Constraint generation approaches for submodular function maximization leveraging graph properties

Eszter Csókás () and Tamás Vinkó ()
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Eszter Csókás: University of Szeged
Tamás Vinkó: University of Szeged

Journal of Global Optimization, 2024, vol. 88, issue 2, No 4, 377-394

Abstract: 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.

Keywords: Submodular function maximization; Combinatorial optimization; Integer programming (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01318-4

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