Local Search Algorithm for Unicost Set Covering Problem

The unicost set covering problem is a NP-hard and it has many applications. In this paper we propose a new algorithm based on local search for solving the unicost set covering problem. A fitness function is proposed for this problem and different neighborhood relations are considered for the exploration of the neighborhood of the current solution. A new approach is introduced for effective exploration of the neighborhood during the improvement phase. This approach is based on the upper bound of the best cover, which is found during the search, and using only determined moves. Additionally, in order to avoid cycles during the search, a search history is used. The proposed algorithm is experimentally evaluated for 85 well-known random and combinatorial problems in the literature, and it gives very satisfactory results in a reasonable amount of time. The proposed algorithm improves the best existing solutions for 8 problems in the literature. For a class of combinatorial problems, the best existing results are improved significantly.