The relationship between the covered fraction, completeness and hypervolume indicators



This paper investigates the relationship between the covered fraction, completeness, and (weighted) hypervolume indicators for assessing the quality of the Pareto-front approximations produced by multiobjective optimizers. It is shown that these unary quality indicators are all, by definition, weighted Hausdorff measures of the intersection of the region attained by such an optimizer outcome in objective space with some reference set. Moreover, when the optimizer is stochastic, the indicators considered lead to real-valued random variables following particular probability distributions. Expressions for the expected value of these distributions are derived, and shown to be directly related to the first-order attainment function.


evolutionary computation


Artificial Evolution, 10th International Conference, Evolution Artificielle, EA 2011, Angers, France, October 24-26, 2011, Revised Selected Papers, LNCS 7401, December 2012

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Year 2015 : 1 citations

 Michael T.M. Emmerich, André H. Deutz, Iryna Yevseyeva, "A Bayesian Approach to Portfolio Selection in Multicriteria Group Decision Making," Procedia Computer Science, volume 64, pages 993–1000, 2015.

Year 2013 : 2 citations

 I. Hupkens and M. Emmerich , “Logarithmic-time updates in SMS-EMOA and hypervolume-based archiving,” in EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation IV ( M. Emmerich, A. Deutz, O. Schuetze, T. Bäck, E. Tantar, A.-A. Tantar, P. Del Moral, P. Legrand, P. Bouvry, C. A. Coello, eds.), vol. 227 of Advances in Intelligent Systems and Computing, pp 155-169 Berlin: Springer, 2013.

 K. Narukawa, “Effect of dominance balance in many-objective optimization,” in Evolutionary Multi-Criterion Optimization. 7th International Conference, EMO 2013 (R. C. Purshouse, P. J. Fleming, C. M. Fonseca, S. Greco, and J. Shaw, eds.), vol. 7811 of Lecture Notes in Computer Science, pp. 276-290, Berlin: Springer, 2013.