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- Title
On the Pareto Compliance of the Averaged Hausdorff Distance as a Performance Indicator.
- Authors
Vargas, Andrés
- Abstract
The averaged Hausdorff distance Δp 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 Δp -indicator to the notion of Pareto optimality. Since Δp 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.
- Subjects
PARETO optimum; KEY performance indicators (Management); MODULES (Algebra)
- Publication
Universitas Scientiarum, 2018, Vol 23, Issue 3, p333
- ISSN
0122-7483
- Publication type
Article
- DOI
10.11144/Javeriana.SC23-3.otpc