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Hybrid Genetic Algorithm Within Branch-and-Cut for the Minimum Graph Bisection Problem

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Book cover Evolutionary Computation in Combinatorial Optimization (EvoCOP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3906))

Abstract

We develop a primal heuristic based on a genetic algorithm for the minimum graph bisection problem and incorporate it in a branch-and-cut framework. The problem concerns partitioning the nodes of a weighted graph into two subsets such that the total weight of each set is within some lower and upper bounds. The objective is to minimize the total cost of the edges between both subsets of the partition. We formulate the problem as an integer program. In the genetic algorithm the LP-relaxation of the IP-formulation is exploited. We present several ways of using LP information and demonstrate the computational success.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Chemnitz University of Technology, D-09107, Chemnitz, Germany

    Michael Armbruster & Christoph Helmberg

  2. Department of Mathematics, Darmstadt University of Technology, D-64289, Darmstadt, Germany

    Marzena Fügenschuh, Nikolay Jetchev & Alexander Martin

Authors
  1. Michael Armbruster
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  2. Marzena Fügenschuh
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  3. Christoph Helmberg
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  4. Nikolay Jetchev
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  5. Alexander Martin
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Editor information

Editors and Affiliations

  1. SAP AG, Neurottstr. 16, 69190, Walldorf, Germany

    Jens Gottlieb

  2. Institute of Computer Graphics and Algorithms, Vienna University of Technology, Favoritenstraße 9–11/1861, 1040, Vienna, Austria

    Günther R. Raidl

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© 2006 Springer-Verlag Berlin Heidelberg

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Armbruster, M., Fügenschuh, M., Helmberg, C., Jetchev, N., Martin, A. (2006). Hybrid Genetic Algorithm Within Branch-and-Cut for the Minimum Graph Bisection Problem. In: Gottlieb, J., Raidl, G.R. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2006. Lecture Notes in Computer Science, vol 3906. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11730095_1

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  • DOI: https://doi.org/10.1007/11730095_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33178-0

  • Online ISBN: 978-3-540-33179-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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