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Instance: clay0205m

Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized.
Formats ams gms lp mod nl osil pip
Primal Bounds
8092.50000000 p1 ( gdx sol )
(infeas: 3e-11)
Dual Bounds
8092.50000000 (ALPHAECP)
8092.50000000 (ANTIGONE)
8092.50000000 (BARON)
8092.50000000 (BONMIN)
8092.50000000 (COUENNE)
5645.01920000 (LINDO)
8092.50000000 (SCIP)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source CLay0205M.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBQCP
#Variables 80
#Binary Variables 50
#Integer Variables 0
#Nonlinear Variables 10
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 20
#Nonlinear Nonzeros in Objective 0
#Constraints 135
#Linear Constraints 95
#Quadratic Constraints 40
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 410
#Nonlinear Nonzeros in Jacobian 80
#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
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
*        136       16       40       80        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         81       31       50        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        431      351       80        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,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
          ,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,objvar;

Positive Variables  x61,x62,x63,x64,x65,x66,x67,x68,x69,x70,x71,x72,x73,x74
          ,x75,x76,x77,x78,x79,x80;

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,b51,b52,b53,b54,b55,b56,b57,b58,b59
          ,b60;

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..  - 300*x61 - 240*x62 - 210*x63 - 50*x64 - 100*x65 - 150*x66 - 30*x67
      - 120*x68 - 25*x69 - 60*x70 - 300*x71 - 240*x72 - 210*x73 - 50*x74
      - 100*x75 - 150*x76 - 30*x77 - 120*x78 - 25*x79 - 60*x80 + objvar =E= 0;

e2..  - x1 + x2 + x61 =G= 0;

e3..  - x1 + x3 + x62 =G= 0;

e4..  - x1 + x4 + x63 =G= 0;

e5..  - x1 + x5 + x64 =G= 0;

e6..  - x2 + x3 + x65 =G= 0;

e7..  - x2 + x4 + x66 =G= 0;

e8..  - x2 + x5 + x67 =G= 0;

e9..  - x3 + x4 + x68 =G= 0;

e10..  - x3 + x5 + x69 =G= 0;

e11..  - x4 + x5 + x70 =G= 0;

e12..    x1 - x2 + x61 =G= 0;

e13..    x1 - x3 + x62 =G= 0;

e14..    x1 - x4 + x63 =G= 0;

e15..    x1 - x5 + x64 =G= 0;

e16..    x2 - x3 + x65 =G= 0;

e17..    x2 - x4 + x66 =G= 0;

e18..    x2 - x5 + x67 =G= 0;

e19..    x3 - x4 + x68 =G= 0;

e20..    x3 - x5 + x69 =G= 0;

e21..    x4 - x5 + x70 =G= 0;

e22..  - x6 + x7 + x71 =G= 0;

e23..  - x6 + x8 + x72 =G= 0;

e24..  - x6 + x9 + x73 =G= 0;

e25..  - x6 + x10 + x74 =G= 0;

e26..  - x7 + x8 + x75 =G= 0;

e27..  - x7 + x9 + x76 =G= 0;

e28..  - x7 + x10 + x77 =G= 0;

e29..  - x8 + x9 + x78 =G= 0;

e30..  - x8 + x10 + x79 =G= 0;

e31..  - x9 + x10 + x80 =G= 0;

e32..    x6 - x7 + x71 =G= 0;

e33..    x6 - x8 + x72 =G= 0;

e34..    x6 - x9 + x73 =G= 0;

e35..    x6 - x10 + x74 =G= 0;

e36..    x7 - x8 + x75 =G= 0;

e37..    x7 - x9 + x76 =G= 0;

e38..    x7 - x10 + x77 =G= 0;

e39..    x8 - x9 + x78 =G= 0;

e40..    x8 - x10 + x79 =G= 0;

e41..    x9 - x10 + x80 =G= 0;

e42..    x1 - x2 + 51*b11 =L= 45;

e43..    x1 - x3 + 51*b12 =L= 47;

e44..    x1 - x4 + 51*b13 =L= 47.5;

e45..    x1 - x5 + 51*b14 =L= 44;

e46..    x2 - x3 + 51*b15 =L= 46;

e47..    x2 - x4 + 51*b16 =L= 46.5;

e48..    x2 - x5 + 51*b17 =L= 43;

e49..    x3 - x4 + 51*b18 =L= 48.5;

e50..    x3 - x5 + 51*b19 =L= 45;

e51..    x4 - x5 + 51*b20 =L= 45.5;

e52..  - x1 + x2 + 51*b21 =L= 45;

e53..  - x1 + x3 + 51*b22 =L= 47;

e54..  - x1 + x4 + 51*b23 =L= 47.5;

e55..  - x1 + x5 + 51*b24 =L= 44;

e56..  - x2 + x3 + 51*b25 =L= 46;

e57..  - x2 + x4 + 51*b26 =L= 46.5;

e58..  - x2 + x5 + 51*b27 =L= 43;

e59..  - x3 + x4 + 51*b28 =L= 48.5;

e60..  - x3 + x5 + 51*b29 =L= 45;

e61..  - x4 + x5 + 51*b30 =L= 45.5;

e62..    x6 - x7 + 86*b31 =L= 80.5;

e63..    x6 - x8 + 86*b32 =L= 81.5;

e64..    x6 - x9 + 86*b33 =L= 81.5;

e65..    x6 - x10 + 86*b34 =L= 79.5;

e66..    x7 - x8 + 86*b35 =L= 82;

e67..    x7 - x9 + 86*b36 =L= 82;

e68..    x7 - x10 + 86*b37 =L= 80;

e69..    x8 - x9 + 86*b38 =L= 83;

e70..    x8 - x10 + 86*b39 =L= 81;

e71..    x9 - x10 + 86*b40 =L= 81;

e72..  - x6 + x7 + 86*b41 =L= 80.5;

e73..  - x6 + x8 + 86*b42 =L= 81.5;

e74..  - x6 + x9 + 86*b43 =L= 81.5;

e75..  - x6 + x10 + 86*b44 =L= 79.5;

e76..  - x7 + x8 + 86*b45 =L= 82;

e77..  - x7 + x9 + 86*b46 =L= 82;

e78..  - x7 + x10 + 86*b47 =L= 80;

e79..  - x8 + x9 + 86*b48 =L= 83;

e80..  - x8 + x10 + 86*b49 =L= 81;

e81..  - x9 + x10 + 86*b50 =L= 81;

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;

e92.. sqr((-17.5) + x1) + sqr((-7) + x6) + 7964*b51 =L= 8000;

e93.. sqr((-18.5) + x2) + sqr((-7.5) + x7) + 7808*b52 =L= 7844;

e94.. sqr((-16.5) + x3) + sqr((-8.5) + x8) + 8128*b53 =L= 8164;

e95.. sqr((-16) + x4) + sqr((-8.5) + x9) + 8213*b54 =L= 8249;

e96.. sqr((-19.5) + x5) + sqr((-6.5) + x10) + 7660*b55 =L= 7696;

e97.. sqr((-52.5) + x1) + sqr((-77) + x6) + 6481*b56 =L= 6581;

e98.. sqr((-53.5) + x2) + sqr((-77.5) + x7) + 6622*b57 =L= 6722;

e99.. sqr((-51.5) + x3) + sqr((-78.5) + x8) + 6951.25*b58 =L= 7051.25;

e100.. sqr((-51) + x4) + sqr((-78.5) + x9) + 6910*b59 =L= 7010;

e101.. sqr((-54.5) + x5) + sqr((-76.5) + x10) + 6342*b60 =L= 6442;

e102.. sqr((-17.5) + x1) + sqr((-13) + x6) + 7040*b51 =L= 7076;

e103.. sqr((-18.5) + x2) + sqr((-12.5) + x7) + 7033*b52 =L= 7069;

e104.. sqr((-16.5) + x3) + sqr((-11.5) + x8) + 7657*b53 =L= 7693;

e105.. sqr((-16) + x4) + sqr((-11.5) + x9) + 7742*b54 =L= 7778;

e106.. sqr((-19.5) + x5) + sqr((-13.5) + x10) + 6589*b55 =L= 6625;

e107.. sqr((-52.5) + x1) + sqr((-83) + x6) + 7357*b56 =L= 7457;

e108.. sqr((-53.5) + x2) + sqr((-82.5) + x7) + 7357*b57 =L= 7457;

e109.. sqr((-51.5) + x3) + sqr((-81.5) + x8) + 7398.25*b58 =L= 7498.25;

e110.. sqr((-51) + x4) + sqr((-81.5) + x9) + 7357*b59 =L= 7457;

e111.. sqr((-54.5) + x5) + sqr((-83.5) + x10) + 7357*b60 =L= 7457;

e112.. sqr((-12.5) + x1) + sqr((-7) + x6) + 8389*b51 =L= 8425;

e113.. sqr((-11.5) + x2) + sqr((-7.5) + x7) + 8389*b52 =L= 8425;

e114.. sqr((-13.5) + x3) + sqr((-8.5) + x8) + 8389*b53 =L= 8425;

e115.. sqr((-14) + x4) + sqr((-8.5) + x9) + 8389*b54 =L= 8425;

e116.. sqr((-10.5) + x5) + sqr((-6.5) + x10) + 8389*b55 =L= 8425;

e117.. sqr((-47.5) + x1) + sqr((-77) + x6) + 6096*b56 =L= 6196;

e118.. sqr((-46.5) + x2) + sqr((-77.5) + x7) + 6097*b57 =L= 6197;

e119.. sqr((-48.5) + x3) + sqr((-78.5) + x8) + 6711.25*b58 =L= 6811.25;

e120.. sqr((-49) + x4) + sqr((-78.5) + x9) + 6750*b59 =L= 6850;

e121.. sqr((-45.5) + x5) + sqr((-76.5) + x10) + 5685*b60 =L= 5785;

e122.. sqr((-12.5) + x1) + sqr((-13) + x6) + 7465*b51 =L= 7501;

e123.. sqr((-11.5) + x2) + sqr((-12.5) + x7) + 7614*b52 =L= 7650;

e124.. sqr((-13.5) + x3) + sqr((-11.5) + x8) + 7918*b53 =L= 7954;

e125.. sqr((-14) + x4) + sqr((-11.5) + x9) + 7918*b54 =L= 7954;

e126.. sqr((-10.5) + x5) + sqr((-13.5) + x10) + 7318*b55 =L= 7354;

e127.. sqr((-47.5) + x1) + sqr((-83) + x6) + 6972*b56 =L= 7072;

e128.. sqr((-46.5) + x2) + sqr((-82.5) + x7) + 6832*b57 =L= 6932;

e129.. sqr((-48.5) + x3) + sqr((-81.5) + x8) + 7158.25*b58 =L= 7258.25;

e130.. sqr((-49) + x4) + sqr((-81.5) + x9) + 7197*b59 =L= 7297;

e131.. sqr((-45.5) + x5) + sqr((-83.5) + x10) + 6700*b60 =L= 6800;

e132..    b51 + b56 =E= 1;

e133..    b52 + b57 =E= 1;

e134..    b53 + b58 =E= 1;

e135..    b54 + b59 =E= 1;

e136..    b55 + b60 =E= 1;

* set non-default bounds
x1.lo = 11.5; x1.up = 57.5;
x2.lo = 12.5; x2.up = 56.5;
x3.lo = 10.5; x3.up = 58.5;
x4.lo = 10; x4.up = 59;
x5.lo = 13.5; x5.up = 55.5;
x6.lo = 7; x6.up = 87;
x7.lo = 6.5; x7.up = 87.5;
x8.lo = 5.5; x8.up = 88.5;
x9.lo = 5.5; x9.up = 88.5;
x10.lo = 7.5; x10.up = 86.5;

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: 2018-05-28 Git hash: ac4a64c1
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