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A Heuristic Algorithm for the Set k-Cover Problem

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Optimization and Learning (OLA 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1173))

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Abstract

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.

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Acknowledgment

Amir Salehipour is the recipient of an Australian Research Council Discovery Early Career Researcher Award (project number DE170100234) funded by the Australian Government.

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Authors and Affiliations

  1. School of Mathematical and Physical Sciences, University of Technology Sydney, Sydney, Australia

    Amir Salehipour

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  1. Amir Salehipour
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Correspondence to Amir Salehipour .

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Editors and Affiliations

  1. University of Cádiz, Cádiz, Spain

    Bernabé Dorronsoro

  2. University of Cádiz, Cádiz, Spain

    Patricia Ruiz

  3. University of Cádiz, Cádiz, Spain

    Juan Carlos de la Torre

  4. University of Cádiz, Cádiz, Spain

    Daniel Urda

  5. University of Lille, Lille, France

    El-Ghazali Talbi

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Salehipour, A. (2020). A Heuristic Algorithm for the Set k-Cover Problem. In: Dorronsoro, B., Ruiz, P., de la Torre, J., Urda, D., Talbi, EG. (eds) Optimization and Learning. OLA 2020. Communications in Computer and Information Science, vol 1173. Springer, Cham. https://doi.org/10.1007/978-3-030-41913-4_9

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  • DOI: https://doi.org/10.1007/978-3-030-41913-4_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41912-7

  • Online ISBN: 978-3-030-41913-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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