Initialization and Local Search Methods Applied to the Set Covering Problem: A Systematic Mapping

The set covering problem (SCP) is a classical combinatorial  optimization problem part of Karp's 21 NP-complete problems. Many real-world applications can be modeled as set covering problems (SCPs), such as locating emergency services, military planning, and decision-making in a COVID-19 pandemic context. Among the approaches that this type of problem has solved are heuristic (H) and metaheuristic (MH) algorithms, which integrate iterative methods and procedures to explore and exploit the search space intelligently. In the present research, we carry out a systematic mapping of the literature focused on the initialization and local search methods used in these algorithms that have been applied to the SCP in order to identify them and that they can be applied in other algorithms. This mapping was carried out in three main stages: research planning, implementation, and documentation of results. The results indicate that the most used initialization method is random with heuristic search, and the inclusion of local search methods in MH algorithms improves the results obtained in comparison to those without local search. Moreover, initialization and local search methods can be used to modify other algorithms and evaluate the impact they generate on the results obtained.