MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance tln6
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 15.30000000 (ANTIGONE) 15.30000000 (BARON) 8.71203786 (COUENNE) 15.30000000 (GUROBI) 15.30000000 (LINDO) 15.30000000 (SCIP) 4.05000000 (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 trimlon6.dat |
| 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ⓘ | 36 |
| #Linear Constraintsⓘ | 30 |
| #Quadratic Constraintsⓘ | 6 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 204 |
| #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ⓘ | 5.3000e+02 |
| Infeasibility of initial pointⓘ | 320 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 37 1 0 36 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
* 217 145 72 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,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
,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,objvar;
Binary Variables b1,b2,b3,b4,b5,b6;
Integer Variables 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,i37,i38
,i39,i40,i41,i42,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;
e1.. - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - 0.5*b5 - 0.6*b6 - i7 - i8 - i9
- i10 - i11 - i12 + objvar =E= 0;
e2.. 330*i13 + 360*i19 + 380*i25 + 430*i31 + 490*i37 + 530*i43 =L= 2200;
e3.. 330*i14 + 360*i20 + 380*i26 + 430*i32 + 490*i38 + 530*i44 =L= 2200;
e4.. 330*i15 + 360*i21 + 380*i27 + 430*i33 + 490*i39 + 530*i45 =L= 2200;
e5.. 330*i16 + 360*i22 + 380*i28 + 430*i34 + 490*i40 + 530*i46 =L= 2200;
e6.. 330*i17 + 360*i23 + 380*i29 + 430*i35 + 490*i41 + 530*i47 =L= 2200;
e7.. 330*i18 + 360*i24 + 380*i30 + 430*i36 + 490*i42 + 530*i48 =L= 2200;
e8.. - 330*i13 - 360*i19 - 380*i25 - 430*i31 - 490*i37 - 530*i43 =L= -2100;
e9.. - 330*i14 - 360*i20 - 380*i26 - 430*i32 - 490*i38 - 530*i44 =L= -2100;
e10.. - 330*i15 - 360*i21 - 380*i27 - 430*i33 - 490*i39 - 530*i45 =L= -2100;
e11.. - 330*i16 - 360*i22 - 380*i28 - 430*i34 - 490*i40 - 530*i46 =L= -2100;
e12.. - 330*i17 - 360*i23 - 380*i29 - 430*i35 - 490*i41 - 530*i47 =L= -2100;
e13.. - 330*i18 - 360*i24 - 380*i30 - 430*i36 - 490*i42 - 530*i48 =L= -2100;
e14.. i13 + i19 + i25 + i31 + i37 + i43 =L= 5;
e15.. i14 + i20 + i26 + i32 + i38 + i44 =L= 5;
e16.. i15 + i21 + i27 + i33 + i39 + i45 =L= 5;
e17.. i16 + i22 + i28 + i34 + i40 + i46 =L= 5;
e18.. i17 + i23 + i29 + i35 + i41 + i47 =L= 5;
e19.. i18 + i24 + i30 + i36 + i42 + i48 =L= 5;
e20.. b1 - i7 =L= 0;
e21.. b2 - i8 =L= 0;
e22.. b3 - i9 =L= 0;
e23.. b4 - i10 =L= 0;
e24.. b5 - i11 =L= 0;
e25.. b6 - i12 =L= 0;
e26.. - 16*b1 + i7 =L= 0;
e27.. - 16*b2 + i8 =L= 0;
e28.. - 16*b3 + i9 =L= 0;
e29.. - 16*b4 + i10 =L= 0;
e30.. - 16*b5 + i11 =L= 0;
e31.. - 16*b6 + i12 =L= 0;
e32.. -(i7*i13 + i8*i14 + i9*i15 + i10*i16 + i11*i17 + i12*i18) =L= -8;
e33.. -(i7*i19 + i8*i20 + i9*i21 + i10*i22 + i11*i23 + i12*i24) =L= -16;
e34.. -(i7*i25 + i8*i26 + i9*i27 + i10*i28 + i11*i29 + i12*i30) =L= -12;
e35.. -(i7*i31 + i8*i32 + i9*i33 + i10*i34 + i11*i35 + i12*i36) =L= -7;
e36.. -(i7*i37 + i8*i38 + i9*i39 + i10*i40 + i11*i41 + i12*i42) =L= -14;
e37.. -(i7*i43 + i8*i44 + i9*i45 + i10*i46 + i11*i47 + i12*i48) =L= -16;
* set non-default bounds
i7.up = 16;
i8.up = 16;
i9.up = 16;
i10.up = 16;
i11.up = 16;
i12.up = 16;
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;
i37.up = 5;
i38.up = 5;
i39.up = 5;
i40.up = 5;
i41.up = 5;
i42.up = 5;
i43.up = 5;
i44.up = 5;
i45.up = 5;
i46.up = 5;
i47.up = 5;
i48.up = 5;
* set non-default levels
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;
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;
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