MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance tloss

Formatsⓘ	ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)ⓘ	16.30000000 p1 ( gdx sol ) (infeas: 0)
Other points (infeas > 1e-08)ⓘ
Dual Boundsⓘ	16.30000000 (ANTIGONE) 16.30000000 (BARON) 16.30000000 (COUENNE) 16.30000000 (GUROBI) 16.30000000 (LINDO) 16.30000000 (SCIP) 16.30000000 (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, GAMS Model Library model trimloss
Applicationⓘ	Trim loss minimization problem
Added to libraryⓘ	01 May 2001
Problem typeⓘ	MIQCP
#Variablesⓘ	48
#Binary Variablesⓘ	6
#Integer Variablesⓘ	42
#Nonlinear Variablesⓘ	42
#Nonlinear Binary Variablesⓘ	0
#Nonlinear Integer Variablesⓘ	42
Objective Senseⓘ	min
Objective typeⓘ	linear
Objective curvatureⓘ	linear
#Nonzeros in Objectiveⓘ	12
#Nonlinear Nonzeros in Objectiveⓘ	0
#Constraintsⓘ	53
#Linear Constraintsⓘ	47
#Quadratic Constraintsⓘ	6
#Polynomial Constraintsⓘ	0
#Signomial Constraintsⓘ	0
#General Nonlinear Constraintsⓘ	0
Operands in Gen. Nonlin. Functionsⓘ
Constraints curvatureⓘ	indefinite
#Nonzeros in Jacobianⓘ	290
#Nonlinear Nonzeros in Jacobianⓘ	72
#Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ	72
#Nonzeros in Diagonal of Hessian of Lagrangianⓘ	0
#Blocks in Hessian of Lagrangianⓘ	6
Minimal blocksize in Hessian of Lagrangianⓘ	7
Maximal blocksize in Hessian of Lagrangianⓘ	7
Average blocksize in Hessian of Lagrangianⓘ	7.0
#Semicontinuitiesⓘ	0
#Nonlinear Semicontinuitiesⓘ	0
#SOS type 1ⓘ	0
#SOS type 2ⓘ	0
Minimal coefficientⓘ	1.0000e-01
Maximal coefficientⓘ	2.2000e+03
Infeasibility of initial pointⓘ	16
Sparsity Jacobianⓘ
Sparsity Hessian of Lagrangianⓘ

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*         54        1       13       40        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*         49        1        6       42        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        303      231       72        0
*
*  Solve m using MINLP minimizing objvar;


Variables  i1,i2,i3,i4,i5,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,i36
          ,b37,b38,b39,b40,b41,b42,i43,i44,i45,i46,i47,i48,objvar;

Binary Variables  b37,b38,b39,b40,b41,b42;

Integer Variables  i1,i2,i3,i4,i5,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,i36,i43,i44,i45,i46,i47,i48;

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;


e1..  - 0.1*b37 - 0.2*b38 - 0.3*b39 - 0.4*b40 - 0.5*b41 - 0.6*b42 - i43 - i44
      - i45 - i46 - i47 - i48 + objvar =E= 0;

e2.. i43*i1 + i44*i2 + i45*i3 + i46*i4 + i47*i5 + i48*i6 =G= 8;

e3.. i43*i7 + i44*i8 + i45*i9 + i46*i10 + i47*i11 + i48*i12 =G= 16;

e4.. i43*i13 + i44*i14 + i45*i15 + i46*i16 + i47*i17 + i48*i18 =G= 12;

e5.. i43*i19 + i44*i20 + i45*i21 + i46*i22 + i47*i23 + i48*i24 =G= 7;

e6.. i43*i25 + i44*i26 + i45*i27 + i46*i28 + i47*i29 + i48*i30 =G= 14;

e7.. i43*i31 + i44*i32 + i45*i33 + i46*i34 + i47*i35 + i48*i36 =G= 16;

e8..    330*i1 + 360*i7 + 380*i13 + 430*i19 + 490*i25 + 530*i31 - 2100*b37
      =G= 0;

e9..    330*i2 + 360*i8 + 380*i14 + 430*i20 + 490*i26 + 530*i32 - 2100*b38
      =G= 0;

e10..    330*i3 + 360*i9 + 380*i15 + 430*i21 + 490*i27 + 530*i33 - 2100*b39
       =G= 0;

e11..    330*i4 + 360*i10 + 380*i16 + 430*i22 + 490*i28 + 530*i34 - 2100*b40
       =G= 0;

e12..    330*i5 + 360*i11 + 380*i17 + 430*i23 + 490*i29 + 530*i35 - 2100*b41
       =G= 0;

e13..    330*i6 + 360*i12 + 380*i18 + 430*i24 + 490*i30 + 530*i36 - 2100*b42
       =G= 0;

e14..    330*i1 + 360*i7 + 380*i13 + 430*i19 + 490*i25 + 530*i31 - 2200*b37
       =L= 0;

e15..    330*i2 + 360*i8 + 380*i14 + 430*i20 + 490*i26 + 530*i32 - 2200*b38
       =L= 0;

e16..    330*i3 + 360*i9 + 380*i15 + 430*i21 + 490*i27 + 530*i33 - 2200*b39
       =L= 0;

e17..    330*i4 + 360*i10 + 380*i16 + 430*i22 + 490*i28 + 530*i34 - 2200*b40
       =L= 0;

e18..    330*i5 + 360*i11 + 380*i17 + 430*i23 + 490*i29 + 530*i35 - 2200*b41
       =L= 0;

e19..    330*i6 + 360*i12 + 380*i18 + 430*i24 + 490*i30 + 530*i36 - 2200*b42
       =L= 0;

e20..  - i1 - i7 - i13 - i19 - i25 - i31 + b37 =L= 0;

e21..  - i2 - i8 - i14 - i20 - i26 - i32 + b38 =L= 0;

e22..  - i3 - i9 - i15 - i21 - i27 - i33 + b39 =L= 0;

e23..  - i4 - i10 - i16 - i22 - i28 - i34 + b40 =L= 0;

e24..  - i5 - i11 - i17 - i23 - i29 - i35 + b41 =L= 0;

e25..  - i6 - i12 - i18 - i24 - i30 - i36 + b42 =L= 0;

e26..    i1 + i7 + i13 + i19 + i25 + i31 - 5*b37 =L= 0;

e27..    i2 + i8 + i14 + i20 + i26 + i32 - 5*b38 =L= 0;

e28..    i3 + i9 + i15 + i21 + i27 + i33 - 5*b39 =L= 0;

e29..    i4 + i10 + i16 + i22 + i28 + i34 - 5*b40 =L= 0;

e30..    i5 + i11 + i17 + i23 + i29 + i35 - 5*b41 =L= 0;

e31..    i6 + i12 + i18 + i24 + i30 + i36 - 5*b42 =L= 0;

e32..    b37 - i43 =L= 0;

e33..    b38 - i44 =L= 0;

e34..    b39 - i45 =L= 0;

e35..    b40 - i46 =L= 0;

e36..    b41 - i47 =L= 0;

e37..    b42 - i48 =L= 0;

e38..  - 15*b37 + i43 =L= 0;

e39..  - 12*b38 + i44 =L= 0;

e40..  - 8*b39 + i45 =L= 0;

e41..  - 7*b40 + i46 =L= 0;

e42..  - 4*b41 + i47 =L= 0;

e43..  - 2*b42 + i48 =L= 0;

e44..    i43 + i44 + i45 + i46 + i47 + i48 =G= 16;

e45..  - b37 + b38 =L= 0;

e46..  - b38 + b39 =L= 0;

e47..  - b39 + b40 =L= 0;

e48..  - b40 + b41 =L= 0;

e49..  - b41 + b42 =L= 0;

e50..  - i43 + i44 =L= 0;

e51..  - i44 + i45 =L= 0;

e52..  - i45 + i46 =L= 0;

e53..  - i46 + i47 =L= 0;

e54..  - i47 + i48 =L= 0;

* set non-default bounds
i1.up = 5;
i2.up = 5;
i3.up = 5;
i4.up = 5;
i5.up = 5;
i6.up = 5;
i7.up = 5;
i8.up = 5;
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;
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;
i36.up = 5;
i43.up = 15;
i44.up = 12;
i45.up = 8;
i46.up = 7;
i47.up = 4;
i48.up = 2;

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;