Details

Autor(en) / Beteiligte

• Schütze, Oliver
• Hernández, Carlos

Titel

Computing Gap Free Pareto Fronts

Ist Teil von

• Archiving Strategies for Evolutionary Multi-Objective Optimization Algorithms, 2021, Vol.938, p.67-94

Ort / Verlag

Switzerland: Springer International Publishing AG

Erscheinungsjahr

2021

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• So far, we have discussed the archiver that stores all non-dominated solutions out of the set of candidate solutions, and two archivers that are entirely based on the concept of ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-dominance. While the applicability of ArchiveUpdatePQ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ArchiveUpdateP_Q$$\end{document} is restricted since it stores too many points during the run of the search process, the opposite can happen for the two ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-dominance based archivers. To see the latter, consider the extreme examples depicted in Fig. 7.1. Both sub-figures show Pareto fronts that contain flat parts and an “approximation” of this set that consists of three elements. Both approximations indeed form ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-Pareto fronts for relatively small entries of ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document} (compared to the length of the entire Pareto front).