Fixed Parameter Evolutionary Algorithms and Maximum Leaf Spanning Trees: A Matter of Mutation

  • Stefan Kratsch
  • Per Kristian Lehre
  • Frank Neumann
  • Pietro Simone Oliveto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6238)

Abstract

Evolutionary algorithms have been shown to be very successful for a wide range of NP-hard combinatorial optimization problems. We investigate the NP-hard problem of computing a spanning tree that has a maximal number of leaves by evolutionary algorithms in the context of fixed parameter tractability (FPT) where the maximum number of leaves is the parameter under consideration. Our results show that simple evolutionary algorithms working with an edge-set encoding are confronted with local optima whose size of the inferior neighborhood grows with the value of an optimal solution. Investigating two common mutation operators, we show that an operator related to spanning tree problems leads to an FPT running time in contrast to a general mutation operator that does not have this property.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stefan Kratsch
    • 1
  • Per Kristian Lehre
    • 2
    • 3
  • Frank Neumann
    • 1
  • Pietro Simone Oliveto
    • 3
  1. 1.Algorithms and ComplexityMax-Planck-Institut für InformatikSaarbrückenGermany
  2. 2.DTU InformaticsTechnical University of DenmarkLyngbyDenmark
  3. 3.School of Computer ScienceUniversity of BirminghamBirminghamUnited Kingdom

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