FSU

MOPLIB

ZIB

About

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.

Maintainers

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.

News

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)

File Formats

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.

Problem Classes

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;

Available Solvers

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)

Instances

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

Download

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.

Multi-objective linear programming instances

Multi-objective binary programming instances

Multi-objective integer programming instances

Vector linear programming instances