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

Authors:
Zhi-Gang Ren;Zu-Ren Feng;Liang-Jun Ke;Zhao-Jun Zhang
Affiliations:
State Key Laboratory for Manufacturing Systems Engineering, Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China;State Key Laboratory for Manufacturing Systems Engineering, Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China;State Key Laboratory for Manufacturing Systems Engineering, Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China;State Key Laboratory for Manufacturing Systems Engineering, Systems Engineering Institute, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China
Venue:
Computers and Industrial Engineering
Year:
2010

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Abstract

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.