Analyzing Hypervolume Indicator Based Algorithms

  • Dimo Brockhoff
  • Tobias Friedrich
  • Frank Neumann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


Indicator-based methods to tackle multiobjective problems have become popular recently, mainly because they allow to incorporate user preferences into the search explicitly. Multiobjective Evolutionary Algorithms (MOEAs) using the hypervolume indicator in particular showed better performance than classical MOEAs in experimental comparisons. In this paper, the use of indicator-based MOEAs is investigated for the first time from a theoretical point of view. We carry out running time analyses for an evolutionary algorithm with a (μ + 1)-selection scheme based on the hypervolume indicator as it is used in most of the recently proposed MOEAs. Our analyses point out two important aspects of the search process. First, we examine how such algorithms can approach the Pareto front. Later on, we point out how they can achieve a good approximation for an exponentially large Pareto front.


Pareto Front Multiobjective Optimization Pareto Optimal Solution Objective Vector Multiobjective Evolutionary Algorithm 
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 2008

Authors and Affiliations

  • Dimo Brockhoff
    • 1
  • Tobias Friedrich
    • 2
  • Frank Neumann
    • 2
  1. 1.Computer Engineering and Networks LabETH ZurichZurichSwitzerland
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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