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Instance: slay06m

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
Primal Bounds (infeas ≤ 1e-08)
32757.02018000 p1 ( gdx sol )
(infeas: 1e-13)
Other points (infeas > 1e-08)  
Dual Bounds
29761.12900000 (ALPHAECP)
32757.01956000 (ANTIGONE)
32757.02015000 (BARON)
32757.02000000 (BONMIN)
32757.02000000 (COUENNE)
32757.02018000 (LINDO)
32757.02018000 (SCIP)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source SLay06M.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBQP
#Variables 102
#Binary Variables 60
#Integer Variables 0
#Nonlinear Variables 12
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 42
#Nonlinear Nonzeros in Objective 12
#Constraints 135
#Linear Constraints 135
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 420
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 12
#Nonzeros in Diagonal of Hessian of Lagrangian 12
#Blocks in Hessian of Lagrangian 12
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 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
*        136       16       60       60        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        103       43       60        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        463      451       12        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,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,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
          ,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,objvar;

Positive Variables  x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102;

Binary Variables  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,b51,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61
          ,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72;

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,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
          ,e130,e131,e132,e133,e134,e135,e136;


e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x7)) + 390*(sqr((-10) + x2) + sqr((-15
     ) + x8)) + 240*(sqr((-7) + x3) + sqr((-9) + x9)) + 70*(sqr((-3) + x4) + 
     sqr((-3) + x10)) + 165*(sqr((-20) + x5) + sqr((-17) + x11)) + 100*(sqr((-
     18) + x6) + sqr((-8) + x12))) - 300*x73 - 240*x74 - 210*x75 - 140*x76
      - 300*x77 - 100*x78 - 150*x79 - 220*x80 - 200*x81 - 120*x82 - 300*x83
      - 150*x84 - 100*x85 - 120*x86 - 130*x87 - 300*x88 - 240*x89 - 210*x90
      - 140*x91 - 300*x92 - 100*x93 - 150*x94 - 220*x95 - 200*x96 - 120*x97
      - 300*x98 - 150*x99 - 100*x100 - 120*x101 - 130*x102 + objvar =E= 0;

e2..  - x1 + x2 + x73 =G= 0;

e3..  - x1 + x3 + x74 =G= 0;

e4..  - x1 + x4 + x75 =G= 0;

e5..  - x1 + x5 + x76 =G= 0;

e6..  - x1 + x6 + x77 =G= 0;

e7..  - x2 + x3 + x78 =G= 0;

e8..  - x2 + x4 + x79 =G= 0;

e9..  - x2 + x5 + x80 =G= 0;

e10..  - x2 + x6 + x81 =G= 0;

e11..  - x3 + x4 + x82 =G= 0;

e12..  - x3 + x5 + x83 =G= 0;

e13..  - x3 + x6 + x84 =G= 0;

e14..  - x4 + x5 + x85 =G= 0;

e15..  - x4 + x6 + x86 =G= 0;

e16..  - x5 + x6 + x87 =G= 0;

e17..    x1 - x2 + x73 =G= 0;

e18..    x1 - x3 + x74 =G= 0;

e19..    x1 - x4 + x75 =G= 0;

e20..    x1 - x5 + x76 =G= 0;

e21..    x1 - x6 + x77 =G= 0;

e22..    x2 - x3 + x78 =G= 0;

e23..    x2 - x4 + x79 =G= 0;

e24..    x2 - x5 + x80 =G= 0;

e25..    x2 - x6 + x81 =G= 0;

e26..    x3 - x4 + x82 =G= 0;

e27..    x3 - x5 + x83 =G= 0;

e28..    x3 - x6 + x84 =G= 0;

e29..    x4 - x5 + x85 =G= 0;

e30..    x4 - x6 + x86 =G= 0;

e31..    x5 - x6 + x87 =G= 0;

e32..  - x7 + x8 + x88 =G= 0;

e33..  - x7 + x9 + x89 =G= 0;

e34..  - x7 + x10 + x90 =G= 0;

e35..  - x7 + x11 + x91 =G= 0;

e36..  - x7 + x12 + x92 =G= 0;

e37..  - x8 + x9 + x93 =G= 0;

e38..  - x8 + x10 + x94 =G= 0;

e39..  - x8 + x11 + x95 =G= 0;

e40..  - x8 + x12 + x96 =G= 0;

e41..  - x9 + x10 + x97 =G= 0;

e42..  - x9 + x11 + x98 =G= 0;

e43..  - x9 + x12 + x99 =G= 0;

e44..  - x10 + x11 + x100 =G= 0;

e45..  - x10 + x12 + x101 =G= 0;

e46..  - x11 + x12 + x102 =G= 0;

e47..    x7 - x8 + x88 =G= 0;

e48..    x7 - x9 + x89 =G= 0;

e49..    x7 - x10 + x90 =G= 0;

e50..    x7 - x11 + x91 =G= 0;

e51..    x7 - x12 + x92 =G= 0;

e52..    x8 - x9 + x93 =G= 0;

e53..    x8 - x10 + x94 =G= 0;

e54..    x8 - x11 + x95 =G= 0;

e55..    x8 - x12 + x96 =G= 0;

e56..    x9 - x10 + x97 =G= 0;

e57..    x9 - x11 + x98 =G= 0;

e58..    x9 - x12 + x99 =G= 0;

e59..    x10 - x11 + x100 =G= 0;

e60..    x10 - x12 + x101 =G= 0;

e61..    x11 - x12 + x102 =G= 0;

e62..    x1 - x2 + 30*b13 =L= 24;

e63..    x1 - x3 + 30*b14 =L= 26;

e64..    x1 - x4 + 30*b15 =L= 26.5;

e65..    x1 - x5 + 30*b16 =L= 25.5;

e66..    x1 - x6 + 30*b17 =L= 25;

e67..    x2 - x3 + 30*b18 =L= 25;

e68..    x2 - x4 + 30*b19 =L= 25.5;

e69..    x2 - x5 + 30*b20 =L= 24.5;

e70..    x2 - x6 + 30*b21 =L= 24;

e71..    x3 - x4 + 30*b22 =L= 27.5;

e72..    x3 - x5 + 30*b23 =L= 26.5;

e73..    x3 - x6 + 30*b24 =L= 26;

e74..    x4 - x5 + 30*b25 =L= 27;

e75..    x4 - x6 + 30*b26 =L= 26.5;

e76..    x5 - x6 + 30*b27 =L= 25.5;

e77..  - x1 + x2 + 30*b28 =L= 24;

e78..  - x1 + x3 + 30*b29 =L= 26;

e79..  - x1 + x4 + 30*b30 =L= 26.5;

e80..  - x1 + x5 + 30*b31 =L= 25.5;

e81..  - x1 + x6 + 30*b32 =L= 25;

e82..  - x2 + x3 + 30*b33 =L= 25;

e83..  - x2 + x4 + 30*b34 =L= 25.5;

e84..  - x2 + x5 + 30*b35 =L= 24.5;

e85..  - x2 + x6 + 30*b36 =L= 24;

e86..  - x3 + x4 + 30*b37 =L= 27.5;

e87..  - x3 + x5 + 30*b38 =L= 26.5;

e88..  - x3 + x6 + 30*b39 =L= 26;

e89..  - x4 + x5 + 30*b40 =L= 27;

e90..  - x4 + x6 + 30*b41 =L= 26.5;

e91..  - x5 + x6 + 30*b42 =L= 25.5;

e92..    x7 - x8 + 30*b43 =L= 24.5;

e93..    x7 - x9 + 30*b44 =L= 25.5;

e94..    x7 - x10 + 30*b45 =L= 25.5;

e95..    x7 - x11 + 30*b46 =L= 25;

e96..    x7 - x12 + 30*b47 =L= 26;

e97..    x8 - x9 + 30*b48 =L= 26;

e98..    x8 - x10 + 30*b49 =L= 26;

e99..    x8 - x11 + 30*b50 =L= 25.5;

e100..    x8 - x12 + 30*b51 =L= 26.5;

e101..    x9 - x10 + 30*b52 =L= 27;

e102..    x9 - x11 + 30*b53 =L= 26.5;

e103..    x9 - x12 + 30*b54 =L= 27.5;

e104..    x10 - x11 + 30*b55 =L= 26.5;

e105..    x10 - x12 + 30*b56 =L= 27.5;

e106..    x11 - x12 + 30*b57 =L= 27;

e107..  - x7 + x8 + 30*b58 =L= 24.5;

e108..  - x7 + x9 + 30*b59 =L= 25.5;

e109..  - x7 + x10 + 30*b60 =L= 25.5;

e110..  - x7 + x11 + 30*b61 =L= 25;

e111..  - x7 + x12 + 30*b62 =L= 26;

e112..  - x8 + x9 + 30*b63 =L= 26;

e113..  - x8 + x10 + 30*b64 =L= 26;

e114..  - x8 + x11 + 30*b65 =L= 25.5;

e115..  - x8 + x12 + 30*b66 =L= 26.5;

e116..  - x9 + x10 + 30*b67 =L= 27;

e117..  - x9 + x11 + 30*b68 =L= 26.5;

e118..  - x9 + x12 + 30*b69 =L= 27.5;

e119..  - x10 + x11 + 30*b70 =L= 26.5;

e120..  - x10 + x12 + 30*b71 =L= 27.5;

e121..  - x11 + x12 + 30*b72 =L= 27;

e122..    b13 + b28 + b43 + b58 =E= 1;

e123..    b14 + b29 + b44 + b59 =E= 1;

e124..    b15 + b30 + b45 + b60 =E= 1;

e125..    b16 + b31 + b46 + b61 =E= 1;

e126..    b17 + b32 + b47 + b62 =E= 1;

e127..    b18 + b33 + b48 + b63 =E= 1;

e128..    b19 + b34 + b49 + b64 =E= 1;

e129..    b20 + b35 + b50 + b65 =E= 1;

e130..    b21 + b36 + b51 + b66 =E= 1;

e131..    b22 + b37 + b52 + b67 =E= 1;

e132..    b23 + b38 + b53 + b68 =E= 1;

e133..    b24 + b39 + b54 + b69 =E= 1;

e134..    b25 + b40 + b55 + b70 =E= 1;

e135..    b26 + b41 + b56 + b71 =E= 1;

e136..    b27 + b42 + b57 + b72 =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 = 2.5; x6.up = 27.5;
x7.lo = 3; x7.up = 27;
x8.lo = 2.5; x8.up = 27.5;
x9.lo = 1.5; x9.up = 28.5;
x10.lo = 1.5; x10.up = 28.5;
x11.lo = 2; x11.up = 28;
x12.lo = 1; x12.up = 29;

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: 2019-06-04 Git hash: 78444eaa
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