On the Computation of the Empirical Attainment Function

  • Carlos M. Fonseca
  • Andreia P. Guerreiro
  • Manuel López-Ibáñez
  • Luís Paquete
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6576)

Abstract

The attainment function provides a description of the location of the distribution of a random non-dominated point set. This function can be estimated from experimental data via its empirical counterpart, the empirical attainment function (EAF). However, computation of the EAF in more than two dimensions is a non-trivial task. In this article, the problem of computing the empirical attainment function is formalised, and upper and lower bounds on the corresponding number of output points are presented. In addition, efficient algorithms for the two and three-dimensional cases are proposed, and their time complexities are related to lower bounds derived for each case.

Keywords

Empirical attainment function algorithms multiobjective optimiser performance estimation 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Carlos M. Fonseca
    • 1
    • 2
    • 3
  • Andreia P. Guerreiro
    • 4
  • Manuel López-Ibáñez
    • 5
  • Luís Paquete
    • 6
  1. 1.Department of Informatics EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.CEG-IST, Instituto Superior TécnicoTechnical University of LisbonLisboaPortugal
  3. 3.DEEI, Faculty of Science and TechnologyUniversity of AlgarveFaroPortugal
  4. 4.Instituto Superior TécnicoTechnical University of LisbonLisboaPortugal
  5. 5.IRIDIAUniversité Libre de Bruxelles (ULB)BrusselsBelgium
  6. 6.CISUC, Department of Informatics EngineeringUniversity of CoimbraCoimbraPortugal

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