The set multicovering or set K-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least K times. The problem finds applications in the design of communication networks and in computational biology. We describe a GRASP with path-relinking heuristic for the set K-covering problem, as well as the template of a family of Lagrangean heuristics. The hybrid GRASP Lagrangean heuristic employs the GRASP with path-relinking heuristic using modified costs to obtain solutions for the Lagrangean relaxation problem. Computational experiments carried out on 135 test instances show experimentally that the Lagrangean heuristics performed consistently better than GRASP. By properly tuning the parameters of the GRASP Lagrangean heuristic, it is possible to obtain a good trade-off between solution quality and running times. Furthermore, the GRASP Lagrangean heuristic makes better use of the dual information provided by subgradient optimization and is able to discover better solutions and to escape from locally optimal solutions even after the stabilization of the lower bounds, when other strategies fail to find new improving solutions.
AT&T Labs Research Technical Report, Florham Park, New Jersey, December 2010.