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Computing Minimum Cuts by Randomized Search Heuristics

Algorithmica volume 59, pages 323–342 (2011)Cite this article

Abstract

We study the minimum s-t-cut problem in graphs with costs on the edges in the context of evolutionary algorithms. Minimum cut problems belong to the class of basic network optimization problems that occur as crucial subproblems in many real-world optimization problems and have a variety of applications in several different areas. We prove that there exist instances of the minimum s-t-cut problem that cannot be solved by standard single-objective evolutionary algorithms in reasonable time. On the other hand, we develop a bi-criteria approach based on the famous maximum-flow minimum-cut theorem that enables evolutionary algorithms to find an optimal solution in expected polynomial time.

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Affiliations

  1. Algorithms and Complexity, Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Frank Neumann

  2. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Joachim Reichel & Martin Skutella

Authors
  1. Frank Neumann
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  2. Joachim Reichel
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  3. Martin Skutella
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Corresponding author

Correspondence to Frank Neumann.

Additional information

A conference version appeared in GECCO 2008 [17].

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Neumann, F., Reichel, J. & Skutella, M. Computing Minimum Cuts by Randomized Search Heuristics. Algorithmica 59, 323–342 (2011). https://doi.org/10.1007/s00453-009-9370-8

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  • DOI: https://doi.org/10.1007/s00453-009-9370-8

  • Evolutionary algorithms
  • Minimum s-t-cuts
  • Multi-objective optimization
  • Randomized search heuristics