MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance wastepaper6

Layout-Optimization of Screening Systems in Recovered Paper Production - 6 Screens
Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
0.00027084 p1 ( gdx sol )
(infeas: 2e-16)
0.00014556 p2 ( gdx sol )
(infeas: 2e-16)
0.00012637 p3 ( gdx sol )
(infeas: 2e-13)
Other points (infeas > 1e-08)  
Dual Bounds
0.00000000 (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 136
#Binary Variables 90
#Integer Variables 0
#Nonlinear Variables 126
#Nonlinear Binary Variables 84
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 54
#Linear Constraints 26
#Quadratic Constraints 16
#Polynomial Constraints 0
#Signomial Constraints 12
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 527
#Nonlinear Nonzeros in Jacobian 360
#Nonzeros in (Upper-Left) Hessian of Lagrangian 366
#Nonzeros in Diagonal of Hessian of Lagrangian 6
#Blocks in Hessian of Lagrangian 18
Minimal blocksize in Hessian of Lagrangian 3
Maximal blocksize in Hessian of Lagrangian 9
Average blocksize in Hessian of Lagrangian 7.0
#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
*         55       54        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        137       47       90        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        529      169      360        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,x41,x42,x43,x44,x45,x46,x47,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,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115
          ,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128
          ,b129,b130,b131,b132,b133,b134,b135,b136,b137;

Positive Variables  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;

Binary Variables  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,b106,b107,b108,b109,b110
          ,b111,b112,b113,b114,b115,b116,b117,b118,b119,b120,b121,b122,b123
          ,b124,b125,b126,b127,b128,b129,b130,b131,b132,b133,b134,b135,b136
          ,b137;

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;


e1..    objvar - x29 =E= 0;

e2..    x8 =L= 0.0675;

e3..    x10 - x11 + x12 =E= 0;

e4..    x13 - x14 + x15 =E= 0;

e5..    x16 - x17 + x18 =E= 0;

e6..    x19 - x20 + x21 =E= 0;

e7..    x22 - x23 + x24 =E= 0;

e8..    x25 - x26 + x27 =E= 0;

e9..    x30 - x31 + x32 =E= 0;

e10..    x33 - x34 + x35 =E= 0;

e11..    x36 - x37 + x38 =E= 0;

e12..    x39 - x40 + x41 =E= 0;

e13..    x42 - x43 + x44 =E= 0;

e14..    x45 - x46 + x47 =E= 0;

e15.. x2**0.29*x11 - x12 =E= 0;

e16.. x3**0.13*x14 - x15 =E= 0;

e17.. x4**0.06*x17 - x18 =E= 0;

e18.. x5**0.15*x20 - x21 =E= 0;

e19.. x6**0.2*x23 - x24 =E= 0;

e20.. x7**0.17*x26 - x27 =E= 0;

e21.. x2**0.74*x31 - x32 =E= 0;

e22.. x3**0.79*x34 - x35 =E= 0;

e23.. x4**0.71*x37 - x38 =E= 0;

e24.. x5**0.8*x40 - x41 =E= 0;

e25.. x6**0.7*x43 - x44 =E= 0;

e26.. x7**0.85*x46 - x47 =E= 0;

e27.. b48*x10 + b54*x12 + b60*x13 + b66*x15 + b72*x16 + b78*x18 + b84*x19 + b90
      *x21 + b96*x22 + b102*x24 + b108*x25 + b114*x27 - x11 + 0.675*b120 =E= 0;

e28.. b49*x10 + b55*x12 + b61*x13 + b67*x15 + b73*x16 + b79*x18 + b85*x19 + b91
      *x21 + b97*x22 + b103*x24 + b109*x25 + b115*x27 - x14 + 0.675*b121 =E= 0;

e29.. b50*x10 + b56*x12 + b62*x13 + b68*x15 + b74*x16 + b80*x18 + b86*x19 + b92
      *x21 + b98*x22 + b104*x24 + b110*x25 + b116*x27 - x17 + 0.675*b122 =E= 0;

e30.. b51*x10 + b57*x12 + b63*x13 + b69*x15 + b75*x16 + b81*x18 + b87*x19 + b93
      *x21 + b99*x22 + b105*x24 + b111*x25 + b117*x27 - x20 + 0.675*b123 =E= 0;

e31.. b52*x10 + b58*x12 + b64*x13 + b70*x15 + b76*x16 + b82*x18 + b88*x19 + b94
      *x21 + b100*x22 + b106*x24 + b112*x25 + b118*x27 - x23 + 0.675*b124 =E= 0
      ;

e32.. b53*x10 + b59*x12 + b65*x13 + b71*x15 + b77*x16 + b83*x18 + b89*x19 + b95
      *x21 + b101*x22 + b107*x24 + b113*x25 + b119*x27 - x26 + 0.675*b125 =E= 0
      ;

e33.. b48*x30 + b54*x32 + b60*x33 + b66*x35 + b72*x36 + b78*x38 + b84*x39 + b90
      *x41 + b96*x42 + b102*x44 + b108*x45 + b114*x47 - x31 + 0.649*b120 =E= 0;

e34.. b49*x30 + b55*x32 + b61*x33 + b67*x35 + b73*x36 + b79*x38 + b85*x39 + b91
      *x41 + b97*x42 + b103*x44 + b109*x45 + b115*x47 - x34 + 0.649*b121 =E= 0;

e35.. b50*x30 + b56*x32 + b62*x33 + b68*x35 + b74*x36 + b80*x38 + b86*x39 + b92
      *x41 + b98*x42 + b104*x44 + b110*x45 + b116*x47 - x37 + 0.649*b122 =E= 0;

e36.. b51*x30 + b57*x32 + b63*x33 + b69*x35 + b75*x36 + b81*x38 + b87*x39 + b93
      *x41 + b99*x42 + b105*x44 + b111*x45 + b117*x47 - x40 + 0.649*b123 =E= 0;

e37.. b52*x30 + b58*x32 + b64*x33 + b70*x35 + b76*x36 + b82*x38 + b88*x39 + b94
      *x41 + b100*x42 + b106*x44 + b112*x45 + b118*x47 - x43 + 0.649*b124 =E= 0
      ;

e38.. b53*x30 + b59*x32 + b65*x33 + b71*x35 + b77*x36 + b83*x38 + b89*x39 + b95
      *x41 + b101*x42 + b107*x44 + b113*x45 + b119*x47 - x46 + 0.649*b125 =E= 0
      ;

e39.. b126*x10 + b127*x13 + b128*x16 + b129*x19 + b130*x22 + b131*x25 - x8
       =E= 0;

e40.. b126*x30 + b127*x33 + b128*x36 + b129*x39 + b130*x42 + b131*x45 - x28
       =E= 0;

e41.. b132*x12 + b133*x15 + b134*x18 + b135*x21 + b136*x24 + b137*x27 - x9
       =E= 0;

e42.. b132*x32 + b133*x35 + b134*x38 + b135*x41 + b136*x44 + b137*x47 - x29
       =E= 0;

e43..    b48 + b49 + b50 + b51 + b52 + b53 + b126 =E= 1;

e44..    b60 + b61 + b62 + b63 + b64 + b65 + b127 =E= 1;

e45..    b72 + b73 + b74 + b75 + b76 + b77 + b128 =E= 1;

e46..    b84 + b85 + b86 + b87 + b88 + b89 + b129 =E= 1;

e47..    b96 + b97 + b98 + b99 + b100 + b101 + b130 =E= 1;

e48..    b108 + b109 + b110 + b111 + b112 + b113 + b131 =E= 1;

e49..    b54 + b55 + b56 + b57 + b58 + b59 + b132 =E= 1;

e50..    b66 + b67 + b68 + b69 + b70 + b71 + b133 =E= 1;

e51..    b78 + b79 + b80 + b81 + b82 + b83 + b134 =E= 1;

e52..    b90 + b91 + b92 + b93 + b94 + b95 + b135 =E= 1;

e53..    b102 + b103 + b104 + b105 + b106 + b107 + b136 =E= 1;

e54..    b114 + b115 + b116 + b117 + b118 + b119 + b137 =E= 1;

e55..    b120 + b121 + b122 + b123 + b124 + b125 =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.lo = 0.1; x7.up = 0.9;
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;
x41.up = 10;
x42.up = 10;
x43.up = 10;
x44.up = 10;
x45.up = 10;
x46.up = 10;
x47.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
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