Metaheuristics provide the means to approximately solve complex optimisation problems when exact optimisers cannot be utilised. This led to an explosion in the number of novel metaheuristics, most of them metaphor-based, using nature as a source of inspiration. Thus, keeping track of their capabilities and innovative components is an increasingly difficult task. This can be resolved by an exhaustive classification system. Trying to classify metaheuristics is common in research, but no consensus on a classification system and the necessary criteria has been established so far. Furthermore, a proposed classification system can not be deemed complete if inherently different metaheuristics are assigned to the same class by the system. In this paper we provide the basis for a new comprehensive classification system for metaheuristics. We first summarise and discuss previous classification attempts and the utilised criteria. Then we present a multi-level architecture and suitable criteria for the task of classifying metaheuristics. A classification system of this kind can solve three main problems when applied to metaheuristics: organise the huge set of existing metaheuristics, clarify the innovation in novel metaheuristics and identify metaheuristics suitable to solve specific optimisation tasks.
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.
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