# Metaheuristics for the Minimum Set Cover Problem: A Comparison

### Lukas Rosenbauer, Anthony Stein, Helena Stegherr, Jörg Hähner

#### 2020

#### Abstract

The minimum set cover problem (MSCP) is one of the first NP-hard optimization problems discovered. Theoretically it has a bad worst case approximation ratio. As the MSCP turns out to appear in several real world problems, various approaches exist where evolutionary algorithms and metaheuristics are utilized in order to achieve good average case results. This work is intended to revisit and compare current results regarding the application of metaheuristics for the MSCP. Therefore, a recapitulation of the MSCP and its classification into the class of NP-hard optimization problems are provided first. After an overview of notable approximation methods, the focus is shifted towards a brief review of existing metaheuristics which were adapted for the MSCP. In order to allow for a targeted comparison of the existing algorithms, the theoretical worst case complexities in terms of the big O-notation are derived first. This is followed by an empirical study where the identified metaheuristics are examined. Here we use Steiner triple systems, Beasley’s OR library, and introduce a new class of instances. Several of the considered approaches achieve close to optimal results. However, our analysis reveals significant differences in terms of runtime and shows that some approaches may even have exponential runtime.

Download#### Paper Citation

#### in Harvard Style

Rosenbauer L., Stein A., Stegherr H. and Hähner J. (2020). **Metaheuristics for the Minimum Set Cover Problem: A Comparison**. In *Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020) - Volume 1: ECTA*; ISBN 978-989-758-475-6, SciTePress, pages 123-130. DOI: 10.5220/0010019901230130

#### in Bibtex Style

@conference{ecta20,

author={Lukas Rosenbauer and Anthony Stein and Helena Stegherr and Jörg Hähner},

title={Metaheuristics for the Minimum Set Cover Problem: A Comparison},

booktitle={Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020) - Volume 1: ECTA},

year={2020},

pages={123-130},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010019901230130},

isbn={978-989-758-475-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020) - Volume 1: ECTA

TI - Metaheuristics for the Minimum Set Cover Problem: A Comparison

SN - 978-989-758-475-6

AU - Rosenbauer L.

AU - Stein A.

AU - Stegherr H.

AU - Hähner J.

PY - 2020

SP - 123

EP - 130

DO - 10.5220/0010019901230130

PB - SciTePress