A Heuristic Algorithm for the Set k-Cover Problem
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The set k-cover problem (SkCP) is an extension of the classical set cover problem (SCP), in which each row needs to be covered by at least k columns while the coverage cost is minimized. The case of \(k=1\) refers to the classical SCP. SkCP has many applications including in computational biology. We develop a simple and effective heuristic for both weighted and unweighted SkCP. In the weighted SkCP, there is a cost associated with a column and in the unweighted variant, all columns have the identical cost. The proposed heuristic first generates a lower bound and then builds a feasible solution from the lower bound. We improve the feasible solution through several procedures including a removal local search. We consider three different values for k and test the heuristic on 45 benchmark instances of SCP from OR library. Therefore, we solve 135 instances. Over the solved instances, we show that our proposed heuristic obtains quality solutions.
KeywordsSet cover problem Multiple coverage Heuristic
Amir Salehipour is the recipient of an Australian Research Council Discovery Early Career Researcher Award (project number DE170100234) funded by the Australian Government.
- 3.Balas, E., Ho, A.: Set covering algorithms using cutting planes, heuristics, and subgradient optimization: a computational study. In: Padberg, M.W. (ed.) Combinatorial Optimization. Mathematical Programming Studies, vol. 12, pp. 37–60. Springer, Heidelberg (1980). https://doi.org/10.1007/BFb0120886CrossRefzbMATHGoogle Scholar
- 11.Caserta, M.: Tabu search-based metaheuristic algorithm for large-scale set covering problems. In: Doerner, K.F., Gendreau, M., Greistorfer, P., Gutjahr, W., Hartl, R.F., Reimann, M. (eds.) Metaheuristics. ORSIS, vol. 39, pp. 43–63. Springer, Boston (2007). https://doi.org/10.1007/978-0-387-71921-4_3CrossRefGoogle Scholar