New ideas for applying ant colony optimization to the set covering problem

The set covering problem (SCP) is a well known NP-hard problem with many practical applications. In this research, a new approach based on ant colony optimization (ACO) is proposed to solve the SCP. The main differences between it and the existing ACO-based approaches lie in three aspects. First, it adopts a novel method, called single-row-oriented method, to construct solutions. When choosing a new column, it first randomly selects an uncovered row and only considers the columns covering this row, rather than all the unselected columns as candidate solution components. Second, a kind of dynamic heuristic information is used in this approach. It takes into account Lagrangian dual information associated with currently uncovered rows. Finally, a simple local search procedure is developed to improve solutions constructed by ants while keeping their feasibility. The proposed algorithm has been tested on a number of benchmark instances. Computational results show that it is able to produce competitive solutions in comparison with other metaheuristics.