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

Multi-objective Database Queries in Combined Knapsack and Set Covering Problem Domains

Database queries are one of the most important functions of a relational database. Users are interested in viewing a variety of data representations, and this may vary based on database purpose and the nature of the stored data. The Air Force Institute of Technology has approximately 100 data logs which will be converted to the standardized Scorpion Data Model format. A relational database is designed to house this data and its associated sensor and non-sensor metadata. Deterministic polynomial-time queries were used to test the performance of this schema against two other schemas, with databases of 100 and 1000 logs of repeated data and randomized metadata. Of these approaches, the one that had the best performance was chosen as AFIT’s database solution, and now more complex and useful queries need to be developed to enable filter research. To this end, consider the combined Multi-Objective Knapsack/Set Covering Database Query. Algorithms which address The Set Covering Problem or Knapsack Problem could be used individually to achieve useful results, but together they could offer additional power to a potential user. This paper explores the NP-Hard problem domain of the Multi-Objective KP/SCP, proposes Genetic and Hill Climber algorithms, implements these algorithms using Java, populates their data structures using SQL queries from two test databases, and finally compares how these algorithms perform