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

  • Michael Armbruster
  • Marzena Fügenschuh
  • Christoph Helmberg
  • Nikolay Jetchev
  • Alexander Martin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3906)


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.


Genetic Algorithm Valid Inequality Hybrid Genetic Algorithm Edge Cost Primal Heuristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael Armbruster
    • 1
  • Marzena Fügenschuh
    • 2
  • Christoph Helmberg
    • 1
  • Nikolay Jetchev
    • 2
  • Alexander Martin
    • 2
  1. 1.Department of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Department of MathematicsDarmstadt University of TechnologyDarmstadtGermany

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