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Constraint generation approaches for submodular function maximization leveraging graph properties

Author

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  • Eszter Csókás

    (University of Szeged)

  • Tamás Vinkó

    (University of Szeged)

Abstract

Submodular function maximization is an attractive optimization model and also a well-studied problem with a variety of algorithms available. Constraint generation (CG) approaches are appealing techniques to tackle the problem with, as the mixed-integer programming formulation of the problem suffers from the exponential size of the number of constraints. Most of the problems in these topics are of combinatorial nature and involve graphs on which the maximization is defined. Inspired by the recent work of Uematsu et al. (J Oper Res Soc Jpn 63:41–59, 2020), in this paper we introduce variants of the CG algorithm which take into account certain properties of the input graph aiming at informed selection of the constraints. Benchmarking results are shown to demonstrate the efficiency of the proposed methods.

Suggested Citation

  • Eszter Csókás & Tamás Vinkó, 2024. "Constraint generation approaches for submodular function maximization leveraging graph properties," Journal of Global Optimization, Springer, vol. 88(2), pages 377-394, February.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:2:d:10.1007_s10898-023-01318-4
    DOI: 10.1007/s10898-023-01318-4
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    References listed on IDEAS

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    1. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions," LIDAM Reprints CORE 341, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Nemhauser, G.L. & Wolsey, L.A., 1981. "Maximizing submodular set functions: formulations and analysis of algorithms," LIDAM Reprints CORE 455, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Fisher, M.L. & Nemhauser, G.L. & Wolsey, L.A., 1978. "An analysis of approximations for maximizing submodular set functions - 1," LIDAM Reprints CORE 334, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Cheng Lu & Wenguo Yang & Suixiang Gao, 2022. "A new greedy strategy for maximizing monotone submodular function under a cardinality constraint," Journal of Global Optimization, Springer, vol. 83(2), pages 235-247, June.
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