On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator

The averaged Hausdorff distance ∆p is an inframetric, recently introduced in evolutionary multiobjective optimization (EMO) as a tool to measure the optimality of finite size approximations to the Pareto front associated to a multiobjective optimization problem (MOP). Tools of this kind are call...

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Autor principal:	Andrés Vargas
Formato:	article
Lenguaje:	EN ES
Publicado:	Pontificia Universidad Javeriana 2018
Materias:	averaged hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; pareto optimality; performance indicator. Science (General) Q1-390
Acceso en línea:	https://doaj.org/article/bc668f37a124422793978b8a1213ac4c
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spelling	oai:doaj.org-article:bc668f37a124422793978b8a1213ac4c2021-11-16T13:45:49ZOn the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator10.11144/Javeriana.SC23-3.otpc0122-74832027-1352https://doaj.org/article/bc668f37a124422793978b8a1213ac4c2018-09-01T00:00:00Zhttps://revistas.javeriana.edu.co/index.php/scientarium/article/view/23272https://doaj.org/toc/0122-7483https://doaj.org/toc/2027-1352The averaged Hausdorff distance ∆p is an inframetric, recently introduced in evolutionary multiobjective optimization (EMO) as a tool to measure the optimality of finite size approximations to the Pareto front associated to a multiobjective optimization problem (MOP). Tools of this kind are called performance indicators, and their quality depends on the useful criteria they provide to evaluate the suitability of different candidate solutions to a given MOP. We present here a purely theoretical study of the compliance of the ∆p -indicator to the notion of Pareto optimality. Since ∆p is defined in terms of a modified version of other well-known indicators, namely the generational distance GDp , and the inverted generational distance IGDp , specific criteria for the Pareto compliance of each one of them is discussed in detail. In doing so, we review some previously available knowledge on the behavior of these indicators, correcting inaccuracies found in the literature, and establish new and more general results, including detailed proofs and examples of illustrative situations. Andrés VargasPontificia Universidad Javerianaarticleaveraged hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; pareto optimality; performance indicator.Science (General)Q1-390ENESUniversitas Scientiarum, Vol 23, Iss 3, Pp 333-355 (2018)
institution	DOAJ
collection	DOAJ
language	EN ES
topic	averaged hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; pareto optimality; performance indicator. Science (General) Q1-390
spellingShingle	averaged hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; pareto optimality; performance indicator. Science (General) Q1-390 Andrés Vargas On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator
description	The averaged Hausdorff distance ∆p is an inframetric, recently introduced in evolutionary multiobjective optimization (EMO) as a tool to measure the optimality of finite size approximations to the Pareto front associated to a multiobjective optimization problem (MOP). Tools of this kind are called performance indicators, and their quality depends on the useful criteria they provide to evaluate the suitability of different candidate solutions to a given MOP. We present here a purely theoretical study of the compliance of the ∆p -indicator to the notion of Pareto optimality. Since ∆p is defined in terms of a modified version of other well-known indicators, namely the generational distance GDp , and the inverted generational distance IGDp , specific criteria for the Pareto compliance of each one of them is discussed in detail. In doing so, we review some previously available knowledge on the behavior of these indicators, correcting inaccuracies found in the literature, and establish new and more general results, including detailed proofs and examples of illustrative situations.
format	article
author	Andrés Vargas
author_facet	Andrés Vargas
author_sort	Andrés Vargas
title	On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator
title_short	On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator
title_full	On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator
title_fullStr	On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator
title_full_unstemmed	On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator
title_sort	on the pareto compliance of the averaged hausdorff distance as a performance indicator
publisher	Pontificia Universidad Javeriana
publishDate	2018
url	https://doaj.org/article/bc668f37a124422793978b8a1213ac4c
work_keys_str_mv	AT andresvargas ontheparetocomplianceoftheaveragedhausdorffdistanceasaperformanceindicator
_version_	1718426501970395136

On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator

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