Metaheuristics for the Minimum Set Cover Problem: A Comparison

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.

Effect of Deploying Routing and Facility Location Methods on Power Transmission to Increase the Reliability of the Power Network and Minimize the Total Logistics Cost

“…Study will deploy two algorithms i.e. Travelling Salesman Problem (TSP) (Sorma et al, 2020) and Set Cover Problem (SCP) (Rosenbauer et al, 2020) to observe the current situation of power transmission mechanism, number of maintenance teams and number of members in each team. Furthermore, study will look into the areas where overall expenses can be cut down without increasing the profit margin.…”