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Instance slay07m

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)
68938.51673000 p1 ( gdx sol )
(infeas: 2e-15)
64748.82529000 p2 ( gdx sol )
(infeas: 2e-15)
Other points (infeas > 1e-08)  
Dual Bounds
34119.82700000 (ALPHAECP)
64748.82251000 (ANTIGONE)
64748.82523000 (BARON)
64748.82500000 (BONMIN)
64748.82500000 (COUENNE)
64748.82529000 (CPLEX)
64748.82529000 (GUROBI)
64748.82529000 (LINDO)
64748.82529000 (SCIP)
64748.82529000 (SHOT)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source SLay07M.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBQP
#Variables 140
#Binary Variables 84
#Integer Variables 0
#Nonlinear Variables 14
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 56
#Nonlinear Nonzeros in Objective 14
#Constraints 189
#Linear Constraints 189
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 588
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 14
#Nonzeros in Diagonal of Hessian of Lagrangian 14
#Blocks in Hessian of Lagrangian 14
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 3
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
*        190       22       84       84        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        141       57       84        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        645      631       14        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,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,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
          ,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,x99,x100,x101,x102,x103
          ,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116
          ,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
          ,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,objvar;

Positive Variables  x99,x100,x101,x102,x103,x104,x105,x106,x107,x108,x109,x110
          ,x111,x112,x113,x114,x115,x116,x117,x118,x119,x120,x121,x122,x123
          ,x124,x125,x126,x127,x128,x129,x130,x131,x132,x133,x134,x135,x136
          ,x137,x138,x139,x140;

Binary Variables  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,b73,b74,b75,b76,b77,b78,b79,b80
          ,b81,b82,b83,b84,b85,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97
          ,b98;

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,e137,e138,e139,e140,e141,e142
          ,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
          ,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
          ,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
          ,e182,e183,e184,e185,e186,e187,e188,e189,e190;


e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x8)) + 390*(sqr((-10) + x2) + sqr((-15
     ) + x9)) + 240*(sqr((-7) + x3) + sqr((-9) + x10)) + 70*(sqr((-3) + x4) + 
     sqr((-3) + x11)) + 165*(sqr((-20) + x5) + sqr((-17) + x12)) + 100*(sqr((-
     18) + x6) + sqr((-8) + x13)) + 200*(sqr((-30) + x7) + sqr((-20) + x14)))
      - 300*x99 - 240*x100 - 210*x101 - 140*x102 - 300*x103 - 250*x104
      - 100*x105 - 150*x106 - 220*x107 - 200*x108 - 300*x109 - 120*x110
      - 300*x111 - 150*x112 - 150*x113 - 100*x114 - 120*x115 - 180*x116
      - 130*x117 - 190*x118 - 220*x119 - 300*x120 - 240*x121 - 210*x122
      - 140*x123 - 300*x124 - 250*x125 - 100*x126 - 150*x127 - 220*x128
      - 200*x129 - 300*x130 - 120*x131 - 300*x132 - 150*x133 - 150*x134
      - 100*x135 - 120*x136 - 180*x137 - 130*x138 - 190*x139 - 220*x140
      + objvar =E= 0;

e2..  - x1 + x2 + x99 =G= 0;

e3..  - x1 + x3 + x100 =G= 0;

e4..  - x1 + x4 + x101 =G= 0;

e5..  - x1 + x5 + x102 =G= 0;

e6..  - x1 + x6 + x103 =G= 0;

e7..  - x1 + x7 + x104 =G= 0;

e8..  - x2 + x3 + x105 =G= 0;

e9..  - x2 + x4 + x106 =G= 0;

e10..  - x2 + x5 + x107 =G= 0;

e11..  - x2 + x6 + x108 =G= 0;

e12..  - x2 + x7 + x109 =G= 0;

e13..  - x3 + x4 + x110 =G= 0;

e14..  - x3 + x5 + x111 =G= 0;

e15..  - x3 + x6 + x112 =G= 0;

e16..  - x3 + x7 + x113 =G= 0;

e17..  - x4 + x5 + x114 =G= 0;

e18..  - x4 + x6 + x115 =G= 0;

e19..  - x4 + x7 + x116 =G= 0;

e20..  - x5 + x6 + x117 =G= 0;

e21..  - x5 + x7 + x118 =G= 0;

e22..  - x6 + x7 + x119 =G= 0;

e23..    x1 - x2 + x99 =G= 0;

e24..    x1 - x3 + x100 =G= 0;

e25..    x1 - x4 + x101 =G= 0;

e26..    x1 - x5 + x102 =G= 0;

e27..    x1 - x6 + x103 =G= 0;

e28..    x1 - x7 + x104 =G= 0;

e29..    x2 - x3 + x105 =G= 0;

e30..    x2 - x4 + x106 =G= 0;

e31..    x2 - x5 + x107 =G= 0;

e32..    x2 - x6 + x108 =G= 0;

e33..    x2 - x7 + x109 =G= 0;

e34..    x3 - x4 + x110 =G= 0;

e35..    x3 - x5 + x111 =G= 0;

e36..    x3 - x6 + x112 =G= 0;

e37..    x3 - x7 + x113 =G= 0;

e38..    x4 - x5 + x114 =G= 0;

e39..    x4 - x6 + x115 =G= 0;

e40..    x4 - x7 + x116 =G= 0;

e41..    x5 - x6 + x117 =G= 0;

e42..    x5 - x7 + x118 =G= 0;

e43..    x6 - x7 + x119 =G= 0;

e44..  - x8 + x9 + x120 =G= 0;

e45..  - x8 + x10 + x121 =G= 0;

e46..  - x8 + x11 + x122 =G= 0;

e47..  - x8 + x12 + x123 =G= 0;

e48..  - x8 + x13 + x124 =G= 0;

e49..  - x8 + x14 + x125 =G= 0;

e50..  - x9 + x10 + x126 =G= 0;

e51..  - x9 + x11 + x127 =G= 0;

e52..  - x9 + x12 + x128 =G= 0;

e53..  - x9 + x13 + x129 =G= 0;

e54..  - x9 + x14 + x130 =G= 0;

e55..  - x10 + x11 + x131 =G= 0;

e56..  - x10 + x12 + x132 =G= 0;

e57..  - x10 + x13 + x133 =G= 0;

e58..  - x10 + x14 + x134 =G= 0;

e59..  - x11 + x12 + x135 =G= 0;

e60..  - x11 + x13 + x136 =G= 0;

e61..  - x11 + x14 + x137 =G= 0;

e62..  - x12 + x13 + x138 =G= 0;

e63..  - x12 + x14 + x139 =G= 0;

e64..  - x13 + x14 + x140 =G= 0;

e65..    x8 - x9 + x120 =G= 0;

e66..    x8 - x10 + x121 =G= 0;

e67..    x8 - x11 + x122 =G= 0;

e68..    x8 - x12 + x123 =G= 0;

e69..    x8 - x13 + x124 =G= 0;

e70..    x8 - x14 + x125 =G= 0;

e71..    x9 - x10 + x126 =G= 0;

e72..    x9 - x11 + x127 =G= 0;

e73..    x9 - x12 + x128 =G= 0;

e74..    x9 - x13 + x129 =G= 0;

e75..    x9 - x14 + x130 =G= 0;

e76..    x10 - x11 + x131 =G= 0;

e77..    x10 - x12 + x132 =G= 0;

e78..    x10 - x13 + x133 =G= 0;

e79..    x10 - x14 + x134 =G= 0;

e80..    x11 - x12 + x135 =G= 0;

e81..    x11 - x13 + x136 =G= 0;

e82..    x11 - x14 + x137 =G= 0;

e83..    x12 - x13 + x138 =G= 0;

e84..    x12 - x14 + x139 =G= 0;

e85..    x13 - x14 + x140 =G= 0;

e86..    x1 - x2 + 40*b15 =L= 34;

e87..    x1 - x3 + 40*b16 =L= 36;

e88..    x1 - x4 + 40*b17 =L= 36.5;

e89..    x1 - x5 + 40*b18 =L= 35.5;

e90..    x1 - x6 + 40*b19 =L= 35;

e91..    x1 - x7 + 40*b20 =L= 33.5;

e92..    x2 - x3 + 40*b21 =L= 35;

e93..    x2 - x4 + 40*b22 =L= 35.5;

e94..    x2 - x5 + 40*b23 =L= 34.5;

e95..    x2 - x6 + 40*b24 =L= 34;

e96..    x2 - x7 + 40*b25 =L= 32.5;

e97..    x3 - x4 + 40*b26 =L= 37.5;

e98..    x3 - x5 + 40*b27 =L= 36.5;

e99..    x3 - x6 + 40*b28 =L= 36;

e100..    x3 - x7 + 40*b29 =L= 34.5;

e101..    x4 - x5 + 40*b30 =L= 37;

e102..    x4 - x6 + 40*b31 =L= 36.5;

e103..    x4 - x7 + 40*b32 =L= 35;

e104..    x5 - x6 + 40*b33 =L= 35.5;

e105..    x5 - x7 + 40*b34 =L= 34;

e106..    x6 - x7 + 40*b35 =L= 33.5;

e107..  - x1 + x2 + 40*b36 =L= 34;

e108..  - x1 + x3 + 40*b37 =L= 36;

e109..  - x1 + x4 + 40*b38 =L= 36.5;

e110..  - x1 + x5 + 40*b39 =L= 35.5;

e111..  - x1 + x6 + 40*b40 =L= 35;

e112..  - x1 + x7 + 40*b41 =L= 33.5;

e113..  - x2 + x3 + 40*b42 =L= 35;

e114..  - x2 + x4 + 40*b43 =L= 35.5;

e115..  - x2 + x5 + 40*b44 =L= 34.5;

e116..  - x2 + x6 + 40*b45 =L= 34;

e117..  - x2 + x7 + 40*b46 =L= 32.5;

e118..  - x3 + x4 + 40*b47 =L= 37.5;

e119..  - x3 + x5 + 40*b48 =L= 36.5;

e120..  - x3 + x6 + 40*b49 =L= 36;

e121..  - x3 + x7 + 40*b50 =L= 34.5;

e122..  - x4 + x5 + 40*b51 =L= 37;

e123..  - x4 + x6 + 40*b52 =L= 36.5;

e124..  - x4 + x7 + 40*b53 =L= 35;

e125..  - x5 + x6 + 40*b54 =L= 35.5;

e126..  - x5 + x7 + 40*b55 =L= 34;

e127..  - x6 + x7 + 40*b56 =L= 33.5;

e128..    x8 - x9 + 40*b57 =L= 34.5;

e129..    x8 - x10 + 40*b58 =L= 35.5;

e130..    x8 - x11 + 40*b59 =L= 35.5;

e131..    x8 - x12 + 40*b60 =L= 35;

e132..    x8 - x13 + 40*b61 =L= 36;

e133..    x8 - x14 + 40*b62 =L= 34;

e134..    x9 - x10 + 40*b63 =L= 36;

e135..    x9 - x11 + 40*b64 =L= 36;

e136..    x9 - x12 + 40*b65 =L= 35.5;

e137..    x9 - x13 + 40*b66 =L= 36.5;

e138..    x9 - x14 + 40*b67 =L= 34.5;

e139..    x10 - x11 + 40*b68 =L= 37;

e140..    x10 - x12 + 40*b69 =L= 36.5;

e141..    x10 - x13 + 40*b70 =L= 37.5;

e142..    x10 - x14 + 40*b71 =L= 35.5;

e143..    x11 - x12 + 40*b72 =L= 36.5;

e144..    x11 - x13 + 40*b73 =L= 37.5;

e145..    x11 - x14 + 40*b74 =L= 35.5;

e146..    x12 - x13 + 40*b75 =L= 37;

e147..    x12 - x14 + 40*b76 =L= 35;

e148..    x13 - x14 + 40*b77 =L= 36;

e149..  - x8 + x9 + 40*b78 =L= 34.5;

e150..  - x8 + x10 + 40*b79 =L= 35.5;

e151..  - x8 + x11 + 40*b80 =L= 35.5;

e152..  - x8 + x12 + 40*b81 =L= 35;

e153..  - x8 + x13 + 40*b82 =L= 36;

e154..  - x8 + x14 + 40*b83 =L= 34;

e155..  - x9 + x10 + 40*b84 =L= 36;

e156..  - x9 + x11 + 40*b85 =L= 36;

e157..  - x9 + x12 + 40*b86 =L= 35.5;

e158..  - x9 + x13 + 40*b87 =L= 36.5;

e159..  - x9 + x14 + 40*b88 =L= 34.5;

e160..  - x10 + x11 + 40*b89 =L= 37;

e161..  - x10 + x12 + 40*b90 =L= 36.5;

e162..  - x10 + x13 + 40*b91 =L= 37.5;

e163..  - x10 + x14 + 40*b92 =L= 35.5;

e164..  - x11 + x12 + 40*b93 =L= 36.5;

e165..  - x11 + x13 + 40*b94 =L= 37.5;

e166..  - x11 + x14 + 40*b95 =L= 35.5;

e167..  - x12 + x13 + 40*b96 =L= 37;

e168..  - x12 + x14 + 40*b97 =L= 35;

e169..  - x13 + x14 + 40*b98 =L= 36;

e170..    b15 + b36 + b57 + b78 =E= 1;

e171..    b16 + b37 + b58 + b79 =E= 1;

e172..    b17 + b38 + b59 + b80 =E= 1;

e173..    b18 + b39 + b60 + b81 =E= 1;

e174..    b19 + b40 + b61 + b82 =E= 1;

e175..    b20 + b41 + b62 + b83 =E= 1;

e176..    b21 + b42 + b63 + b84 =E= 1;

e177..    b22 + b43 + b64 + b85 =E= 1;

e178..    b23 + b44 + b65 + b86 =E= 1;

e179..    b24 + b45 + b66 + b87 =E= 1;

e180..    b25 + b46 + b67 + b88 =E= 1;

e181..    b26 + b47 + b68 + b89 =E= 1;

e182..    b27 + b48 + b69 + b90 =E= 1;

e183..    b28 + b49 + b70 + b91 =E= 1;

e184..    b29 + b50 + b71 + b92 =E= 1;

e185..    b30 + b51 + b72 + b93 =E= 1;

e186..    b31 + b52 + b73 + b94 =E= 1;

e187..    b32 + b53 + b74 + b95 =E= 1;

e188..    b33 + b54 + b75 + b96 =E= 1;

e189..    b34 + b55 + b76 + b97 =E= 1;

e190..    b35 + b56 + b77 + b98 =E= 1;

* set non-default bounds
x1.lo = 2.5; x1.up = 37.5;
x2.lo = 3.5; x2.up = 36.5;
x3.lo = 1.5; x3.up = 38.5;
x4.lo = 1; x4.up = 39;
x5.lo = 2; x5.up = 38;
x6.lo = 2.5; x6.up = 37.5;
x7.lo = 4; x7.up = 36;
x8.lo = 3; x8.up = 37;
x9.lo = 2.5; x9.up = 37.5;
x10.lo = 1.5; x10.up = 38.5;
x11.lo = 1.5; x11.up = 38.5;
x12.lo = 2; x12.up = 38;
x13.lo = 1; x13.up = 39;
x14.lo = 3; x14.up = 37;

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: 2022-08-11 Git hash: f176bd52
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