Fixed parameter evolutionary algorithms and maximum leaf spanning trees: a matter of mutation

Authors:
Stefan Kratsch;Per Kristian Lehre;Frank Neumann;Pietro Simone Oliveto
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;DTU Informatics, Technical University of Denmark, Lyngby, Denmark;Max-Planck-Institut für Informatik, Saarbrücken, Germany and School of Computer Science, University of Birmingham, Birmingham, United Kingdom;School of Computer Science, University of Birmingham, Birmingham, United Kingdom
Venue:
PPSN'10 Proceedings of the 11th international conference on Parallel problem solving from nature: Part I
Year:
2010

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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.