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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: tln4

Formats ams gms lp mod nl osil pip
Primal Bounds (infeas ≤ 1e-08)
8.30000000 p1 ( gdx sol )
(infeas: 0)
Other points (infeas > 1e-08)  
Dual Bounds
8.30000000 (ANTIGONE)
8.30000000 (BARON)
8.30000000 (COUENNE)
8.30000000 (LINDO)
8.30000000 (SCIP)
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 trimlon4.dat
Application Trim loss minimization problem
Added to library 01 May 2001
Problem type MIQCP
#Variables 24
#Binary Variables 4
#Integer Variables 20
#Nonlinear Variables 20
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 20
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 8
#Nonlinear Nonzeros in Objective 0
#Constraints 24
#Linear Constraints 20
#Quadratic Constraints 4
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 96
#Nonlinear Nonzeros in Jacobian 32
#Nonzeros in (Upper-Left) Hessian of Lagrangian 32
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 4
Minimal blocksize in Hessian of Lagrangian 5
Maximal blocksize in Hessian of Lagrangian 5
Average blocksize in Hessian of Lagrangian 5.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 210
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        1        0       24        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         25        1        4       20        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        105       73       32        0
*
*  Solve m using MINLP minimizing objvar;


Variables  b1,b2,b3,b4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19
          ,i20,i21,i22,i23,i24,objvar;

Binary Variables  b1,b2,b3,b4;

Integer Variables  i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19,i20
          ,i21,i22,i23,i24;

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 - 0.3*b3 - 0.4*b4 - i5 - i6 - i7 - i8 + objvar =E= 0;

e2..    330*i9 + 360*i13 + 385*i17 + 415*i21 =L= 1900;

e3..    330*i10 + 360*i14 + 385*i18 + 415*i22 =L= 1900;

e4..    330*i11 + 360*i15 + 385*i19 + 415*i23 =L= 1900;

e5..    330*i12 + 360*i16 + 385*i20 + 415*i24 =L= 1900;

e6..  - 330*i9 - 360*i13 - 385*i17 - 415*i21 =L= -1700;

e7..  - 330*i10 - 360*i14 - 385*i18 - 415*i22 =L= -1700;

e8..  - 330*i11 - 360*i15 - 385*i19 - 415*i23 =L= -1700;

e9..  - 330*i12 - 360*i16 - 385*i20 - 415*i24 =L= -1700;

e10..    i9 + i13 + i17 + i21 =L= 5;

e11..    i10 + i14 + i18 + i22 =L= 5;

e12..    i11 + i15 + i19 + i23 =L= 5;

e13..    i12 + i16 + i20 + i24 =L= 5;

e14..    b1 - i5 =L= 0;

e15..    b2 - i6 =L= 0;

e16..    b3 - i7 =L= 0;

e17..    b4 - i8 =L= 0;

e18..  - 12*b1 + i5 =L= 0;

e19..  - 12*b2 + i6 =L= 0;

e20..  - 12*b3 + i7 =L= 0;

e21..  - 12*b4 + i8 =L= 0;

e22.. -(i5*i9 + i6*i10 + i7*i11 + i8*i12) =L= -8;

e23.. -(i5*i13 + i6*i14 + i7*i15 + i8*i16) =L= -7;

e24.. -(i5*i17 + i6*i18 + i7*i19 + i8*i20) =L= -12;

e25.. -(i5*i21 + i6*i22 + i7*i23 + i8*i24) =L= -11;

* set non-default bounds
i5.up = 12;
i6.up = 12;
i7.up = 12;
i8.up = 12;
i9.up = 5;
i10.up = 5;
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;

* set non-default levels
i5.l = 1;
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;

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: 2019-07-12 Git hash: 46a7b4f1
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