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Bicriterion assignment and multi modal assignment problems

This is an example on how an readme file can look, see this file for info about how to contribute.

The paper consider 10 instances for the classical bi-objective linear assignment problem.

How to cite

To cite the paper use

@ARTICLE{Pedersen08,
   Author = {Pedersen, C.R. and Nielsen, L.R. and Andersen, K.A.},
   Title = {The Bicriterion Multi Modal Assignment Problem: Introduction, Analysis, and Experimental Results},
   Year = {2008},
   Volume = {20},
   Number = {3},
   Journal = {Informs Journal on Computing},
   Institution = {Department of Operations Research, University of Aarhus},
   School = {Department of Operations Research, University of Aarhus},
   Pages = {400–-411},
   Doi = {10.1287/ijoc.1070.0253}
}

To cite this repository use

@Electronic{MOrepo-Pedersen08,
  Title = {Bicriterion assignment and multi modal assignment problems (MOrepo-Pedersen08)},
  Author = {Pedersen, C.R. and Nielsen, L.R.},
  Url = {https://github.com/MCDMSociety/MOrepo-Pedersen08},
  Year = {2008},
  Note = {Instance and result files at MOrepo.}
}

To cite the Multi-Objective Optimization Repository use

@Electronic{MOrepo,
  Title = {Multi-Objective Optimization Repository (MOrepo)},
  Author = {L. R. Nielsen},
  Url = {https://github.com/MCDMSociety/MOrepo},
  Year = {2017},
}

In a paper (written using LaTeX) you may write:

Instances from \cite{Pedersen} are tested which are available from the Multi-Objective 
Optimization Repository (MOrepo) (\cite{MOrepo, MOrepo-Pedersen08}).

Always remember to cite the research paper and not the repository if you don't want to include all citations.

Test instances

Instances are named Template_AP_n<n>.<raw/xml> where n is the size of the problem. The paper considers instances of size 5-50; however, the instance set also contains 5 instances of size 60-100. Costs are generated random in [0,30].

All instance files are given in both xml and raw format. The xml format is self explainable (see e.g. ex1).

Raw format description (AP)

We use the following parameter names:

  • $n$ = dimension/size
  • $c^{k}_{r,c}$ = $k$'th cost of assigning row $r$ to column $c$.

The instances have the following format:

n 
c^{0}_{0,0}... c^{0}_{0,n-1}
c^{0}_{1,0}... c^{0}_{1,n-1}
...
c^{0}_{n-1,0}... c^{0}_{n-1,n-1}
c^{1}_{0,0}... c^{1}_{0,n-1}
c^{1}_{1,0}... c^{1}_{1,n-1}
...
c^{1}_{n-1,0}... c^{1}_{n-1,n-1}

That is, first the dimension, then the costs for the first criterion and next the cost for the second criterion.

Multi modal assignment problems (MMAP)

The instances are contained in the sub folder MMAP. Instances are named Template_MMAP_d<n>_e<I1>_c<I2>_m<M>_s<S>_<Y>.xml where Y is the instance number of a BiMMAP of size $n$ with entry range I1 and cost range I2 using method M and shape S.

A total of 8000 instances are provided. That is, 100 instances of each of the following 80 possible configurations were generated:

  • n: 4, 6, 8, 10.
  • I1: 2-8 (not for method 2) and 10-30.
  • I2: 0-500 and 0-10000.
  • (M,S): (1, −60), (1,0), (1, 60), (2, 3), (2, 4), (3, 0).

Results

Restults are given in the results folder using the json format (see Step 3).