13..    x1 - x3 + x52 =G= 0;

e14..    x1 - x4 + x53 =G= 0;

e15..    x1 - x5 + x54 =G= 0;

e16..    x2 - x3 + x55 =G= 0;

e17..    x2 - x4 + x56 =G= 0;

e18..    x2 - x5 + x57 =G= 0;

e19..    x3 - x4 + x58 =G= 0;

e20..    x3 - x5 + x59 =G= 0;

e21..    x4 - x5 + x60 =G= 0;

e22..  - x6 + x7 + x61 =G= 0;

e23..  - x6 + x8 + x62 =G= 0;

e24..  - x6 + x9 + x63 =G= 0;

e25..  - x6 + x10 + x64 =G= 0;

e26..  - x7 + x8 + x65 =G= 0;

e27..  - x7 + x9 + x66 =G= 0;

e28..  - x7 + x10 + x67 =G= 0;

e29..  - x8 + x9 + x68 =G= 0;

e30..  - x8 + x10 + x69 =G= 0;

e31..  - x9 + x10 + x70 =G= 0;

e32..    x6 - x7 + x61 =G= 0;

e33..    x6 - x8 + x62 =G= 0;

e34..    x6 - x9 + x63 =G= 0;

e35..    x6 - x10 + x64 =G= 0;

e36..    x7 - x8 + x65 =G= 0;

e37..    x7 - x9 + x66 =G= 0;

e38..    x7 - x10 + x67 =G= 0;

e39..    x8 - x9 + x68 =G= 0;

e40..    x8 - x10 + x69 =G= 0;

e41..    x9 - x10 + x70 =G= 0;

e42..    x1 - x2 + 30*b11 =L= 24;

e43..    x1 - x3 + 30*b12 =L= 26;

e44..    x1 - x4 + 30*b13 =L= 26.5;

e45..    x1 - x5 + 30*b14 =L= 25.5;

e46..    x2 - x3 + 30*b15 =L= 25;

e47..    x2 - x4 + 30*b16 =L= 25.5;

e48..    x2 - x5 + 30*b17 =L= 24.5;

e49..    x3 - x4 + 30*b18 =L= 27.5;

e50..    x3 - x5 + 30*b19 =L= 26.5;

e51..    x4 - x5 + 30*b20 =L= 27;

e52..  - x1 + x2 + 30*b21 =L= 24;

e53..  - x1 + x3 + 30*b22 =L= 26;

e54..  - x1 + x4 + 30*b23 =L= 26.5;

e55..  - x1 + x5 + 30*b24 =L= 25.5;

e56..  - x2 + x3 + 30*b25 =L= 25;

e57..  - x2 + x4 + 30*b26 =L= 25.5;

e58..  - x2 + x5 + 30*b27 =L= 24.5;

e59..  - x3 + x4 + 30*b28 =L= 27.5;

e60..  - x3 + x5 + 30*b29 =L= 26.5;

e61..  - x4 + x5 + 30*b30 =L= 27;

e62..    x6 - x7 + 30*b31 =L= 24.5;

e63..    x6 - x8 + 30*b32 =L= 25.5;

e64..    x6 - x9 + 30*b33 =L= 25.5;

e65..    x6 - x10 + 30*b34 =L= 25;

e66..    x7 - x8 + 30*b35 =L= 26;

e67..    x7 - x9 + 30*b36 =L= 26;

e68..    x7 - x10 + 30*b37 =L= 25.5;

e69..    x8 - x9 + 30*b38 =L= 27;

e70..    x8 - x10 + 30*b39 =L= 26.5;

e71..    x9 - x10 + 30*b40 =L= 26.5;

e72..  - x6 + x7 + 30*b41 =L= 24.5;

e73..  - x6 + x8 + 30*b42 =L= 25.5;

e74..  - x6 + x9 + 30*b43 =L= 25.5;

e75..  - x6 + x10 + 30*b44 =L= 25;

e76..  - x7 + x8 + 30*b45 =L= 26;

e77..  - x7 + x9 + 30*b46 =L= 26;

e78..  - x7 + x10 + 30*b47 =L= 25.5;

e79..  - x8 + x9 + 30*b48 =L= 27;

e80..  - x8 + x10 + 30*b49 =L= 26.5;

e81..  - x9 + x10 + 30*b50 =L= 26.5;

e82..    b11 + b21 + b31 + b41 =E= 1;

e83..    b12 + b22 + b32 + b42 =E= 1;

e84..    b13 + b23 + b33 + b43 =E= 1;

e85..    b14 + b24 + b34 + b44 =E= 1;

e86..    b15 + b25 + b35 + b45 =E= 1;

e87..    b16 + b26 + b36 + b46 =E= 1;

e88..    b17 + b27 + b37 + b47 =E= 1;

e89..    b18 + b28 + b38 + b48 =E= 1;

e90..    b19 + b29 + b39 + b49 =E= 1;

e91..    b20 + b30 + b40 + b50 =E= 1;

* set non-default bounds
x1.lo = 2.5; x1.up = 27.5;
x2.lo = 3.5; x2.up = 26.5;
x3.lo = 1.5; x3.up = 28.5;
x4.lo = 1; x4.up = 29;
x5.lo = 2; x5.up = 28;
x6.lo = 3; x6.up = 27;
x7.lo = 2.5; x7.up = 27.5;
x8.lo = 1.5; x8.up = 28.5;
x9.lo = 1.5; x9.up = 28.5;
x10.lo = 2; x10.up = 28;

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: 2022-10-14 Git hash: 2be6d7c0
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