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International Conference on Parallel Problem Solving from Nature

PPSN 2014: Parallel Problem Solving from Nature – PPSN XIII pp 922–931Cite as

Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8672))

Abstract

Many combinatorial optimization problems have underlying goal functions that are submodular. The classical goal is to find a good solution for a given submodular function f under a given set of constraints. In this paper, we investigate the runtime of a multi-objective evolutionary algorithm called GSEMO until it has obtained a good approximation for submodular functions. For the case of monotone submodular functions and uniform cardinality constraints we show that GSEMO achieves a (1 − 1/e)-approximation in expected time \(\mathcal{O}(n^2\,(\log n+k))\), where k is the value of the given constraint. For the case of non-monotone submodular functions with k matroid intersection constraints, we show that GSEMO achieves a 1/(k + 2 + 1/k + ε)-approximation in expected time \(\mathcal{O}(n^{k+5}\log (n) / \varepsilon )\).

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Author information

Authors and Affiliations

  1. Friedrich-Schiller-Universität Jena, 07743, Jena, Germany

    Tobias Friedrich

  2. Optimisation and Logistics, School of Computer Science, The University of Adelaide, Adelaide, SA, 5005, Australia

    Frank Neumann

Authors
  1. Tobias Friedrich
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  2. Frank Neumann
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Editor information

Editors and Affiliations

  1. Faculty of Computer and Engineering Sciences, Cologne University of Applied Sciences, Steinmüllerallee 1, 51643, Gummersbach, Germany

    Thomas Bartz-Beielstein

  2. Warwick Business School, University of Warwick, CV8 2SY, Coventry, UK

    Jürgen Branke

  3. Department of Intelligent Systems, JožefStefan Institute, Jamova cesta 39, 1000, Ljubljana, Slovenia

    Bogdan Filipič

  4. Department of Computer Science and Creative Technologies, University of the West of England, BS16 1QY, Bristol, UK

    Jim Smith

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Friedrich, T., Neumann, F. (2014). Maximizing Submodular Functions under Matroid Constraints by Multi-objective Evolutionary Algorithms. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_91

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  • DOI: https://doi.org/10.1007/978-3-319-10762-2_91

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10761-5

  • Online ISBN: 978-3-319-10762-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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