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Instance slay04h

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)
9859.65970800 p1 ( gdx sol )
(infeas: 9e-15)
Other points (infeas > 1e-08)  
Dual Bounds
9859.65940000 (ALPHAECP)
9859.65938400 (ANTIGONE)
9859.65970000 (BARON)
9859.65970000 (BONMIN)
9859.65948700 (COUENNE)
9859.65970800 (CPLEX)
9859.65970800 (GUROBI)
9859.65970000 (LINDO)
9859.65970700 (SCIP)
9859.65970800 (SHOT)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source SLay04H.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBQP
#Variables 140
#Binary Variables 24
#Integer Variables 0
#Nonlinear Variables 8
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 8
#Constraints 174
#Linear Constraints 174
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 480
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 8
#Nonzeros in Diagonal of Hessian of Lagrangian 8
#Blocks in Hessian of Lagrangian 8
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 3.5
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
*        175       31       24      120        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        141      117       24        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        501      493        8        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,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
          ,x71,x72,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,x103
          ,x104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
          ,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,x129
          ,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,objvar;

Positive Variables  x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23
          ,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38,x39,x40
          ,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53,x54,x55,x56,x57
          ,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70,x71,x72,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,x103,x104,x129,x130
          ,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140;

Binary Variables  b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
          ,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128;

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;


e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x5)) + 390*(sqr((-10) + x2) + sqr((-15
     ) + x6)) + 240*(sqr((-7) + x3) + sqr((-9) + x7)) + 70*(sqr((-3) + x4) + 
     sqr((-3) + x8))) - 300*x129 - 240*x130 - 210*x131 - 100*x132 - 150*x133
      - 120*x134 - 300*x135 - 240*x136 - 210*x137 - 100*x138 - 150*x139
      - 120*x140 + objvar =E= 0;

e2..  - x1 + x2 + x129 =G= 0;

e3..  - x1 + x3 + x130 =G= 0;

e4..  - x1 + x4 + x131 =G= 0;

e5..  - x2 + x3 + x132 =G= 0;

e6..  - x2 + x4 + x133 =G= 0;

e7..  - x3 + x4 + x134 =G= 0;

e8..    x1 - x2 + x129 =G= 0;

e9..    x1 - x3 + x130 =G= 0;

e10..    x1 - x4 + x131 =G= 0;

e11..    x2 - x3 + x132 =G= 0;

e12..    x2 - x4 + x133 =G= 0;

e13..    x3 - x4 + x134 =G= 0;

e14..  - x5 + x6 + x135 =G= 0;

e15..  - x5 + x7 + x136 =G= 0;

e16..  - x5 + x8 + x137 =G= 0;

e17..  - x6 + x7 + x138 =G= 0;

e18..  - x6 + x8 + x139 =G= 0;

e19..  - x7 + x8 + x140 =G= 0;

e20..    x5 - x6 + x135 =G= 0;

e21..    x5 - x7 + x136 =G= 0;

e22..    x5 - x8 + x137 =G= 0;

e23..    x6 - x7 + x138 =G= 0;

e24..    x6 - x8 + x139 =G= 0;

e25..    x7 - x8 + x140 =G= 0;

e26..    x1 - x9 - x12 - x15 - x18 =E= 0;

e27..    x1 - x10 - x13 - x16 - x19 =E= 0;

e28..    x1 - x11 - x14 - x17 - x20 =E= 0;

e29..    x2 - x21 - x24 - x27 - x30 =E= 0;

e30..    x2 - x22 - x25 - x28 - x31 =E= 0;

e31..    x2 - x23 - x26 - x29 - x32 =E= 0;

e32..    x3 - x33 - x36 - x39 - x42 =E= 0;

e33..    x3 - x34 - x37 - x40 - x43 =E= 0;

e34..    x3 - x35 - x38 - x41 - x44 =E= 0;

e35..    x4 - x45 - x48 - x51 - x54 =E= 0;

e36..    x4 - x46 - x49 - x52 - x55 =E= 0;

e37..    x4 - x47 - x50 - x53 - x56 =E= 0;

e38..    x5 - x57 - x60 - x63 - x66 =E= 0;

e39..    x5 - x58 - x61 - x64 - x67 =E= 0;

e40..    x5 - x59 - x62 - x65 - x68 =E= 0;

e41..    x6 - x69 - x72 - x75 - x78 =E= 0;

e42..    x6 - x70 - x73 - x76 - x79 =E= 0;

e43..    x6 - x71 - x74 - x77 - x80 =E= 0;

e44..    x7 - x81 - x84 - x87 - x90 =E= 0;

e45..    x7 - x82 - x85 - x88 - x91 =E= 0;

e46..    x7 - x83 - x86 - x89 - x92 =E= 0;

e47..    x8 - x93 - x96 - x99 - x102 =E= 0;

e48..    x8 - x94 - x97 - x100 - x103 =E= 0;

e49..    x8 - x95 - x98 - x101 - x104 =E= 0;

e50..    x9 - 27.5*b105 =L= 0;

e51..    x10 - 27.5*b106 =L= 0;

e52..    x11 - 27.5*b107 =L= 0;

e53..    x12 - 27.5*b111 =L= 0;

e54..    x13 - 27.5*b112 =L= 0;

e55..    x14 - 27.5*b113 =L= 0;

e56..    x15 - 27.5*b117 =L= 0;

e57..    x16 - 27.5*b118 =L= 0;

e58..    x17 - 27.5*b119 =L= 0;

e59..    x18 - 27.5*b123 =L= 0;

e60..    x19 - 27.5*b124 =L= 0;

e61..    x20 - 27.5*b125 =L= 0;

e62..    x21 - 27.5*b105 =L= 0;

e63..    x22 - 26.5*b108 =L= 0;

e64..    x23 - 26.5*b109 =L= 0;

e65..    x24 - 27.5*b111 =L= 0;

e66..    x25 - 26.5*b114 =L= 0;

e67..    x26 - 26.5*b115 =L= 0;

e68..    x27 - 27.5*b117 =L= 0;

e69..    x28 - 26.5*b120 =L= 0;

e70..    x29 - 26.5*b121 =L= 0;

e71..    x30 - 27.5*b123 =L= 0;

e72..    x31 - 26.5*b126 =L= 0;

e73..    x32 - 26.5*b127 =L= 0;

e74..    x33 - 27.5*b106 =L= 0;

e75..    x34 - 26.5*b108 =L= 0;

e76..    x35 - 28.5*b110 =L= 0;

e77..    x36 - 27.5*b112 =L= 0;

e78..    x37 - 26.5*b114 =L= 0;

e79..    x38 - 28.5*b116 =L= 0;

e80..    x39 - 27.5*b118 =L= 0;

e81..    x40 - 26.5*b120 =L= 0;

e82..    x41 - 28.5*b122 =L= 0;

e83..    x42 - 27.5*b124 =L= 0;

e84..    x43 - 26.5*b126 =L= 0;

e85..    x44 - 28.5*b128 =L= 0;

e86..    x45 - 27.5*b107 =L= 0;

e87..    x46 - 26.5*b109 =L= 0;

e88..    x47 - 28.5*b110 =L= 0;

e89..    x48 - 27.5*b113 =L= 0;

e90..    x49 - 26.5*b115 =L= 0;

e91..    x50 - 28.5*b116 =L= 0;

e92..    x51 - 27.5*b119 =L= 0;

e93..    x52 - 26.5*b121 =L= 0;

e94..    x53 - 28.5*b122 =L= 0;

e95..    x54 - 27.5*b125 =L= 0;

e96..    x55 - 26.5*b127 =L= 0;

e97..    x56 - 28.5*b128 =L= 0;

e98..    x57 - 27*b105 =L= 0;

e99..    x58 - 27*b106 =L= 0;

e100..    x59 - 27*b107 =L= 0;

e101..    x60 - 27*b111 =L= 0;

e102..    x61 - 27*b112 =L= 0;

e103..    x62 - 27*b113 =L= 0;

e104..    x63 - 27*b117 =L= 0;

e105..    x64 - 27*b118 =L= 0;

e106..    x65 - 27*b119 =L= 0;

e107..    x66 - 27*b123 =L= 0;

e108..    x67 - 27*b124 =L= 0;

e109..    x68 - 27*b125 =L= 0;

e110..    x69 - 27*b105 =L= 0;

e111..    x70 - 27.5*b108 =L= 0;

e112..    x71 - 27.5*b109 =L= 0;

e113..    x72 - 27*b111 =L= 0;

e114..    x73 - 27.5*b114 =L= 0;

e115..    x74 - 27.5*b115 =L= 0;

e116..    x75 - 27*b117 =L= 0;

e117..    x76 - 27.5*b120 =L= 0;

e118..    x77 - 27.5*b121 =L= 0;

e119..    x78 - 27*b123 =L= 0;

e120..    x79 - 27.5*b126 =L= 0;

e121..    x80 - 27.5*b127 =L= 0;

e122..    x81 - 27*b106 =L= 0;

e123..    x82 - 27.5*b108 =L= 0;

e124..    x83 - 28.5*b110 =L= 0;

e125..    x84 - 27*b112 =L= 0;

e126..    x85 - 27.5*b114 =L= 0;

e127..    x86 - 28.5*b116 =L= 0;

e128..    x87 - 27*b118 =L= 0;

e129..    x88 - 27.5*b120 =L= 0;

e130..    x89 - 28.5*b122 =L= 0;

e131..    x90 - 27*b124 =L= 0;

e132..    x91 - 27.5*b126 =L= 0;

e133..    x92 - 28.5*b128 =L= 0;

e134..    x93 - 27*b107 =L= 0;

e135..    x94 - 27.5*b109 =L= 0;

e136..    x95 - 28.5*b110 =L= 0;

e137..    x96 - 27*b113 =L= 0;

e138..    x97 - 27.5*b115 =L= 0;

e139..    x98 - 28.5*b116 =L= 0;

e140..    x99 - 27*b119 =L= 0;

e141..    x100 - 27.5*b121 =L= 0;

e142..    x101 - 28.5*b122 =L= 0;

e143..    x102 - 27*b125 =L= 0;

e144..    x103 - 27.5*b127 =L= 0;

e145..    x104 - 28.5*b128 =L= 0;

e146..    x9 - x21 + 6*b105 =L= 0;

e147..    x10 - x33 + 4*b106 =L= 0;

e148..    x11 - x45 + 3.5*b107 =L= 0;

e149..    x22 - x34 + 5*b108 =L= 0;

e150..    x23 - x46 + 4.5*b109 =L= 0;

e151..    x35 - x47 + 2.5*b110 =L= 0;

e152..  - x12 + x24 + 6*b111 =L= 0;

e153..  - x13 + x36 + 4*b112 =L= 0;

e154..  - x14 + x48 + 3.5*b113 =L= 0;

e155..  - x25 + x37 + 5*b114 =L= 0;

e156..  - x26 + x49 + 4.5*b115 =L= 0;

e157..  - x38 + x50 + 2.5*b116 =L= 0;

e158..    x63 - x75 + 5.5*b117 =L= 0;

e159..    x64 - x87 + 4.5*b118 =L= 0;

e160..    x65 - x99 + 4.5*b119 =L= 0;

e161..    x76 - x88 + 4*b120 =L= 0;

e162..    x77 - x100 + 4*b121 =L= 0;

e163..    x89 - x101 + 3*b122 =L= 0;

e164..  - x66 + x78 + 5.5*b123 =L= 0;

e165..  - x67 + x90 + 4.5*b124 =L= 0;

e166..  - x68 + x102 + 4.5*b125 =L= 0;

e167..  - x79 + x91 + 4*b126 =L= 0;

e168..  - x80 + x103 + 4*b127 =L= 0;

e169..  - x92 + x104 + 3*b128 =L= 0;

e170..    b105 + b111 + b117 + b123 =E= 1;

e171..    b106 + b112 + b118 + b124 =E= 1;

e172..    b107 + b113 + b119 + b125 =E= 1;

e173..    b108 + b114 + b120 + b126 =E= 1;

e174..    b109 + b115 + b121 + b127 =E= 1;

e175..    b110 + b116 + b122 + b128 =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 = 3; x5.up = 27;
x6.lo = 2.5; x6.up = 27.5;
x7.lo = 1.5; x7.up = 28.5;
x8.lo = 1.5; x8.up = 28.5;

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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