Do additional objectives make a problem harder?

  • Authors:
  • Dimo Brockhoff;Tobias Friedrich;Nils Hebbinghaus;Christian Klein;Frank Neumann;Eckart Zitzler

  • Affiliations:
  • ETH Zurich, Zurich, Switzerland;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany;ETH Zurich, Zurich, Switzerland

  • Venue:
  • Proceedings of the 9th annual conference on Genetic and evolutionary computation
  • Year:
  • 2007

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Abstract

In this paper, we examine how adding objectives to a given optimization problem affects the computation effort required to generate the set of Pareto-optimal solutions. Experimental studies show that additional objectives may change the runtime behavior of an algorithm drastically. Often it is assumed that more objectives make a problem harder as the number of different trade-offs may increase with the problem dimension. We show that additional objectives, however, may be both beneficial and obstructive depending on the chosen objective. Our results are obtained by rigorous runtime analyses that show the different effects of adding objectives to a well-known plateau-function.