MOPLIB (short for Multi-Objective Problem LIBrary) is a problem library for multi-objective linear, multi-objective (mixed) integer and vector linear programs. The name MOPLIB intentionally resembles and was inspired by the (single-objective) mixed integer problem library MIPLIB. The goal behind MOPLIB is to offer problem instances for available multi-objective solvers modelling a wide variety of applications as well as to support an input format for multi-objective problems. The long-term goal is to make it into a standard test set to be able to compare the performance of different available solvers.

MOPLIB was coined and is currently maintained by Andreas Löhne and Sebastian Schenker. If you develop a solver for multi-criteria optimization or vector optimization or if you use available solvers and you would like to contribute to MOPLIB, please do not hesitate to contact us.

15/Dec/2015 | Website launched. |

11/Mar/2016 | First instances (.mop files) added. |

01/04/2016 | New instances added. |

02/06/2016 | New (molp) instances added (contributed by László Csirmaz) |

Currently two file formats (.mop and .vlp) are supported by MOPLIB.

The .mop (short for Multi-Objective Problem) input format is based on the MPS file format. For more information see the MOP description.

The .vlp input format is an extension of the GLPK LP/MIP format. For more information see the VLP description.

MOPLIB distinguishes the following problem classes:

Problem class | Abbreaviation | Description |
---|---|---|

Multi-objective linear program | molp | Several linear objectives; feasible region is a convex polytope/polyhedron; |

Multi-objective binary program | mobp | Several linear objectives; feasible region is a convex polytope/polyhedron; all variables are restricted to be binary; |

Multi-objective integer program | moip | Several linear objectives; feasible region is a convex polytope/polyhedron; all variables are restricted to be integer; |

Multi-objective mixed integer program | momip | Several linear objectives; feasible region is a convex polytope/polyhedron; some but not all of the variables are restricted to be integer; |

Vector linear program | vlp | Minimization (or maximization) is defined w.r.t. partial ordering induced by a polyhedral cone; it generalizes multi-objective linear programs; |

Bensolve is a vector and multi-objective linear programming solver supporting the .vlp input format and solving instances of the problem classes: molp, vlp

Inner is a multi-objective linear programming solver supporting the .vlp input format and solving instances of the problem class: molp

PolySCIP is a multi-objective integer and linear programming solver supporting the .mop input format and solving instances of the problem classes: molp, mobp, moip (,momip experimentally)

All test instances come without any warranty. You are free to use, copy and change them for your research/work. We would kindly ask you to acknowledge the MOPLIB in your publication if you use some of the test instances.

The following notation will be used:

identifier | standing for |
---|---|

class | problem class the instance belongs to |

objs | number of objectives of the instance |

vars | number of variables of the instance |

cons | number of constraints of the instance |

description (optional) | string describing the instance |

.mop | file format is MOP |

.vlp | file format is VLP |

The naming of an instance comprises of the above identifiers in the following way:

class_objs_vars_cons_description**.**mop|vlp

The following instances come without any guarantee. They can be downloaded and used for free. If you use them for your research, we would appreciate a reference to MOPLIB in your publication.

molp_3_100_20_assignment.mop
molp_3_100_20_assignment.vlp
molp_4_900_60_assignment.mop
molp_4_900_60_assignment.vlp
molp_10_900_60_assignment.mop
molp_10_900_60_assignment.vlp
molp_10_779_10174_entropy.mop
molp_10_779_10174_entropy.vlp
molp_19_376_1917_entropy.mop
molp_19_376_1917_entropy.vlp
molp_21_31_138_entropy.mop
molp_21_31_138_entropy.vlp
molp_22_43_213_entropy.mop
molp_22_43_213_entropy.vlp
molp_23_28_218_entropy.mop
molp_23_28_218_entropy.vlp
molp_27_28_218_entropy.mop
molp_27_28_218_entropy.vlp
vlp_3_1143_1211_befi.mop
vlp_3_1143_1211_befi.vlp
vlp_2_3799_6161_befi.mop
vlp_2_3799_6161_befi.vlp
molp_4_729_729_bensolvehedron.mop
molp_4_729_729_bensolvehedron.vlp
molp_4_4492_1003_dc.mop
molp_4_4492_1003_dc.vlp
molp_12_21_30_dc.mop
molp_12_21_30_dc.vlp
molp_7_150_80_mpp.mop
molp_7_150_80_mpp.vlp
molp_9_100_60_mpp.mop
molp_9_100_60_mpp.vlp
molp_10_150_80_mpp.mop
molp_10_150_80_mpp.vlp

mobp_3_100_20_assignment.mop
mobp_4_900_60_assignment.mop
mobp_10_900_60_assignment.mop
mobp_2_30_1_knapsack.mop
mobp_3_100_1_knapsack.mop