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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| Format: | Article |
| Language: | English |
| Published: |
Pontificia Universidad Javeriana
2018-09-01
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| Series: | Universitas Scientiarum |
| Subjects: | |
| Online Access: | https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23272 |
| _version_ | 1798027352678072320 |
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| author | Andrés Vargas |
| author_facet | Andrés Vargas |
| author_sort | Andrés Vargas |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-11T18:50:03Z |
| format | Article |
| id | doaj.art-bc668f37a124422793978b8a1213ac4c |
| institution | Directory Open Access Journal |
| issn | 0122-7483 2027-1352 |
| language | English |
| last_indexed | 2024-04-11T18:50:03Z |
| publishDate | 2018-09-01 |
| publisher | Pontificia Universidad Javeriana |
| record_format | Article |
| series | Universitas Scientiarum |
| spelling | doaj.art-bc668f37a124422793978b8a1213ac4c2022-12-22T04:08:27ZengPontificia Universidad JaverianaUniversitas Scientiarum0122-74832027-13522018-09-0123333335510.11144/Javeriana.SC23-3.otpcOn the Pareto Compliance of the Averaged Hausdorff Distance as a Performance IndicatorAndrés Vargas0Departamento de Matemáticas, Pontificia Universidad Javeriana, Bogotá, Colombia.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.https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23272averaged hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; pareto optimality; performance indicator. |
| spellingShingle | Andrés Vargas On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator Universitas Scientiarum averaged hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; pareto optimality; performance indicator. |
| title | 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_short | 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 |
| topic | averaged hausdorff distance; generational distance; inverted generational distance; multiobjective optimization; pareto optimality; performance indicator. |
| url | https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23272 |
| work_keys_str_mv | AT andresvargas ontheparetocomplianceoftheaveragedhausdorffdistanceasaperformanceindicator |