Metaheuristics for the Minimum Set Cover Problem: A Comparison

Lukas Rosenbauer, Anthony Stein, Helena Stegherr, Jörg Hähner

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