On the computation of the empirical attainment function

Authors:
Carlos M. Fonseca;Andreia P. Guerreiro;Manuel López-Ibáñez;Luís Paquete
Affiliations:
Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal and CEG-IST, Instituto Superior Técnico, Technical University of Lisbon, Lisboa, Portugal and DEEI, Faculty of ...;Instituto Superior Técnico, Technical University of Lisbon, Lisboa, Portugal;IRIDIA, Université Libre de Bruxelles (ULB), Brussels, Belgium;CISUC, Department of Informatics Engineering, University of Coimbra, Coimbra, Portugal
Venue:
EMO'11 Proceedings of the 6th international conference on Evolutionary multi-criterion optimization
Year:
2011

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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.