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Constraint generation approaches for submodular function maximization leveraging graph properties

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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.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. Note that problem (6) is referred as BIP(Q) in Uematsu et al. [15].

  2. \((z_{UB} - z_{LB})/z_{LB} \times 100\), where \(z_{UB}\) and \(z_{LB}\) are the upper and lower bounds reported by the algorithms, respectively.

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Acknowledgements

We thank our reviewers for their critical comments and valuable suggestions that highlighted important details and helped us in improving our paper. The research leading to these results has received funding from the national project TKP2021-NVA-09. Project no. TKP2021-NVA-09 has been implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Fund, financed under the TKP2021-NVA funding scheme. The work was also supported by the grant SNN-135643 of the National Research, Development and Innovation Office, Hungary.

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  1. Department of Computational Optimization, University of Szeged, Szeged, Hungary

    Eszter Csókás & Tamás Vinkó

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  1. Eszter Csókás
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Correspondence to Eszter Csókás.

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Csókás, E., Vinkó, T. Constraint generation approaches for submodular function maximization leveraging graph properties. J Glob Optim 88, 377–394 (2024). https://doi.org/10.1007/s10898-023-01318-4

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