This repository is a response to the needs of researchers from the MCDM society to access multi-objective (MO) optimization instances. The repository contains instances, results, generators etc. for different MO problems and is continuously updated. The repository can be used as a test set for testing new algorithms, validating existing results and for reproducibility. All researchers within MO optimization are welcome to contribute.

The repository consists of a main repository MOrepo at GitHub and a set of sub-repositories, one for each contribution. Sub-repositories are named MOrepo-<name> where name normally is the surname of the first author and year of the study. All repositories are located within the MCDMSociety organization at GitHub.

The main repository contains documentation about how to use and contribute to MOrepo. Moreover, a set of tools are given in the R package MOrepoTools which can be used to retrieve info about test instance groups, results and problem classes.

Maintainers of MOrepo are Lars Relund Nielsen [email protected] and Sune Gadegaard [email protected].

Current maintainers of sub-repositories are Sune Lauth Gadegaard [email protected], Lars Relund [email protected], Thomas Stidsen [email protected], Nathan Adelgren [email protected] and Lars Relund [email protected].

Current contributors to the repository are S.L. Gadegaard, A. Klose, L.R. Nielsen, C.R. Pedersen, K.A. Andersen, D. Tuyttens, J. Teghem, Ph. Fortemps, K. Van Nieuwenhuyze, M.P. Hansen, N. Adelgren, A. Gupte, N. Forget, K. Klamroth, A. Przybylski, list(list(given = “M.”, family = “Lyngesen”, role = NULL, email = NULL, comment = NULL), list(given = “Gadegaard”, family = “S.L.”, role = NULL, email = NULL, comment = NULL), list(given = “L.R.”, family = “Nielsen”, role = NULL, email = NULL, comment = NULL)), list(list(given = “M.”, family = “Lyngesen”, role = NULL, email = NULL, comment = NULL), list(given = c(“L.”, “R.”), family = “Nielsen”, role = NULL, email = NULL, comment = NULL)), list(list(given = “Duleabom”, family = “An”, role = NULL, email = NULL, comment = NULL), list(given = c(“Sophie”, “N.”), family = “Parragh”, role = NULL, email = NULL, comment = NULL), list(given = “Markus”, family = “Sinnl”, role = NULL, email = NULL, comment = NULL), list(given = “Fabien”, family = “Tricoire”, role = NULL, email = NULL, comment = NULL)), list(list(given = “D.”, family = “An”, role = NULL, email = NULL, comment = NULL), list(given = “S.N.”, family = “Parragh”, role = NULL, email = NULL, comment = NULL), list(given = “N.”, family = “Sinnl”, role = NULL, email = NULL, comment = NULL), list(given = “F.”, family = “Tricoire”, role = NULL, email = NULL, comment = NULL)), G. Kirlik and S. Sayın.

Instances can be downloaded in different ways depending on usage:

• If you want a whole sub-repository, download it as a zip file or clone it on GitHub.
• Browse to a single instance and download it using the raw format at GitHub.
• Use the R package MOrepoTools to download instances.

All researchers are welcome to contribute to MOrepo. The repository mainly contains MO test instances and results from various sources. However, also generators, format converters, algorithms etc. related to MO optimization are welcome. Have a look at the contribute file which describes different ways to do it.

MOrepo contains instances for different problem classes. The contributions listed after class are:

MOrepo contains instances for problem classes Facility Location, Assignment, Traveling Salesman, MILP, Knapsack, Production Planning, Minkowski Sum - Subset, Minkowski Sum and ILP. A detailed description of the contributions are:

Source: Gadegaard, S., A. Klose, and L. Nielsen (2016). “A bi-objective approach to discrete cost-bottleneck location problems”. In: Annals of Operations Research, pp. 1-23. DOI: 10.1007/s10479-016-2360-8.

Test problem classes: Facility Location
Subfolders: CFLP_UFLP and SSCFLP
Formats: raw

Source: Pedersen, C., L. Nielsen, and K. Andersen (2008). “The Bicriterion Multi Modal Assignment Problem: Introduction, Analysis, and Experimental Results”. In: Informs Journal on Computing 20.3, pp. 400-411. DOI: 10.1287/ijoc.1070.0253.

Test problem classes: Assignment
Subfolders: AP and MMAP
Formats: xml

Source: Tuyttens, D., J. Teghem, P. Fortemps, et al. (2000). “Performance of the MOSA Method for the Bicriteria Assignment Problem”. In: Journal of Heuristics 6.3, pp. 295-310. DOI: 10.1023/A:1009670112978.

Test problem classes: Assignment
Formats: raw and xml

Source: Hansen, M. (2000). “Use of Substitute Scalarizing Functions to Guide a Local Search Based Heuristic: The Case of moTSP”. In: Journal of Heuristics 6.3, pp. 419-431. DOI: 10.1023/A:1009690717521.

Test problem classes: Traveling Salesman
Formats: raw

Source: Adelgren, N. and A. Gupte (2016). Branch-and-bound for biobjective mixed-integer programming. Optimization Online. Research rep. URL: https://www.optimization-online.org/DB_HTML/2016/10/5676.html.

Test problem classes: MILP
Subfolders: LP_1, LP_2, LP_3, LP_4, LP_5 and LP_6
Formats: lp

Source: Forget, N., S. Gadegaard, K. Klamroth, et al. (2020). Branch-and-bound and objective branching with three objectives. Optimization Online. URL: https://www.optimization-online.org/DB_FILE/2020/12/8158.pdf.

Test problem classes: Assignment, Knapsack and Facility Location
Subfolders: AP, KP and UFLP
Formats: raw

Source: Forget, N., S. Gadegaard, and L. Nielsen (2021). Linear relaxation based branch-and-bound for multi-objective integer programming with warm-starting. Optimizaton Online. URL: https://www.optimization-online.org/DB_HTML/2021/08/8531.html.

Test problem classes: Production Planning and Facility Location
Subfolders: PPP/3obj, PPP/4obj, PPP/5obj, UFLP/3obj, UFLP/4obj and UFLP/5obj
Formats: fgt

Source: Lyngesen, M., G. S.L., and L. Nielsen (2024). “Generator sets for Minkowski Sums - Theory and Insights”. In: ??.

Test problem classes: Minkowski Sum - Subset and Minkowski Sum
Subfolders: sp/2obj, sp/3obj, sp/4obj, sp/5obj, msp/2obj, msp/3obj, msp/4obj and msp/5obj
Formats: json

Source: An, D., S. N. Parragh, M. Sinnl, et al. (2024). “A matheuristic for tri-objective binary integer linear programming”. In: Computers & Operations Research 161, p. 106397. ISSN: 0305-0548. DOI: 10.1016/j.cor.2023.106397. URL: https://dx.doi.org/10.1016/j.cor.2023.106397.

Test problem classes: Facility Location
Subfolders: CFLP
Formats: fgt

Source: Kirlik, G. and S. Sayın (2014). “A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems”. In: European Journal of Operational Research 232.3, pp. 479 - 488. DOI: 10.1016/j.ejor.2013.08.001.

Test problem classes: ILP and Knapsack
Subfolders: ILP/3obj, ILP/4obj, ILP/5obj, KP/3obj, KP/4obj and KP/5obj
Formats: fgt

MOrepo contains results for some of the instances in problem classes:

MOrepo contains results for some of the instances in problem classes Assignment, Knapsack, Facility Location, Minkowski Sum - Subset and Minkowski Sum. The contributions are:

Source: Pedersen, C., L. Nielsen, and K. Andersen (2008). “The Bicriterion Multi Modal Assignment Problem: Introduction, Analysis, and Experimental Results”. In: Informs Journal on Computing 20.3, pp. 400-411. DOI: 10.1287/ijoc.1070.0253.

Results given for contributions: Pedersen08 and Tuyttens00

Source: Forget, N., S. Gadegaard, K. Klamroth, et al. (2020). Branch-and-bound and objective branching with three objectives. Optimization Online. URL: https://www.optimization-online.org/DB_FILE/2020/12/8158.pdf.

Results given for contributions: Forget20

Source: Lyngesen, M., G. S.L., and L. Nielsen (2024). “Generator sets for Minkowski Sums - Theory and Insights”. In: ??.

Results given for contributions: Lyngesen24

To cite use

## @Electronic{MOrepo,
##   title = {Multi-Objective Optimization Repository (MOrepo)},
##   author = {L. R. Nielsen},
##   url = {https://github.com/MCDMSociety/MOrepo},
##   year = {2017},
## }

You may use the R package MOrepoTools to download instances. You don’t need much knowledge about R to use the package. But of course it is preferable. You need R and preferable RStudio installed on your computer. First you have to install the MOrepoTools package. From the R command line write:

library(devtools)   # if the package is missing see ?install.package 
install_github("MCDMSociety/MOrepo/misc/R/MOrepoTools")

To get an overview over the current problem classes run:

library(MOrepoTools)
getProblemClasses()  # current problem classes in MOrepo
## [1] "Facility Location"      "Assignment"             "Traveling Salesman"    
## [4] "MILP"                   "Knapsack"               "Production Planning"   
## [7] "Minkowski Sum - Subset" "Minkowski Sum"          "ILP"
getInstanceInfo(class = "Assignment")  # info about instances for the assignment problem
## 
## #### Contribution Pedersen08
## 
## Source: Pedersen, C., L. Nielsen, and K. Andersen (2008). "The Bicriterion
## Multi Modal Assignment Problem: Introduction, Analysis, and
## Experimental Results". In: _Informs Journal on Computing_ 20.3, pp.
## 400-411. DOI:
## [10.1287/ijoc.1070.0253](https://doi.org/10.1287%2Fijoc.1070.0253).
## 
## Test problem classes: Assignment  
## Subfolders: AP and MMAP  
## Formats: xml  
## 
## #### Contribution Tuyttens00
## 
## Source: Tuyttens, D., J. Teghem, P. Fortemps, et al. (2000). "Performance of
## the MOSA Method for the Bicriteria Assignment Problem". In: _Journal of
## Heuristics_ 6.3, pp. 295-310. DOI:
## [10.1023/A:1009670112978](https://doi.org/10.1023%2FA%3A1009670112978).
## 
## Test problem classes: Assignment  
## Formats: raw and xml  
## 
## #### Contribution Forget20
## 
## Source: Forget, N., S. Gadegaard, K. Klamroth, et al. (2020). _Branch-and-bound
## and objective branching with three objectives_. Optimization Online.
## URL:
## [https://www.optimization-online.org/DB_FILE/2020/12/8158.pdf](https://www.optimization-online.org/DB_FILE/2020/12/8158.pdf).
## 
## Test problem classes: Assignment, Knapsack and Facility Location  
## Subfolders: AP, KP and UFLP  
## Formats: raw

Now download the Tuyttens00 contribution as a zip file using

getContributionAsZip("Tuyttens00")
## Download MOrepo-Tuyttens00.zip ... finished.