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Theoretically Investigating Optimal μ-Distributions for the Hypervolume Indicator: First Results For Three Objectives
Abstract : Several indicator-based evolutionary multiobjective optimization algorithms have been proposed in the literature. The notion of optimal μ-distributions formalizes the optimization goal of such algorithms: find a set of μ solutions that maximizes the underlying indicator among all sets with μ solutions. In particular for the often used hypervolume indicator, optimal μ-distributions have been theoretically analyzed recently. All those results, however, cope with bi-objective problems only. It is the main goal of this paper to extend some of the results to the 3-objective case. This generalization is shown to be not straight-forward as a solution's hypervolume contribution has not a simple geometric shape anymore in opposition to the bi-objective case where it is always rectangular. In addition, we investigate the influence of the reference point on optimal μ-distributions and prove that also in the 3-objective case situations exist for which the Pareto front's extreme points cannot be guaranteed in optimal μ-distributions.
Cited literature [19 references]
https://hal.inria.fr/inria-00534906
Contributor : Dimo Brockhoff <>
Submitted on : Wednesday, November 10, 2010 - 8:03:21 PM
Last modification on : Wednesday, September 16, 2020 - 5:04:55 PM
Long-term archiving on: : Friday, February 11, 2011 - 3:16:44 AM
Contributor : Dimo Brockhoff <>
Submitted on : Wednesday, November 10, 2010 - 8:03:21 PM
Last modification on : Wednesday, September 16, 2020 - 5:04:55 PM
Long-term archiving on: : Friday, February 11, 2011 - 3:16:44 AM
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