MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance tls2

Formats ams gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
5.30000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
5.30000000 (ALPHAECP)
5.30000000 (ANTIGONE)
5.30000000 (BARON)
5.30000000 (BONMIN)
5.30000000 (COUENNE)
5.30000000 (LINDO)
5.30000000 (SCIP)
5.30000000 (SHOT)
References Harjunkoski, Iiro, Westerlund, Tapio, Pörn, Ray, and Skrifvars, Hans, Different Transformations for Solving Non-Convex Trim Loss Problems by MINLP, European Journal of Operational Research, 105:3, 1998, 594-603.
Source MacMINLP model trimlon.mod with trimloss2.dat
Application Trim loss minimization problem
Added to library 01 May 2001
Problem type MINLP
#Variables 37
#Binary Variables 31
#Integer Variables 2
#Nonlinear Variables 6
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 2
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 17
#Nonlinear Nonzeros in Objective 0
#Constraints 24
#Linear Constraints 22
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 2
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature convex
#Nonzeros in Jacobian 192
#Nonlinear Nonzeros in Jacobian 8
#Nonzeros in (Upper-Left) Hessian of Lagrangian 14
#Nonzeros in Diagonal of Hessian of Lagrangian 6
#Blocks in Hessian of Lagrangian 2
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
Minimal coefficient 1.0000e-01
Maximal coefficient 1.8400e+03
Infeasibility of initial point 1700
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
*         25        7        0       18        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         38        5       31        2        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        210      202        8        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,i3,i4,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,objvar;

Binary Variables  b1,b2,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;

Integer Variables  i3,i4;

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;


e1..  - 0.1*b1 - 0.2*b2 - b9 - 2*b10 - 3*b11 - 4*b12 - 5*b13 - 6*b14 - 7*b15
      - 8*b16 - b17 - 2*b18 - 3*b19 - 4*b20 - 5*b21 - 6*b22 - 7*b23 + objvar
      =E= 0;

e2..    460*b24 + 920*b25 + 1380*b26 + 1840*b27 + 570*b32 + 1140*b33 + 1710*b34
      =L= 1900;

e3..    460*b28 + 920*b29 + 1380*b30 + 1840*b31 + 570*b35 + 1140*b36 + 1710*b37
      =L= 1900;

e4..  - 460*b24 - 920*b25 - 1380*b26 - 1840*b27 - 570*b32 - 1140*b33 - 1710*b34
      =L= -1700;

e5..  - 460*b28 - 920*b29 - 1380*b30 - 1840*b31 - 570*b35 - 1140*b36 - 1710*b37
      =L= -1700;

e6..    b24 + 2*b25 + 3*b26 + 4*b27 + b32 + 2*b33 + 3*b34 =L= 5;

e7..    b28 + 2*b29 + 3*b30 + 4*b31 + b35 + 2*b36 + 3*b37 =L= 5;

e8..    b1 - b9 - 2*b10 - 3*b11 - 4*b12 - 5*b13 - 6*b14 - 7*b15 - 8*b16 =L= 0;

e9..    b2 - b17 - 2*b18 - 3*b19 - 4*b20 - 5*b21 - 6*b22 - 7*b23 =L= 0;

e10..  - 8*b1 + b9 + 2*b10 + 3*b11 + 4*b12 + 5*b13 + 6*b14 + 7*b15 + 8*b16
       =L= 0;

e11..  - 7*b2 + b17 + 2*b18 + 3*b19 + 4*b20 + 5*b21 + 6*b22 + 7*b23 =L= 0;

e12..    i3 - 3*b9 - 8*b10 - 15*b11 - 24*b12 - 35*b13 - 48*b14 - 63*b15
       - 80*b16 =E= 1;

e13..    i4 - 3*b17 - 8*b18 - 15*b19 - 24*b20 - 35*b21 - 48*b22 - 63*b23 =E= 1;

e14..    b9 + b10 + b11 + b12 + b13 + b14 + b15 + b16 =L= 1;

e15..    b17 + b18 + b19 + b20 + b21 + b22 + b23 =L= 1;

e16..    x5 - 3*b24 - 8*b25 - 15*b26 - 24*b27 =E= 1;

e17..    x6 - 3*b28 - 8*b29 - 15*b30 - 24*b31 =E= 1;

e18..    x7 - 3*b32 - 8*b33 - 15*b34 =E= 1;

e19..    x8 - 3*b35 - 8*b36 - 15*b37 =E= 1;

e20..    b24 + b25 + b26 + b27 =L= 1;

e21..    b28 + b29 + b30 + b31 =L= 1;

e22..    b32 + b33 + b34 =L= 1;

e23..    b35 + b36 + b37 =L= 1;

e24.. -(sqrt(i3*x5) + sqrt(i4*x6)) + b9 + 2*b10 + 3*b11 + 4*b12 + 5*b13 + 6*b14
       + 7*b15 + 8*b16 + b17 + 2*b18 + 3*b19 + 4*b20 + 5*b21 + 6*b22 + 7*b23
       + b24 + 2*b25 + 3*b26 + 4*b27 + b28 + 2*b29 + 3*b30 + 4*b31 =L= -10;

e25.. -(sqrt(i3*x7) + sqrt(i4*x8)) + b9 + 2*b10 + 3*b11 + 4*b12 + 5*b13 + 6*b14
       + 7*b15 + 8*b16 + b17 + 2*b18 + 3*b19 + 4*b20 + 5*b21 + 6*b22 + 7*b23
       + b32 + 2*b33 + 3*b34 + b35 + 2*b36 + 3*b37 =L= -9;

* set non-default bounds
i3.lo = 1; i3.up = 100;
i4.lo = 1; i4.up = 100;
x5.lo = 1;
x6.lo = 1;
x7.lo = 1;
x8.lo = 1;

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