MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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


Instance tln5

Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
10.30000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
10.30000000 (ANTIGONE)
10.30000000 (BARON)
7.36196364 (COUENNE)
10.30000000 (GUROBI)
10.30000000 (LINDO)
10.30000000 (SCIP)
5.04000000 (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 trimlon5.dat
Application Trim loss minimization problem
Added to library 01 May 2001
Problem type MIQCP
#Variables 35
#Binary Variables 5
#Integer Variables 30
#Nonlinear Variables 30
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 30
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 10
#Nonlinear Nonzeros in Objective 0
#Constraints 30
#Linear Constraints 25
#Quadratic Constraints 5
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 145
#Nonlinear Nonzeros in Jacobian 50
#Nonzeros in (Upper-Left) Hessian of Lagrangian 50
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 5
Minimal blocksize in Hessian of Lagrangian 6
Maximal blocksize in Hessian of Lagrangian 6
Average blocksize in Hessian of Lagrangian 6.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e-01
Maximal coefficient 4.3500e+02
Infeasibility of initial point 10
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
*         31        1        0       30        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         36        1        5       30        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        156      106       50        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,b4,b5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
          ,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35
          ,objvar;

Binary Variables  b1,b2,b3,b4,b5;

Integer Variables  i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19,i20,i21
          ,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35;

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..  - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - 0.5*b5 - i6 - i7 - i8 - i9 - i10
      + objvar =E= 0;

e2..    330*i11 + 360*i16 + 370*i21 + 415*i26 + 435*i31 =L= 2000;

e3..    330*i12 + 360*i17 + 370*i22 + 415*i27 + 435*i32 =L= 2000;

e4..    330*i13 + 360*i18 + 370*i23 + 415*i28 + 435*i33 =L= 2000;

e5..    330*i14 + 360*i19 + 370*i24 + 415*i29 + 435*i34 =L= 2000;

e6..    330*i15 + 360*i20 + 370*i25 + 415*i30 + 435*i35 =L= 2000;

e7..  - 330*i11 - 360*i16 - 370*i21 - 415*i26 - 435*i31 =L= -1800;

e8..  - 330*i12 - 360*i17 - 370*i22 - 415*i27 - 435*i32 =L= -1800;

e9..  - 330*i13 - 360*i18 - 370*i23 - 415*i28 - 435*i33 =L= -1800;

e10..  - 330*i14 - 360*i19 - 370*i24 - 415*i29 - 435*i34 =L= -1800;

e11..  - 330*i15 - 360*i20 - 370*i25 - 415*i30 - 435*i35 =L= -1800;

e12..    i11 + i16 + i21 + i26 + i31 =L= 5;

e13..    i12 + i17 + i22 + i27 + i32 =L= 5;

e14..    i13 + i18 + i23 + i28 + i33 =L= 5;

e15..    i14 + i19 + i24 + i29 + i34 =L= 5;

e16..    i15 + i20 + i25 + i30 + i35 =L= 5;

e17..    b1 - i6 =L= 0;

e18..    b2 - i7 =L= 0;

e19..    b3 - i8 =L= 0;

e20..    b4 - i9 =L= 0;

e21..    b5 - i10 =L= 0;

e22..  - 15*b1 + i6 =L= 0;

e23..  - 15*b2 + i7 =L= 0;

e24..  - 15*b3 + i8 =L= 0;

e25..  - 15*b4 + i9 =L= 0;

e26..  - 15*b5 + i10 =L= 0;

e27.. -(i6*i11 + i7*i12 + i8*i13 + i9*i14 + i10*i15) =L= -12;

e28.. -(i6*i16 + i7*i17 + i8*i18 + i9*i19 + i10*i20) =L= -6;

e29.. -(i6*i21 + i7*i22 + i8*i23 + i9*i24 + i10*i25) =L= -15;

e30.. -(i6*i26 + i7*i27 + i8*i28 + i9*i29 + i10*i30) =L= -6;

e31.. -(i6*i31 + i7*i32 + i8*i33 + i9*i34 + i10*i35) =L= -9;

* set non-default bounds
i6.up = 15;
i7.up = 15;
i8.up = 15;
i9.up = 15;
i10.up = 15;
i11.up = 5;
i12.up = 5;
i13.up = 5;
i14.up = 5;
i15.up = 5;
i16.up = 5;
i17.up = 5;
i18.up = 5;
i19.up = 5;
i20.up = 5;
i21.up = 5;
i22.up = 5;
i23.up = 5;
i24.up = 5;
i25.up = 5;
i26.up = 5;
i27.up = 5;
i28.up = 5;
i29.up = 5;
i30.up = 5;
i31.up = 5;
i32.up = 5;
i33.up = 5;
i34.up = 5;
i35.up = 5;

* set non-default levels
i6.l = 1;
i7.l = 1;
i8.l = 1;
i9.l = 1;
i10.l = 1;
i11.l = 1;
i12.l = 1;
i13.l = 1;
i14.l = 1;
i15.l = 1;
i16.l = 1;
i17.l = 1;
i18.l = 1;
i19.l = 1;
i20.l = 1;
i21.l = 1;
i22.l = 1;
i23.l = 1;
i24.l = 1;
i25.l = 1;
i26.l = 1;
i27.l = 1;
i28.l = 1;
i29.l = 1;
i30.l = 1;
i31.l = 1;
i32.l = 1;
i33.l = 1;
i34.l = 1;
i35.l = 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: 2022-04-26 Git hash: de668763
Imprint / Privacy Policy / License: CC-BY 4.0