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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance wastepaper3

Layout-Optimization of Screening Systems in Recovered Paper Production - 3 Screens

Formatsⓘ	ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)ⓘ	0.01891837 p1 ( gdx sol ) (infeas: 8e-14)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	0.01891806 (ANTIGONE) 0.01891824 (BARON) 0.01891837 (LINDO) 0.01891830 (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ⓘ	52
#Binary Variablesⓘ	27
#Integer Variablesⓘ	0
#Nonlinear Variablesⓘ	45
#Nonlinear Binary Variablesⓘ	24
#Nonlinear Integer Variablesⓘ	0
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	1
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	30
#Linear Constraintsⓘ	14
#Quadratic Constraintsⓘ	10
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	6
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	176
#Nonlinear Nonzeros in Jacobianⓘ	108
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	111
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	3
#Blocks in Hessian of Lagrangianⓘ	9
Minimal blocksize in Hessian of Lagrangianⓘ	3
Maximal blocksize in Hessian of Lagrangianⓘ	6
Average blocksize in Hessian of Lagrangianⓘ	5.0
#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 Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         31       30        0        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         53       26       27        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        178       70      108        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,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;

Positive Variables  x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20
          ,x21,x22,x23,x24,x25,x26;

Binary Variables  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;

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;


e1..    objvar - x17 =E= 0;

e2..    x5 =L= 0.0675;

e3..    x7 - x8 + x9 =E= 0;

e4..    x10 - x11 + x12 =E= 0;

e5..    x13 - x14 + x15 =E= 0;

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

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

e8..    x24 - x25 + x26 =E= 0;

e9.. x2**0.29*x8 - x9 =E= 0;

e10.. x3**0.13*x11 - x12 =E= 0;

e11.. x4**0.06*x14 - x15 =E= 0;

e12.. x2**0.74*x19 - x20 =E= 0;

e13.. x3**0.79*x22 - x23 =E= 0;

e14.. x4**0.71*x25 - x26 =E= 0;

e15.. b27*x7 + b30*x9 + b33*x10 + b36*x12 + b39*x13 + b42*x15 - x8 + 0.675*b45
       =E= 0;

e16.. b28*x7 + b31*x9 + b34*x10 + b37*x12 + b40*x13 + b43*x15 - x11 + 0.675*b46
       =E= 0;

e17.. b29*x7 + b32*x9 + b35*x10 + b38*x12 + b41*x13 + b44*x15 - x14 + 0.675*b47
       =E= 0;

e18.. b27*x18 + b30*x20 + b33*x21 + b36*x23 + b39*x24 + b42*x26 - x19
       + 0.649*b45 =E= 0;

e19.. b28*x18 + b31*x20 + b34*x21 + b37*x23 + b40*x24 + b43*x26 - x22
       + 0.649*b46 =E= 0;

e20.. b29*x18 + b32*x20 + b35*x21 + b38*x23 + b41*x24 + b44*x26 - x25
       + 0.649*b47 =E= 0;

e21.. b48*x7 + b49*x10 + b50*x13 - x5 =E= 0;

e22.. b48*x18 + b49*x21 + b50*x24 - x16 =E= 0;

e23.. b51*x9 + b52*x12 + b53*x15 - x6 =E= 0;

e24.. b51*x20 + b52*x23 + b53*x26 - x17 =E= 0;

e25..    b27 + b28 + b29 + b48 =E= 1;

e26..    b33 + b34 + b35 + b49 =E= 1;

e27..    b39 + b40 + b41 + b50 =E= 1;

e28..    b30 + b31 + b32 + b51 =E= 1;

e29..    b36 + b37 + b38 + b52 =E= 1;

e30..    b42 + b43 + b44 + b53 =E= 1;

e31..    b45 + b46 + b47 =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.up = 10;
x6.up = 10;
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;

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;