MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

Home // Instances // Documentation // Download // Statistics


Instance wastepaper5

Layout-Optimization of Screening Systems in Recovered Paper Production- 5 Screens
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
0.00089880 p1 ( gdx sol )
(infeas: 4e-16)
0.00087880 p2 ( gdx sol )
(infeas: 4e-16)
0.00082120 p3 ( gdx sol )
(infeas: 2e-16)
Other points (infeas > 1e-08)  
Dual Bounds
0.00005278 (ANTIGONE)
0.00000000 (BARON)
0.00000000 (COUENNE)
0.00000000 (LINDO)
0.00000000 (SCIP)
0.00000000 (SHOT)
References Fügenschuh, Armin, Hayn, Christine, and Michaels, Dennis, Mixed-integer linear methods for layout-optimization of screening systems in recovered paper production, Optimization and Engineering, 15, 2014, 533-573.
Application Waste paper treatment
Added to library 03 Jun 2015
Problem type MBNLP
#Variables 104
#Binary Variables 65
#Integer Variables 0
#Nonlinear Variables 95
#Nonlinear Binary Variables 60
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 46
#Linear Constraints 22
#Quadratic Constraints 14
#Polynomial Constraints 0
#Signomial Constraints 10
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 390
#Nonlinear Nonzeros in Jacobian 260
#Nonzeros in (Upper-Left) Hessian of Lagrangian 265
#Nonzeros in Diagonal of Hessian of Lagrangian 5
#Blocks in Hessian of Lagrangian 15
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 8
Average blocksize in Hessian of Lagrangian 6.333333
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 6.0000e-02
Maximal coefficient 1.0000e+00
Infeasibility of initial point 1
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
*         47       46        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        105       40       65        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        392      132      260        0
*
*  Solve m using MINLP minimizing objvar;


Variables  objvar,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,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,b99,b100,b101,b102
          ,b103,b104,b105;

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;

Binary Variables  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,b99,b100,b101,b102,b103,b104
          ,b105;

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;


e1..    objvar - x25 =E= 0;

e2..    x7 =L= 0.0675;

e3..    x9 - x10 + x11 =E= 0;

e4..    x12 - x13 + x14 =E= 0;

e5..    x15 - x16 + x17 =E= 0;

e6..    x18 - x19 + x20 =E= 0;

e7..    x21 - x22 + x23 =E= 0;

e8..    x26 - x27 + x28 =E= 0;

e9..    x29 - x30 + x31 =E= 0;

e10..    x32 - x33 + x34 =E= 0;

e11..    x35 - x36 + x37 =E= 0;

e12..    x38 - x39 + x40 =E= 0;

e13.. x2**0.29*x10 - x11 =E= 0;

e14.. x3**0.13*x13 - x14 =E= 0;

e15.. x4**0.06*x16 - x17 =E= 0;

e16.. x5**0.15*x19 - x20 =E= 0;

e17.. x6**0.2*x22 - x23 =E= 0;

e18.. x2**0.74*x27 - x28 =E= 0;

e19.. x3**0.79*x30 - x31 =E= 0;

e20.. x4**0.71*x33 - x34 =E= 0;

e21.. x5**0.8*x36 - x37 =E= 0;

e22.. x6**0.7*x39 - x40 =E= 0;

e23.. b41*x9 + b46*x11 + b51*x12 + b56*x14 + b61*x15 + b66*x17 + b71*x18 + b76*
      x20 + b81*x21 + b86*x23 - x10 + 0.675*b91 =E= 0;

e24.. b42*x9 + b47*x11 + b52*x12 + b57*x14 + b62*x15 + b67*x17 + b72*x18 + b77*
      x20 + b82*x21 + b87*x23 - x13 + 0.675*b92 =E= 0;

e25.. b43*x9 + b48*x11 + b53*x12 + b58*x14 + b63*x15 + b68*x17 + b73*x18 + b78*
      x20 + b83*x21 + b88*x23 - x16 + 0.675*b93 =E= 0;

e26.. b44*x9 + b49*x11 + b54*x12 + b59*x14 + b64*x15 + b69*x17 + b74*x18 + b79*
      x20 + b84*x21 + b89*x23 - x19 + 0.675*b94 =E= 0;

e27.. b45*x9 + b50*x11 + b55*x12 + b60*x14 + b65*x15 + b70*x17 + b75*x18 + b80*
      x20 + b85*x21 + b90*x23 - x22 + 0.675*b95 =E= 0;

e28.. b41*x26 + b46*x28 + b51*x29 + b56*x31 + b61*x32 + b66*x34 + b71*x35 + b76
      *x37 + b81*x38 + b86*x40 - x27 + 0.649*b91 =E= 0;

e29.. b42*x26 + b47*x28 + b52*x29 + b57*x31 + b62*x32 + b67*x34 + b72*x35 + b77
      *x37 + b82*x38 + b87*x40 - x30 + 0.649*b92 =E= 0;

e30.. b43*x26 + b48*x28 + b53*x29 + b58*x31 + b63*x32 + b68*x34 + b73*x35 + b78
      *x37 + b83*x38 + b88*x40 - x33 + 0.649*b93 =E= 0;

e31.. b44*x26 + b49*x28 + b54*x29 + b59*x31 + b64*x32 + b69*x34 + b74*x35 + b79
      *x37 + b84*x38 + b89*x40 - x36 + 0.649*b94 =E= 0;

e32.. b45*x26 + b50*x28 + b55*x29 + b60*x31 + b65*x32 + b70*x34 + b75*x35 + b80
      *x37 + b85*x38 + b90*x40 - x39 + 0.649*b95 =E= 0;

e33.. b96*x9 + b97*x12 + b98*x15 + b99*x18 + b100*x21 - x7 =E= 0;

e34.. b96*x26 + b97*x29 + b98*x32 + b99*x35 + b100*x38 - x24 =E= 0;

e35.. b101*x11 + b102*x14 + b103*x17 + b104*x20 + b105*x23 - x8 =E= 0;

e36.. b101*x28 + b102*x31 + b103*x34 + b104*x37 + b105*x40 - x25 =E= 0;

e37..    b41 + b42 + b43 + b44 + b45 + b96 =E= 1;

e38..    b51 + b52 + b53 + b54 + b55 + b97 =E= 1;

e39..    b61 + b62 + b63 + b64 + b65 + b98 =E= 1;

e40..    b71 + b72 + b73 + b74 + b75 + b99 =E= 1;

e41..    b81 + b82 + b83 + b84 + b85 + b100 =E= 1;

e42..    b46 + b47 + b48 + b49 + b50 + b101 =E= 1;

e43..    b56 + b57 + b58 + b59 + b60 + b102 =E= 1;

e44..    b66 + b67 + b68 + b69 + b70 + b103 =E= 1;

e45..    b76 + b77 + b78 + b79 + b80 + b104 =E= 1;

e46..    b86 + b87 + b88 + b89 + b90 + b105 =E= 1;

e47..    b91 + b92 + b93 + b94 + b95 =E= 1;

* set non-default bounds
x2.lo = 0.1; x2.up = 0.9;
x3.lo = 0.1; x3.up = 0.9;
x4.lo = 0.1; x4.up = 0.9;
x5.lo = 0.1; x5.up = 0.9;
x6.lo = 0.1; x6.up = 0.9;
x7.up = 10;
x8.up = 10;
x9.up = 10;
x10.up = 10;
x11.up = 10;
x12.up = 10;
x13.up = 10;
x14.up = 10;
x15.up = 10;
x16.up = 10;
x17.up = 10;
x18.up = 10;
x19.up = 10;
x20.up = 10;
x21.up = 10;
x22.up = 10;
x23.up = 10;
x24.up = 10;
x25.up = 10;
x26.up = 10;
x27.up = 10;
x28.up = 10;
x29.up = 10;
x30.up = 10;
x31.up = 10;
x32.up = 10;
x33.up = 10;
x34.up = 10;
x35.up = 10;
x36.up = 10;
x37.up = 10;
x38.up = 10;
x39.up = 10;
x40.up = 10;

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
Imprint / Privacy Policy / License: CC-BY 4.0