MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: clay0203hfsg

Non overlapping rectangular units must be placed within the confines of certain designated areas such that the cost of connecting these units is minimized.
Equivalent perspective reformulation of clay0203.
Formats ams gms mod nl osil
Primal Bounds (infeas ≤ 1e-08)
41573.26252000 p1 ( gdx sol )
(infeas: 6e-14)
Other points (infeas > 1e-08)  
Dual Bounds
41573.26107000 (ALPHAECP)
9002.69454300 (ANTIGONE)
41569.10561000 (BARON)
41573.26252000 (BONMIN)
41573.26173000 (COUENNE)
41573.26252000 (LINDO)
41573.26248000 (SCIP)
References Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006.
Kevin C. Furman, Nicolas W. Sawaya, Ignacio E. Grossmann, A computationally useful algebraic representation of nonlinear disjunctive convex sets using the perspective function, Tech. Rep., 2019.
Application Layout
Added to library 25 Sep 2019
Problem type MBNLP
#Variables 90
#Binary Variables 18
#Integer Variables 0
#Nonlinear Variables 18
#Nonlinear Binary Variables 6
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 6
#Nonlinear Nonzeros in Objective 0
#Constraints 132
#Linear Constraints 108
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 24
Operands in Gen. Nonlin. Functions mul div sqr
Constraints curvature convex
#Nonzeros in Jacobian 360
#Nonlinear Nonzeros in Jacobian 72
#Nonzeros in (Upper-Left) Hessian of Lagrangian 42
#Nonzeros in Diagonal of Hessian of Lagrangian 18
#Blocks in Hessian of Lagrangian 6
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 3
Average blocksize in Hessian of Lagrangian 3.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 12.5
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
*        133       25       12       96        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         91       73       18        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        367      295       72        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,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,x85,x86,x87
          ,x88,x89,x90,objvar;

Positive Variables  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,x85,x86,x87,x88,x89,x90;

Binary Variables  b67,b68,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81
          ,b82,b83,b84;

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;


e1..  - 300*x85 - 240*x86 - 100*x87 - 300*x88 - 240*x89 - 100*x90 + objvar
      =E= 0;

e2..  - x1 + x2 + x85 =G= 0;

e3..  - x1 + x3 + x86 =G= 0;

e4..  - x2 + x3 + x87 =G= 0;

e5..    x1 - x2 + x85 =G= 0;

e6..    x1 - x3 + x86 =G= 0;

e7..    x2 - x3 + x87 =G= 0;

e8..  - x4 + x5 + x88 =G= 0;

e9..  - x4 + x6 + x89 =G= 0;

e10..  - x5 + x6 + x90 =G= 0;

e11..    x4 - x5 + x88 =G= 0;

e12..    x4 - x6 + x89 =G= 0;

e13..    x5 - x6 + x90 =G= 0;

e14..    x1 - x7 - x9 - x11 - x13 =E= 0;

e15..    x1 - x8 - x10 - x12 - x14 =E= 0;

e16..    x2 - x15 - x17 - x19 - x21 =E= 0;

e17..    x2 - x16 - x18 - x20 - x22 =E= 0;

e18..    x3 - x23 - x25 - x27 - x29 =E= 0;

e19..    x3 - x24 - x26 - x28 - x30 =E= 0;

e20..    x4 - x31 - x33 - x35 - x37 =E= 0;

e21..    x4 - x32 - x34 - x36 - x38 =E= 0;

e22..    x5 - x39 - x41 - x43 - x45 =E= 0;

e23..    x5 - x40 - x42 - x44 - x46 =E= 0;

e24..    x6 - x47 - x49 - x51 - x53 =E= 0;

e25..    x6 - x48 - x50 - x52 - x54 =E= 0;

e26..    x7 - 52.5*b67 =L= 0;

e27..    x8 - 52.5*b68 =L= 0;

e28..    x9 - 52.5*b70 =L= 0;

e29..    x10 - 52.5*b71 =L= 0;

e30..    x11 - 52.5*b73 =L= 0;

e31..    x12 - 52.5*b74 =L= 0;

e32..    x13 - 52.5*b76 =L= 0;

e33..    x14 - 52.5*b77 =L= 0;

e34..    x15 - 52.5*b67 =L= 0;

e35..    x16 - 51.5*b69 =L= 0;

e36..    x17 - 52.5*b70 =L= 0;

e37..    x18 - 51.5*b72 =L= 0;

e38..    x19 - 52.5*b73 =L= 0;

e39..    x20 - 51.5*b75 =L= 0;

e40..    x21 - 52.5*b76 =L= 0;

e41..    x22 - 51.5*b78 =L= 0;

e42..    x23 - 52.5*b68 =L= 0;

e43..    x24 - 51.5*b69 =L= 0;

e44..    x25 - 52.5*b71 =L= 0;

e45..    x26 - 51.5*b72 =L= 0;

e46..    x27 - 52.5*b74 =L= 0;

e47..    x28 - 51.5*b75 =L= 0;

e48..    x29 - 52.5*b77 =L= 0;

e49..    x30 - 51.5*b78 =L= 0;

e50..    x31 - 82*b67 =L= 0;

e51..    x32 - 82*b68 =L= 0;

e52..    x33 - 82*b70 =L= 0;

e53..    x34 - 82*b71 =L= 0;

e54..    x35 - 82*b73 =L= 0;

e55..    x36 - 82*b74 =L= 0;

e56..    x37 - 82*b76 =L= 0;

e57..    x38 - 82*b77 =L= 0;

e58..    x39 - 82*b67 =L= 0;

e59..    x40 - 82.5*b69 =L= 0;

e60..    x41 - 82*b70 =L= 0;

e61..    x42 - 82.5*b72 =L= 0;

e62..    x43 - 82*b73 =L= 0;

e63..    x44 - 82.5*b75 =L= 0;

e64..    x45 - 82*b76 =L= 0;

e65..    x46 - 82.5*b78 =L= 0;

e66..    x47 - 82*b68 =L= 0;

e67..    x48 - 82.5*b69 =L= 0;

e68..    x49 - 82*b71 =L= 0;

e69..    x50 - 82.5*b72 =L= 0;

e70..    x51 - 82*b74 =L= 0;

e71..    x52 - 82.5*b75 =L= 0;

e72..    x53 - 82*b77 =L= 0;

e73..    x54 - 82.5*b78 =L= 0;

e74..    x7 - x15 + 6*b67 =L= 0;

e75..    x8 - x23 + 4*b68 =L= 0;

e76..    x16 - x24 + 5*b69 =L= 0;

e77..  - x9 + x17 + 6*b70 =L= 0;

e78..  - x10 + x25 + 4*b71 =L= 0;

e79..  - x18 + x26 + 5*b72 =L= 0;

e80..    x35 - x43 + 5.5*b73 =L= 0;

e81..    x36 - x51 + 4.5*b74 =L= 0;

e82..    x44 - x52 + 4*b75 =L= 0;

e83..  - x37 + x45 + 5.5*b76 =L= 0;

e84..  - x38 + x53 + 4.5*b77 =L= 0;

e85..  - x46 + x54 + 4*b78 =L= 0;

e86..    b67 + b70 + b73 + b76 =E= 1;

e87..    b68 + b71 + b74 + b77 =E= 1;

e88..    b69 + b72 + b75 + b78 =E= 1;

e89..    x1 - x55 - x58 =E= 0;

e90..    x2 - x56 - x59 =E= 0;

e91..    x3 - x57 - x60 =E= 0;

e92..    x4 - x61 - x64 =E= 0;

e93..    x5 - x62 - x65 =E= 0;

e94..    x6 - x63 - x66 =E= 0;

e95..    x55 - 18.5*b79 =L= 0;

e96..    x56 - 17.5*b80 =L= 0;

e97..    x57 - 19.5*b81 =L= 0;

e98..    x58 - 52.5*b82 =L= 0;

e99..    x59 - 51.5*b83 =L= 0;

e100..    x60 - 53.5*b84 =L= 0;

e101..    x61 - 13*b79 =L= 0;

e102..    x62 - 13.5*b80 =L= 0;

e103..    x63 - 14.5*b81 =L= 0;

e104..    x64 - 82*b82 =L= 0;

e105..    x65 - 82.5*b83 =L= 0;

e106..    x66 - 83.5*b84 =L= 0;

e107.. (sqr(x55/(0.001 + 0.999*b79)) - 35*x55/(0.001 + 0.999*b79) + sqr(x61/(
       0.001 + 0.999*b79)) - 14*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) + 
       306.25*b79 + 49*b79 - 36*b79 =L= 0;

e108.. (sqr(x56/(0.001 + 0.999*b80)) - 37*x56/(0.001 + 0.999*b80) + sqr(x62/(
       0.001 + 0.999*b80)) - 15*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) + 
       342.25*b80 + 56.25*b80 - 36*b80 =L= 0;

e109.. (sqr(x57/(0.001 + 0.999*b81)) - 33*x57/(0.001 + 0.999*b81) + sqr(x63/(
       0.001 + 0.999*b81)) - 17*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) + 
       272.25*b81 + 72.25*b81 - 36*b81 =L= 0;

e110.. (sqr(x58/(0.001 + 0.999*b82)) - 105*x58/(0.001 + 0.999*b82) + sqr(x64/(
       0.001 + 0.999*b82)) - 154*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
        + 2756.25*b82 + 5929*b82 - 25*b82 =L= 0;

e111.. (sqr(x59/(0.001 + 0.999*b83)) - 107*x59/(0.001 + 0.999*b83) + sqr(x65/(
       0.001 + 0.999*b83)) - 155*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
        + 2862.25*b83 + 6006.25*b83 - 25*b83 =L= 0;

e112.. (sqr(x60/(0.001 + 0.999*b84)) - 103*x60/(0.001 + 0.999*b84) + sqr(x66/(
       0.001 + 0.999*b84)) - 157*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
        + 2652.25*b84 + 6162.25*b84 - 25*b84 =L= 0;

e113.. (sqr(x55/(0.001 + 0.999*b79)) - 35*x55/(0.001 + 0.999*b79) + sqr(x61/(
       0.001 + 0.999*b79)) - 26*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) + 
       306.25*b79 + 169*b79 - 36*b79 =L= 0;

e114.. (sqr(x56/(0.001 + 0.999*b80)) - 37*x56/(0.001 + 0.999*b80) + sqr(x62/(
       0.001 + 0.999*b80)) - 25*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) + 
       342.25*b80 + 156.25*b80 - 36*b80 =L= 0;

e115.. (sqr(x57/(0.001 + 0.999*b81)) - 33*x57/(0.001 + 0.999*b81) + sqr(x63/(
       0.001 + 0.999*b81)) - 23*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) + 
       272.25*b81 + 132.25*b81 - 36*b81 =L= 0;

e116.. (sqr(x58/(0.001 + 0.999*b82)) - 105*x58/(0.001 + 0.999*b82) + sqr(x64/(
       0.001 + 0.999*b82)) - 166*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
        + 2756.25*b82 + 6889*b82 - 25*b82 =L= 0;

e117.. (sqr(x59/(0.001 + 0.999*b83)) - 107*x59/(0.001 + 0.999*b83) + sqr(x65/(
       0.001 + 0.999*b83)) - 165*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
        + 2862.25*b83 + 6806.25*b83 - 25*b83 =L= 0;

e118.. (sqr(x60/(0.001 + 0.999*b84)) - 103*x60/(0.001 + 0.999*b84) + sqr(x66/(
       0.001 + 0.999*b84)) - 163*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
        + 2652.25*b84 + 6642.25*b84 - 25*b84 =L= 0;

e119.. (sqr(x55/(0.001 + 0.999*b79)) - 25*x55/(0.001 + 0.999*b79) + sqr(x61/(
       0.001 + 0.999*b79)) - 14*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) + 
       156.25*b79 + 49*b79 - 36*b79 =L= 0;

e120.. (sqr(x56/(0.001 + 0.999*b80)) - 23*x56/(0.001 + 0.999*b80) + sqr(x62/(
       0.001 + 0.999*b80)) - 15*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) + 
       132.25*b80 + 56.25*b80 - 36*b80 =L= 0;

e121.. (sqr(x57/(0.001 + 0.999*b81)) - 27*x57/(0.001 + 0.999*b81) + sqr(x63/(
       0.001 + 0.999*b81)) - 17*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) + 
       182.25*b81 + 72.25*b81 - 36*b81 =L= 0;

e122.. (sqr(x58/(0.001 + 0.999*b82)) - 95*x58/(0.001 + 0.999*b82) + sqr(x64/(
       0.001 + 0.999*b82)) - 154*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
        + 2256.25*b82 + 5929*b82 - 25*b82 =L= 0;

e123.. (sqr(x59/(0.001 + 0.999*b83)) - 93*x59/(0.001 + 0.999*b83) + sqr(x65/(
       0.001 + 0.999*b83)) - 155*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
        + 2162.25*b83 + 6006.25*b83 - 25*b83 =L= 0;

e124.. (sqr(x60/(0.001 + 0.999*b84)) - 97*x60/(0.001 + 0.999*b84) + sqr(x66/(
       0.001 + 0.999*b84)) - 157*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
        + 2352.25*b84 + 6162.25*b84 - 25*b84 =L= 0;

e125.. (sqr(x55/(0.001 + 0.999*b79)) - 25*x55/(0.001 + 0.999*b79) + sqr(x61/(
       0.001 + 0.999*b79)) - 26*x61/(0.001 + 0.999*b79))*(0.001 + 0.999*b79) + 
       156.25*b79 + 169*b79 - 36*b79 =L= 0;

e126.. (sqr(x56/(0.001 + 0.999*b80)) - 23*x56/(0.001 + 0.999*b80) + sqr(x62/(
       0.001 + 0.999*b80)) - 25*x62/(0.001 + 0.999*b80))*(0.001 + 0.999*b80) + 
       132.25*b80 + 156.25*b80 - 36*b80 =L= 0;

e127.. (sqr(x57/(0.001 + 0.999*b81)) - 27*x57/(0.001 + 0.999*b81) + sqr(x63/(
       0.001 + 0.999*b81)) - 23*x63/(0.001 + 0.999*b81))*(0.001 + 0.999*b81) + 
       182.25*b81 + 132.25*b81 - 36*b81 =L= 0;

e128.. (sqr(x58/(0.001 + 0.999*b82)) - 95*x58/(0.001 + 0.999*b82) + sqr(x64/(
       0.001 + 0.999*b82)) - 166*x64/(0.001 + 0.999*b82))*(0.001 + 0.999*b82)
        + 2256.25*b82 + 6889*b82 - 25*b82 =L= 0;

e129.. (sqr(x59/(0.001 + 0.999*b83)) - 93*x59/(0.001 + 0.999*b83) + sqr(x65/(
       0.001 + 0.999*b83)) - 165*x65/(0.001 + 0.999*b83))*(0.001 + 0.999*b83)
        + 2162.25*b83 + 6806.25*b83 - 25*b83 =L= 0;

e130.. (sqr(x60/(0.001 + 0.999*b84)) - 97*x60/(0.001 + 0.999*b84) + sqr(x66/(
       0.001 + 0.999*b84)) - 163*x66/(0.001 + 0.999*b84))*(0.001 + 0.999*b84)
        + 2352.25*b84 + 6642.25*b84 - 25*b84 =L= 0;

e131..    b79 + b82 =E= 1;

e132..    b80 + b83 =E= 1;

e133..    b81 + b84 =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 = 7; x4.up = 82;
x5.lo = 6.5; x5.up = 82.5;
x6.lo = 5.5; x6.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: 2019-11-29 Git hash: 4a97e4ed
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