An Iterated Heuristic Algorithm for the Set Covering Problem

The set covering problem is a well-known NP-hard combinatorial optimization problem with wide practical applications. This paper introduces a novel heuristic for the uni-cost set covering problem. An iterated approximation algorithm (ITEG) based on this heuristic is developed: in the rst iteration a cover is constructed, and in the next iterations a new cover is built by starting with part of the best solution so far obtained. The nal output of the algorithm is the best solution obtained in all the iterations. ITEG is empirically evaluated on a set of randomly generated problem instances, on instances originated from the Steiner triple systems, and on instances derived from two challenging combinatorial questions by Erdd os. The performance of ITEG on these benchmark problems is very satisfactory, both in terms of solution quality (i.e., small covers) as well as in terms of running time.