On the Distribution of EMOA Hypervolumes

  • Olaf Mersmann
  • Heike Trautmann
  • Boris Naujoks
  • Claus Weihs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6073)


In recent years, new approaches for multi-modal and multiobjective stochastic optimisation have been developed. It is a rather normal process that these experimental fields develop independently from other scientific areas. However, the connection between stochastic optimisation and statistics is obvious and highly appreciated. Recent works, such as sequential parameter optimisation (SPO, cf. Bartz-Beielstein [1]) or online convergence detection (OCD, cf. Trautmann et al [2]), have combined methods from evolutionary computation and statistics.

One important aspect in statistics is the analysis of stochastic outcomes of experiments and optimization methods, respectively. To this end, the optimisation runs of different evolutionary multi-objective optimisation algorithms (EMOA, cf. Deb [3] or Coello Coello et al. [4]) are treated as experiments to analyse the stochastic behavior of the results and to approximate the distribution of the performance of the EMOA. To combine the outcome of an EMOA and receive a single performance indicator value, the hypervolume (HV) indicator is considered, which is the only known unary quality indicator in this field (cf. Zitzler et al. [5]). The paper at hand investigates and compares the HV indicator outcome of multiple runs of two EMOA on different mathematical test cases.


Evolutionary Computation Kernel Density Estimate Function Evaluation Multi Criterion Optimization Parallel Coordinate Plot 
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 2010

Authors and Affiliations

  • Olaf Mersmann
    • 1
  • Heike Trautmann
    • 1
  • Boris Naujoks
    • 2
  • Claus Weihs
    • 1
  1. 1.Statistics FacultyTU Dortmund UniversityGermany
  2. 2.Log!n GmbH, SchwelmGermany

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