MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance tln7
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 15.00000000 (ANTIGONE) 14.99999999 (BARON) 5.62061580 (COUENNE) 14.70000000 (GUROBI) 14.26029400 (LINDO) 15.00000000 (SCIP) 0.00000000 (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 trimlon7.dat |
| Applicationⓘ | Trim loss minimization problem |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MIQCP |
| #Variablesⓘ | 63 |
| #Binary Variablesⓘ | 7 |
| #Integer Variablesⓘ | 56 |
| #Nonlinear Variablesⓘ | 56 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 56 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 14 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 42 |
| #Linear Constraintsⓘ | 35 |
| #Quadratic Constraintsⓘ | 7 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 273 |
| #Nonlinear Nonzeros in Jacobianⓘ | 98 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 98 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 7 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 8 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 8 |
| Average blocksize in Hessian of Lagrangianⓘ | 8.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e-01 |
| Maximal coefficientⓘ | 8.5000e+02 |
| Infeasibility of initial pointⓘ | 1605 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 43 1 0 42 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 64 1 7 56 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 288 190 98 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,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
,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53
,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,objvar;
Binary Variables b1,b2,b3,b4,b5,b6,b7;
Integer Variables 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,i37,i38,i39
,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53,i54,i55,i56
,i57,i58,i59,i60,i61,i62,i63;
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;
e1.. - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - 0.5*b5 - 0.6*b6 - 0.7*b7 - i8 - i9
- i10 - i11 - i12 - i13 - i14 + objvar =E= 0;
e2.. 550*i15 + 630*i22 + 685*i29 + 720*i36 + 760*i43 + 810*i50 + 850*i57
=L= 3400;
e3.. 550*i16 + 630*i23 + 685*i30 + 720*i37 + 760*i44 + 810*i51 + 850*i58
=L= 3400;
e4.. 550*i17 + 630*i24 + 685*i31 + 720*i38 + 760*i45 + 810*i52 + 850*i59
=L= 3400;
e5.. 550*i18 + 630*i25 + 685*i32 + 720*i39 + 760*i46 + 810*i53 + 850*i60
=L= 3400;
e6.. 550*i19 + 630*i26 + 685*i33 + 720*i40 + 760*i47 + 810*i54 + 850*i61
=L= 3400;
e7.. 550*i20 + 630*i27 + 685*i34 + 720*i41 + 760*i48 + 810*i55 + 850*i62
=L= 3400;
e8.. 550*i21 + 630*i28 + 685*i35 + 720*i42 + 760*i49 + 810*i56 + 850*i63
=L= 3400;
e9.. - 550*i15 - 630*i22 - 685*i29 - 720*i36 - 760*i43 - 810*i50 - 850*i57
=L= -3200;
e10.. - 550*i16 - 630*i23 - 685*i30 - 720*i37 - 760*i44 - 810*i51 - 850*i58
=L= -3200;
e11.. - 550*i17 - 630*i24 - 685*i31 - 720*i38 - 760*i45 - 810*i52 - 850*i59
=L= -3200;
e12.. - 550*i18 - 630*i25 - 685*i32 - 720*i39 - 760*i46 - 810*i53 - 850*i60
=L= -3200;
e13.. - 550*i19 - 630*i26 - 685*i33 - 720*i40 - 760*i47 - 810*i54 - 850*i61
=L= -3200;
e14.. - 550*i20 - 630*i27 - 685*i34 - 720*i41 - 760*i48 - 810*i55 - 850*i62
=L= -3200;
e15.. - 550*i21 - 630*i28 - 685*i35 - 720*i42 - 760*i49 - 810*i56 - 850*i63
=L= -3200;
e16.. i15 + i22 + i29 + i36 + i43 + i50 + i57 =L= 6;
e17.. i16 + i23 + i30 + i37 + i44 + i51 + i58 =L= 6;
e18.. i17 + i24 + i31 + i38 + i45 + i52 + i59 =L= 6;
e19.. i18 + i25 + i32 + i39 + i46 + i53 + i60 =L= 6;
e20.. i19 + i26 + i33 + i40 + i47 + i54 + i61 =L= 6;
e21.. i20 + i27 + i34 + i41 + i48 + i55 + i62 =L= 6;
e22.. i21 + i28 + i35 + i42 + i49 + i56 + i63 =L= 6;
e23.. b1 - i8 =L= 0;
e24.. b2 - i9 =L= 0;
e25.. b3 - i10 =L= 0;
e26.. b4 - i11 =L= 0;
e27.. b5 - i12 =L= 0;
e28.. b6 - i13 =L= 0;
e29.. b7 - i14 =L= 0;
e30.. - 15*b1 + i8 =L= 0;
e31.. - 15*b2 + i9 =L= 0;
e32.. - 15*b3 + i10 =L= 0;
e33.. - 15*b4 + i11 =L= 0;
e34.. - 15*b5 + i12 =L= 0;
e35.. - 15*b6 + i13 =L= 0;
e36.. - 15*b7 + i14 =L= 0;
e37.. -(i8*i15 + i9*i16 + i10*i17 + i11*i18 + i12*i19 + i13*i20 + i14*i21)
=L= -8;
e38.. -(i8*i22 + i9*i23 + i10*i24 + i11*i25 + i12*i26 + i13*i27 + i14*i28)
=L= -11;
e39.. -(i8*i29 + i9*i30 + i10*i31 + i11*i32 + i12*i33 + i13*i34 + i14*i35)
=L= -15;
e40.. -(i8*i36 + i9*i37 + i10*i38 + i11*i39 + i12*i40 + i13*i41 + i14*i42)
=L= -5;
e41.. -(i8*i43 + i9*i44 + i10*i45 + i11*i46 + i12*i47 + i13*i48 + i14*i49)
=L= -8;
e42.. -(i8*i50 + i9*i51 + i10*i52 + i11*i53 + i12*i54 + i13*i55 + i14*i56)
=L= -12;
e43.. -(i8*i57 + i9*i58 + i10*i59 + i11*i60 + i12*i61 + i13*i62 + i14*i63)
=L= -6;
* set non-default bounds
i8.up = 15;
i9.up = 15;
i10.up = 15;
i11.up = 15;
i12.up = 15;
i13.up = 15;
i14.up = 15;
i15.up = 6;
i16.up = 6;
i17.up = 6;
i18.up = 6;
i19.up = 6;
i20.up = 6;
i21.up = 6;
i22.up = 6;
i23.up = 6;
i24.up = 6;
i25.up = 6;
i26.up = 6;
i27.up = 6;
i28.up = 6;
i29.up = 6;
i30.up = 6;
i31.up = 6;
i32.up = 6;
i33.up = 6;
i34.up = 6;
i35.up = 6;
i36.up = 6;
i37.up = 6;
i38.up = 6;
i39.up = 6;
i40.up = 6;
i41.up = 6;
i42.up = 6;
i43.up = 6;
i44.up = 6;
i45.up = 6;
i46.up = 6;
i47.up = 6;
i48.up = 6;
i49.up = 6;
i50.up = 6;
i51.up = 6;
i52.up = 6;
i53.up = 6;
i54.up = 6;
i55.up = 6;
i56.up = 6;
i57.up = 6;
i58.up = 6;
i59.up = 6;
i60.up = 6;
i61.up = 6;
i62.up = 6;
i63.up = 6;
* set non-default levels
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;
i36.l = 1;
i37.l = 1;
i38.l = 1;
i39.l = 1;
i40.l = 1;
i41.l = 1;
i42.l = 1;
i43.l = 1;
i44.l = 1;
i45.l = 1;
i46.l = 1;
i47.l = 1;
i48.l = 1;
i49.l = 1;
i50.l = 1;
i51.l = 1;
i52.l = 1;
i53.l = 1;
i54.l = 1;
i55.l = 1;
i56.l = 1;
i57.l = 1;
i58.l = 1;
i59.l = 1;
i60.l = 1;
i61.l = 1;
i62.l = 1;
i63.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: 2025-08-07 Git hash: e62cedfc