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Maximizing Submodular or Monotone Functions Under Partition Matroid Constraints by Multi-objective Evolutionary Algorithms

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Parallel Problem Solving from Nature – PPSN XVI (PPSN 2020)

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Abstract

Many important problems can be regarded as maximizing submodular functions under some constraints. A simple multi-objective evolutionary algorithm called GSEMO has been shown to achieve good approximation for submodular functions efficiently. While there have been many studies on the subject, most of existing run-time analyses for GSEMO assume a single cardinality constraint. In this work, we extend the theoretical results to partition matroid constraints which generalize cardinality constraints, and show that GSEMO can generally guarantee good approximation performance within polynomial expected run time. Furthermore, we conducted experimental comparison against a baseline GREEDY algorithm in maximizing undirected graph cuts on random graphs, under various partition matroid constraints. The results show GSEMO tends to outperform GREEDY in quadratic run time.

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Acknowledgements

The experiments were run using the HPC service provided by the University of Adelaide.

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Authors and Affiliations

  1. The University of Adelaide, Adelaide, Australia

    Anh Viet Do & Frank Neumann

Authors
  1. Anh Viet Do
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  2. Frank Neumann
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Corresponding author

Correspondence to Frank Neumann .

Editor information

Editors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Thomas Bäck

  2. Leiden University, Leiden, The Netherlands

    Mike Preuss

  3. Leiden University, Leiden, The Netherlands

    André Deutz

  4. Sorbonne University, Paris, France

    Hao Wang

  5. Sorbonne University, Paris, France

    Carola Doerr

  6. Leiden University, Leiden, The Netherlands

    Michael Emmerich

  7. University of Münster, Münster, Germany

    Heike Trautmann

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Do, A.V., Neumann, F. (2020). Maximizing Submodular or Monotone Functions Under Partition Matroid Constraints by Multi-objective Evolutionary Algorithms. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12270. Springer, Cham. https://doi.org/10.1007/978-3-030-58115-2_41

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  • DOI: https://doi.org/10.1007/978-3-030-58115-2_41

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