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Algorithms for the generalized independent set problem based on a quadratic optimization approach

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Abstract

This paper presents two algorithms—a construction heuristic and an exact solution method—for the generalized independent set problem. Both methods take advantage of a nonlinear formulation of this problem and are based on optimization of a quadratic function over a hypersphere. Heuristic solutions are constructed by exploring stationary points of a surrogate problem of this form. The exact method is a combinatorial branch-and-bound algorithm that uses a spherical relaxation of the original feasible region in its pruning subroutine. We show competence of the proposed methods through computational experiments on benchmark instances.

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Acknowledgements

We would like to thank Dr. Renata Mansini for providing the test instances, and the anonymous referees, whose feedback helped us to improve the paper.

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Authors and Affiliations

  1. Texas A&M University, College Station, TX, USA

    Seyedmohammadhossein Hosseinian & Sergiy Butenko

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  1. Seyedmohammadhossein Hosseinian
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  2. Sergiy Butenko
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Correspondence to Seyedmohammadhossein Hosseinian.

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Hosseinian, S., Butenko, S. Algorithms for the generalized independent set problem based on a quadratic optimization approach. Optim Lett 13, 1211–1222 (2019). https://doi.org/10.1007/s11590-019-01418-9

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  • DOI: https://doi.org/10.1007/s11590-019-01418-9

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