Novel algorithm to calculate hypervolume indicator of Pareto approximation set

dc.creatorYang, Qing
dc.creatorDing, Shengchao
dc.date2007-04-10
dc.date.accessioned2026-07-07T07:55:54Z
dc.date.available2026-07-07T07:55:54Z
dc.descriptionHypervolume indicator is a commonly accepted quality measure for comparing Pareto approximation set generated by multi-objective optimizers. The best known algorithm to calculate it for $n$ points in $d$-dimensional space has a run time of $O(n^{d/2})$ with special data structures. This paper presents a recursive, vertex-splitting algorithm for calculating the hypervolume indicator of a set of $n$ non-comparable points in $d>2$ dimensions. It splits out multiple child hyper-cuboids which can not be dominated by a splitting reference point. In special, the splitting reference point is carefully chosen to minimize the number of points in the child hyper-cuboids. The complexity analysis shows that the proposed algorithm achieves $O((\frac{d}{2})^n)$ time and $O(dn^2)$ space complexity in the worst case.
dc.description9 pages, 2 figures. Comments are welcome
dc.identifierhttps://arxiv.org/abs/0704.1196
dc.identifierhttp://arxiv.org/abs/0704.1196
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127123
dc.subjectComputational Geometry
dc.subjectNeural and Evolutionary Computing
dc.titleNovel algorithm to calculate hypervolume indicator of Pareto approximation set
dc.typetext

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