Solution of the set covering problem with genetic algorithm

The Set Covering Problem (SCP) is a combinatorial optimization problem with applications in various fields. It aims to select subsets from a given space to cover all elements while minimizing the total number of selected sets. Genetic Algorithms (GA), inspired by natural evolutionary processes, show promising results in solving complex optimization problems. In this study, a genetic algorithm to overcome SCP using a heuristic that sorts sets by their frequency in the initial population is proposed. Additionally, a formula for selecting subsets that will make a positive contribution to the solution set has been established. The proposed algorithm aims to evolve a population of solutions using genetic operators such as selection, crossover and mutation. The fitness of individuals is determined by their ability to cover all elements with a minimum number of sets. The genetic algorithm iteratively improves solutions over generations and gradually approaches optimum or near-optimal solutions. The results of the proposed algorithm are demonstrated by conducting experiments on various example problems of the SCP.