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Instance: clay0304m

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
40262.38753000 p1 ( gdx sol )
(infeas: 6e-11)
Dual Bounds
40262.36800000 (ALPHAECP)
40262.38700000 (ANTIGONE)
40262.38749000 (BARON)
40262.38700000 (BONMIN)
40262.38724000 (COUENNE)
0.00002694 (LINDO)
40262.38740000 (SCIP)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Source CLay0304M.gms from CMU-IBM MINLP solver project page
Application Layout
Added to library 28 Sep 2013
Problem type MBQCP
#Variables 56
#Binary Variables 36
#Integer Variables 0
#Nonlinear Variables 8
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 12
#Nonlinear Nonzeros in Objective 0
#Constraints 106
#Linear Constraints 58
#Quadratic Constraints 48
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 324
#Nonlinear Nonzeros in Jacobian 96
#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
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
*        107       11       24       72        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         57       21       36        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        337      241       96        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,b9,b10,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,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,objvar;

Positive Variables  x45,x46,x47,x48,x49,x50,x51,x52,x53,x54,x55,x56;

Binary Variables  b9,b10,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;

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;


e1..  - 300*x45 - 240*x46 - 210*x47 - 100*x48 - 150*x49 - 120*x50 - 300*x51
      - 240*x52 - 210*x53 - 100*x54 - 150*x55 - 120*x56 + objvar =E= 0;

e2..  - x1 + x2 + x45 =G= 0;

e3..  - x1 + x3 + x46 =G= 0;

e4..  - x1 + x4 + x47 =G= 0;

e5..  - x2 + x3 + x48 =G= 0;

e6..  - x2 + x4 + x49 =G= 0;

e7..  - x3 + x4 + x50 =G= 0;

e8..    x1 - x2 + x45 =G= 0;

e9..    x1 - x3 + x46 =G= 0;

e10..    x1 - x4 + x47 =G= 0;

e11..    x2 - x3 + x48 =G= 0;

e12..    x2 - x4 + x49 =G= 0;

e13..    x3 - x4 + x50 =G= 0;

e14..  - x5 + x6 + x51 =G= 0;

e15..  - x5 + x7 + x52 =G= 0;

e16..  - x5 + x8 + x53 =G= 0;

e17..  - x6 + x7 + x54 =G= 0;

e18..  - x6 + x8 + x55 =G= 0;

e19..  - x7 + x8 + x56 =G= 0;

e20..    x5 - x6 + x51 =G= 0;

e21..    x5 - x7 + x52 =G= 0;

e22..    x5 - x8 + x53 =G= 0;

e23..    x6 - x7 + x54 =G= 0;

e24..    x6 - x8 + x55 =G= 0;

e25..    x7 - x8 + x56 =G= 0;

e26..    x1 - x2 + 46*b9 =L= 40;

e27..    x1 - x3 + 46*b10 =L= 42;

e28..    x1 - x4 + 46*b11 =L= 42.5;

e29..    x2 - x3 + 46*b12 =L= 41;

e30..    x2 - x4 + 46*b13 =L= 41.5;

e31..    x3 - x4 + 46*b14 =L= 43.5;

e32..  - x1 + x2 + 46*b15 =L= 40;

e33..  - x1 + x3 + 46*b16 =L= 42;

e34..  - x1 + x4 + 46*b17 =L= 42.5;

e35..  - x2 + x3 + 46*b18 =L= 41;

e36..  - x2 + x4 + 46*b19 =L= 41.5;

e37..  - x3 + x4 + 46*b20 =L= 43.5;

e38..    x5 - x6 + 81*b21 =L= 75.5;

e39..    x5 - x7 + 81*b22 =L= 76.5;

e40..    x5 - x8 + 81*b23 =L= 76.5;

e41..    x6 - x7 + 81*b24 =L= 77;

e42..    x6 - x8 + 81*b25 =L= 77;

e43..    x7 - x8 + 81*b26 =L= 78;

e44..  - x5 + x6 + 81*b27 =L= 75.5;

e45..  - x5 + x7 + 81*b28 =L= 76.5;

e46..  - x5 + x8 + 81*b29 =L= 76.5;

e47..  - x6 + x7 + 81*b30 =L= 77;

e48..  - x6 + x8 + 81*b31 =L= 77;

e49..  - x7 + x8 + 81*b32 =L= 78;

e50..    b9 + b15 + b21 + b27 =E= 1;

e51..    b10 + b16 + b22 + b28 =E= 1;

e52..    b11 + b17 + b23 + b29 =E= 1;

e53..    b12 + b18 + b24 + b30 =E= 1;

e54..    b13 + b19 + b25 + b31 =E= 1;

e55..    b14 + b20 + b26 + b32 =E= 1;

e56.. sqr((-17.5) + x1) + sqr((-7) + x5) + 6814*b33 =L= 6850;

e57.. sqr((-18.5) + x2) + sqr((-7.5) + x6) + 6678*b34 =L= 6714;

e58.. sqr((-16.5) + x3) + sqr((-8.5) + x7) + 6958*b35 =L= 6994;

e59.. sqr((-16) + x4) + sqr((-8.5) + x8) + 7033*b36 =L= 7069;

e60.. sqr((-52.5) + x1) + sqr((-77) + x5) + 6556*b37 =L= 6581;

e61.. sqr((-53.5) + x2) + sqr((-77.5) + x6) + 6697*b38 =L= 6722;

e62.. sqr((-51.5) + x3) + sqr((-78.5) + x7) + 6985*b39 =L= 7010;

e63.. sqr((-51) + x4) + sqr((-78.5) + x8) + 6985*b40 =L= 7010;

e64.. sqr((-32.5) + x1) + sqr((-47) + x5) + 2025*b41 =L= 2041;

e65.. sqr((-33.5) + x2) + sqr((-47.5) + x6) + 2106*b42 =L= 2122;

e66.. sqr((-31.5) + x3) + sqr((-48.5) + x7) + 2317*b43 =L= 2333;

e67.. sqr((-31) + x4) + sqr((-48.5) + x8) + 2362*b44 =L= 2378;

e68.. sqr((-17.5) + x1) + sqr((-13) + x5) + 5950*b33 =L= 5986;

e69.. sqr((-18.5) + x2) + sqr((-12.5) + x6) + 5953*b34 =L= 5989;

e70.. sqr((-16.5) + x3) + sqr((-11.5) + x7) + 6517*b35 =L= 6553;

e71.. sqr((-16) + x4) + sqr((-11.5) + x8) + 6592*b36 =L= 6628;

e72.. sqr((-52.5) + x1) + sqr((-83) + x5) + 7432*b37 =L= 7457;

e73.. sqr((-53.5) + x2) + sqr((-82.5) + x6) + 7432*b38 =L= 7457;

e74.. sqr((-51.5) + x3) + sqr((-81.5) + x7) + 7432*b39 =L= 7457;

e75.. sqr((-51) + x4) + sqr((-81.5) + x8) + 7432*b40 =L= 7457;

e76.. sqr((-32.5) + x1) + sqr((-53) + x5) + 2541*b41 =L= 2557;

e77.. sqr((-33.5) + x2) + sqr((-52.5) + x6) + 2541*b42 =L= 2557;

e78.. sqr((-31.5) + x3) + sqr((-51.5) + x7) + 2584*b43 =L= 2600;

e79.. sqr((-31) + x4) + sqr((-51.5) + x8) + 2629*b44 =L= 2645;

e80.. sqr((-12.5) + x1) + sqr((-7) + x5) + 7189*b33 =L= 7225;

e81.. sqr((-11.5) + x2) + sqr((-7.5) + x6) + 7189*b34 =L= 7225;

e82.. sqr((-13.5) + x3) + sqr((-8.5) + x7) + 7189*b35 =L= 7225;

e83.. sqr((-14) + x4) + sqr((-8.5) + x8) + 7189*b36 =L= 7225;

e84.. sqr((-47.5) + x1) + sqr((-77) + x5) + 6171*b37 =L= 6196;

e85.. sqr((-46.5) + x2) + sqr((-77.5) + x6) + 6172*b38 =L= 6197;

e86.. sqr((-48.5) + x3) + sqr((-78.5) + x7) + 6748*b39 =L= 6773;

e87.. sqr((-49) + x4) + sqr((-78.5) + x8) + 6825*b40 =L= 6850;

e88.. sqr((-27.5) + x1) + sqr((-47) + x5) + 2209*b41 =L= 2225;

e89.. sqr((-26.5) + x2) + sqr((-47.5) + x6) + 2290*b42 =L= 2306;

e90.. sqr((-28.5) + x3) + sqr((-48.5) + x7) + 2458*b43 =L= 2474;

e91.. sqr((-29) + x4) + sqr((-48.5) + x8) + 2458*b44 =L= 2474;

e92.. sqr((-12.5) + x1) + sqr((-13) + x5) + 6325*b33 =L= 6361;

e93.. sqr((-11.5) + x2) + sqr((-12.5) + x6) + 6464*b34 =L= 6500;

e94.. sqr((-13.5) + x3) + sqr((-11.5) + x7) + 6748*b35 =L= 6784;

e95.. sqr((-14) + x4) + sqr((-11.5) + x8) + 6748*b36 =L= 6784;

e96.. sqr((-47.5) + x1) + sqr((-83) + x5) + 7047*b37 =L= 7072;

e97.. sqr((-46.5) + x2) + sqr((-82.5) + x6) + 6907*b38 =L= 6932;

e98.. sqr((-48.5) + x3) + sqr((-81.5) + x7) + 7195*b39 =L= 7220;

e99.. sqr((-49) + x4) + sqr((-81.5) + x8) + 7272*b40 =L= 7297;

e100.. sqr((-27.5) + x1) + sqr((-53) + x5) + 2725*b41 =L= 2741;

e101.. sqr((-26.5) + x2) + sqr((-52.5) + x6) + 2725*b42 =L= 2741;

e102.. sqr((-28.5) + x3) + sqr((-51.5) + x7) + 2725*b43 =L= 2741;

e103.. sqr((-29) + x4) + sqr((-51.5) + x8) + 2725*b44 =L= 2741;

e104..    b33 + b37 + b41 =E= 1;

e105..    b34 + b38 + b42 =E= 1;

e106..    b35 + b39 + b43 =E= 1;

e107..    b36 + b40 + b44 =E= 1;

* set non-default bounds
x1.lo = 11.5; x1.up = 52.5;
x2.lo = 12.5; x2.up = 51.5;
x3.lo = 10.5; x3.up = 53.5;
x4.lo = 10; x4.up = 54;
x5.lo = 7; x5.up = 82;
x6.lo = 6.5; x6.up = 82.5;
x7.lo = 5.5; x7.up = 83.5;
x8.lo = 5.5; x8.up = 83.5;

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: 2018-09-14 Git hash: ac5a5314
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