MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance ex1266a
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| 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ⓘ | Floudas, C A, Pardalos, Panos M, Adjiman, C S, Esposito, W R, Gumus, Zeynep H, Harding, S T, Klepeis, John L, Meyer, Clifford A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, 1999. 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ⓘ | Test Problem ex12.6.6 of Chapter 12 of Floudas e.a. handbook |
| 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ⓘ | 11 |
| #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ⓘ | 2170 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 54 1 7 46 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
* 302 230 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 - 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
=L= 0;
e9.. - 330*i2 - 360*i8 - 380*i14 - 430*i20 - 490*i26 - 530*i32 + 2100*b38
=L= 0;
e10.. - 330*i3 - 360*i9 - 380*i15 - 430*i21 - 490*i27 - 530*i33 + 2100*b39
=L= 0;
e11.. - 330*i4 - 360*i10 - 380*i16 - 430*i22 - 490*i28 - 530*i34 + 2100*b40
=L= 0;
e12.. - 330*i5 - 360*i11 - 380*i17 - 430*i23 - 490*i29 - 530*i35 + 2100*b41
=L= 0;
e13.. - 330*i6 - 360*i12 - 380*i18 - 430*i24 - 490*i30 - 530*i36 + 2100*b42
=L= 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;
* set non-default levels
i1.l = 1;
i7.l = 2;
i14.l = 2;
i20.l = 1;
i26.l = 2;
i31.l = 1;
i43.l = 8;
i44.l = 7;
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: 2024-08-26 Git hash: 6cc1607f