MINLPLib
A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance tls4
| Formatsⓘ | ams gms mod nl osil py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 8.30000000 (ALPHAECP) 8.30000000 (ANTIGONE) 8.30000000 (BARON) 5.21403140 (BONMIN) 3.55376071 (COUENNE) 8.30000000 (LINDO) 8.30000000 (SCIP) 8.30000000 (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 with trimloss4.dat |
| Applicationⓘ | Trim loss minimization problem |
| Added to libraryⓘ | 01 May 2001 |
| Problem typeⓘ | MINLP |
| #Variablesⓘ | 105 |
| #Binary Variablesⓘ | 85 |
| #Integer Variablesⓘ | 4 |
| #Nonlinear Variablesⓘ | 20 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 4 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 25 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 64 |
| #Linear Constraintsⓘ | 60 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 4 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | convex |
| #Nonzeros in Jacobianⓘ | 588 |
| #Nonlinear Nonzeros in Jacobianⓘ | 32 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 52 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 20 |
| #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 |
| Minimal coefficientⓘ | 1.0000e-01 |
| Maximal coefficientⓘ | 1.8000e+03 |
| Infeasibility of initial pointⓘ | 1700 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 65 21 0 44 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 106 17 85 4 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 614 582 32 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,i5,i6,i7,i8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
,x20,x21,x22,x23,x24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,objvar;
Binary Variables b1,b2,b3,b4,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105;
Integer Variables i5,i6,i7,i8;
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,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65;
e1.. - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - b25 - 2*b26 - 3*b27 - 4*b28 - 5*b29
- 6*b30 - 7*b31 - 8*b32 - b33 - 2*b34 - 3*b35 - 4*b36 - 5*b37 - 6*b38
- 7*b39 - b40 - 2*b41 - 3*b42 - 4*b43 - b44 - 2*b45 + objvar =E= 0;
e2.. 330*b46 + 660*b47 + 990*b48 + 1320*b49 + 360*b62 + 720*b63 + 1080*b64
+ 1440*b65 + 1800*b66 + 385*b82 + 770*b83 + 1155*b84 + 1540*b85 + 415*b98
+ 830*b99 =L= 1900;
e3.. 330*b50 + 660*b51 + 990*b52 + 1320*b53 + 360*b67 + 720*b68 + 1080*b69
+ 1440*b70 + 1800*b71 + 385*b86 + 770*b87 + 1155*b88 + 1540*b89
+ 415*b100 + 830*b101 =L= 1900;
e4.. 330*b54 + 660*b55 + 990*b56 + 1320*b57 + 360*b72 + 720*b73 + 1080*b74
+ 1440*b75 + 1800*b76 + 385*b90 + 770*b91 + 1155*b92 + 1540*b93
+ 415*b102 + 830*b103 =L= 1900;
e5.. 330*b58 + 660*b59 + 990*b60 + 1320*b61 + 360*b77 + 720*b78 + 1080*b79
+ 1440*b80 + 1800*b81 + 385*b94 + 770*b95 + 1155*b96 + 1540*b97
+ 415*b104 + 830*b105 =L= 1900;
e6.. - 330*b46 - 660*b47 - 990*b48 - 1320*b49 - 360*b62 - 720*b63 - 1080*b64
- 1440*b65 - 1800*b66 - 385*b82 - 770*b83 - 1155*b84 - 1540*b85 - 415*b98
- 830*b99 =L= -1700;
e7.. - 330*b50 - 660*b51 - 990*b52 - 1320*b53 - 360*b67 - 720*b68 - 1080*b69
- 1440*b70 - 1800*b71 - 385*b86 - 770*b87 - 1155*b88 - 1540*b89
- 415*b100 - 830*b101 =L= -1700;
e8.. - 330*b54 - 660*b55 - 990*b56 - 1320*b57 - 360*b72 - 720*b73 - 1080*b74
- 1440*b75 - 1800*b76 - 385*b90 - 770*b91 - 1155*b92 - 1540*b93
- 415*b102 - 830*b103 =L= -1700;
e9.. - 330*b58 - 660*b59 - 990*b60 - 1320*b61 - 360*b77 - 720*b78 - 1080*b79
- 1440*b80 - 1800*b81 - 385*b94 - 770*b95 - 1155*b96 - 1540*b97
- 415*b104 - 830*b105 =L= -1700;
e10.. b46 + 2*b47 + 3*b48 + 4*b49 + b62 + 2*b63 + 3*b64 + 4*b65 + 5*b66
+ b82 + 2*b83 + 3*b84 + 4*b85 + b98 + 2*b99 =L= 5;
e11.. b50 + 2*b51 + 3*b52 + 4*b53 + b67 + 2*b68 + 3*b69 + 4*b70 + 5*b71
+ b86 + 2*b87 + 3*b88 + 4*b89 + b100 + 2*b101 =L= 5;
e12.. b54 + 2*b55 + 3*b56 + 4*b57 + b72 + 2*b73 + 3*b74 + 4*b75 + 5*b76
+ b90 + 2*b91 + 3*b92 + 4*b93 + b102 + 2*b103 =L= 5;
e13.. b58 + 2*b59 + 3*b60 + 4*b61 + b77 + 2*b78 + 3*b79 + 4*b80 + 5*b81
+ b94 + 2*b95 + 3*b96 + 4*b97 + b104 + 2*b105 =L= 5;
e14.. b1 - b25 - 2*b26 - 3*b27 - 4*b28 - 5*b29 - 6*b30 - 7*b31 - 8*b32 =L= 0
;
e15.. b2 - b33 - 2*b34 - 3*b35 - 4*b36 - 5*b37 - 6*b38 - 7*b39 =L= 0;
e16.. b3 - b40 - 2*b41 - 3*b42 - 4*b43 =L= 0;
e17.. b4 - b44 - 2*b45 =L= 0;
e18.. - 8*b1 + b25 + 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32
=L= 0;
e19.. - 7*b2 + b33 + 2*b34 + 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 =L= 0;
e20.. - 4*b3 + b40 + 2*b41 + 3*b42 + 4*b43 =L= 0;
e21.. - 2*b4 + b44 + 2*b45 =L= 0;
e22.. i5 - 3*b25 - 8*b26 - 15*b27 - 24*b28 - 35*b29 - 48*b30 - 63*b31
- 80*b32 =E= 1;
e23.. i6 - 3*b33 - 8*b34 - 15*b35 - 24*b36 - 35*b37 - 48*b38 - 63*b39 =E= 1;
e24.. i7 - 3*b40 - 8*b41 - 15*b42 - 24*b43 =E= 1;
e25.. i8 - 3*b44 - 8*b45 =E= 1;
e26.. b25 + b26 + b27 + b28 + b29 + b30 + b31 + b32 =L= 1;
e27.. b33 + b34 + b35 + b36 + b37 + b38 + b39 =L= 1;
e28.. b40 + b41 + b42 + b43 =L= 1;
e29.. b44 + b45 =L= 1;
e30.. x9 - 3*b46 - 8*b47 - 15*b48 - 24*b49 =E= 1;
e31.. x10 - 3*b50 - 8*b51 - 15*b52 - 24*b53 =E= 1;
e32.. x11 - 3*b54 - 8*b55 - 15*b56 - 24*b57 =E= 1;
e33.. x12 - 3*b58 - 8*b59 - 15*b60 - 24*b61 =E= 1;
e34.. x13 - 3*b62 - 8*b63 - 15*b64 - 24*b65 - 35*b66 =E= 1;
e35.. x14 - 3*b67 - 8*b68 - 15*b69 - 24*b70 - 35*b71 =E= 1;
e36.. x15 - 3*b72 - 8*b73 - 15*b74 - 24*b75 - 35*b76 =E= 1;
e37.. x16 - 3*b77 - 8*b78 - 15*b79 - 24*b80 - 35*b81 =E= 1;
e38.. x17 - 3*b82 - 8*b83 - 15*b84 - 24*b85 =E= 1;
e39.. x18 - 3*b86 - 8*b87 - 15*b88 - 24*b89 =E= 1;
e40.. x19 - 3*b90 - 8*b91 - 15*b92 - 24*b93 =E= 1;
e41.. x20 - 3*b94 - 8*b95 - 15*b96 - 24*b97 =E= 1;
e42.. x21 - 3*b98 - 8*b99 =E= 1;
e43.. x22 - 3*b100 - 8*b101 =E= 1;
e44.. x23 - 3*b102 - 8*b103 =E= 1;
e45.. x24 - 3*b104 - 8*b105 =E= 1;
e46.. b46 + b47 + b48 + b49 =L= 1;
e47.. b50 + b51 + b52 + b53 =L= 1;
e48.. b54 + b55 + b56 + b57 =L= 1;
e49.. b58 + b59 + b60 + b61 =L= 1;
e50.. b62 + b63 + b64 + b65 + b66 =L= 1;
e51.. b67 + b68 + b69 + b70 + b71 =L= 1;
e52.. b72 + b73 + b74 + b75 + b76 =L= 1;
e53.. b77 + b78 + b79 + b80 + b81 =L= 1;
e54.. b82 + b83 + b84 + b85 =L= 1;
e55.. b86 + b87 + b88 + b89 =L= 1;
e56.. b90 + b91 + b92 + b93 =L= 1;
e57.. b94 + b95 + b96 + b97 =L= 1;
e58.. b98 + b99 =L= 1;
e59.. b100 + b101 =L= 1;
e60.. b102 + b103 =L= 1;
e61.. b104 + b105 =L= 1;
e62.. -(sqrt(i5*x9) + sqrt(i6*x10) + sqrt(i7*x11) + sqrt(i8*x12)) + b25 + 2*b26
+ 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34 + 3*b35
+ 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43 + b44
+ 2*b45 + b46 + 2*b47 + 3*b48 + 4*b49 + b50 + 2*b51 + 3*b52 + 4*b53
+ b54 + 2*b55 + 3*b56 + 4*b57 + b58 + 2*b59 + 3*b60 + 4*b61 =L= -12;
e63.. -(sqrt(i5*x13) + sqrt(i6*x14) + sqrt(i7*x15) + sqrt(i8*x16)) + b25
+ 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34
+ 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43
+ b44 + 2*b45 + b62 + 2*b63 + 3*b64 + 4*b65 + 5*b66 + b67 + 2*b68
+ 3*b69 + 4*b70 + 5*b71 + b72 + 2*b73 + 3*b74 + 4*b75 + 5*b76 + b77
+ 2*b78 + 3*b79 + 4*b80 + 5*b81 =L= -11;
e64.. -(sqrt(i5*x17) + sqrt(i6*x18) + sqrt(i7*x19) + sqrt(i8*x20)) + b25
+ 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34
+ 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43
+ b44 + 2*b45 + b82 + 2*b83 + 3*b84 + 4*b85 + b86 + 2*b87 + 3*b88
+ 4*b89 + b90 + 2*b91 + 3*b92 + 4*b93 + b94 + 2*b95 + 3*b96 + 4*b97
=L= -16;
e65.. -(sqrt(i5*x21) + sqrt(i6*x22) + sqrt(i7*x23) + sqrt(i8*x24)) + b25
+ 2*b26 + 3*b27 + 4*b28 + 5*b29 + 6*b30 + 7*b31 + 8*b32 + b33 + 2*b34
+ 3*b35 + 4*b36 + 5*b37 + 6*b38 + 7*b39 + b40 + 2*b41 + 3*b42 + 4*b43
+ b44 + 2*b45 + b98 + 2*b99 + b100 + 2*b101 + b102 + 2*b103 + b104
+ 2*b105 =L= -15;
* set non-default bounds
i5.lo = 1; i5.up = 100;
i6.lo = 1; i6.up = 100;
i7.lo = 1; i7.up = 100;
i8.lo = 1; i8.up = 100;
x9.lo = 1;
x10.lo = 1;
x11.lo = 1;
x12.lo = 1;
x13.lo = 1;
x14.lo = 1;
x15.lo = 1;
x16.lo = 1;
x17.lo = 1;
x18.lo = 1;
x19.lo = 1;
x20.lo = 1;
x21.lo = 1;
x22.lo = 1;
x23.lo = 1;
x24.lo = 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: 2024-08-26 Git hash: 6cc1607f