We continue recent work on the definition of multimodality in multiobjective optimization (MO) and the introduction of a test bed for multimodal MO problems. This goes beyond well-known diversity maintenance approaches but instead focuses on the landscape topology induced by the objective functions. More general multimodal MO problems are considered by allowing ellipsoid contours for single-objective subproblems. An experimental analysis compares two MO algorithms, one that explicitly relies on hypervolume gradient approximation, and one that is based on local search, both on a selection of generated example problems. We do not focus on performance but on the interaction induced by the problems and algorithms, which can be described by means of specific characteristics explicitly designed for the multimodal MO setting. Furthermore, we widen the scope of our analysis by additionally applying visualization techniques in the decision space. This strengthens and extends the foundations for Exploratory Landscape Analysis (ELA) in MO.
%0 Journal Article
%1 Kerschke2019-ld
%A Kerschke, P
%A Wang, H
%A Preuss, M
%A Grimme, C
%A Deutz, A H
%A Trautmann, H
%A Emmerich, M T M
%D 2019
%I MIT Press - Journals
%J Evol. Comput.
%K Multiobjective analysis; ascent; gradient hypervolume landscape multimodality; optimization. optimization; set-based
%N 4
%P 577--609
%T Search dynamics on multimodal multiobjective problems
%V 27
%X We continue recent work on the definition of multimodality in multiobjective optimization (MO) and the introduction of a test bed for multimodal MO problems. This goes beyond well-known diversity maintenance approaches but instead focuses on the landscape topology induced by the objective functions. More general multimodal MO problems are considered by allowing ellipsoid contours for single-objective subproblems. An experimental analysis compares two MO algorithms, one that explicitly relies on hypervolume gradient approximation, and one that is based on local search, both on a selection of generated example problems. We do not focus on performance but on the interaction induced by the problems and algorithms, which can be described by means of specific characteristics explicitly designed for the multimodal MO setting. Furthermore, we widen the scope of our analysis by additionally applying visualization techniques in the decision space. This strengthens and extends the foundations for Exploratory Landscape Analysis (ELA) in MO.
@article{Kerschke2019-ld,
abstract = {We continue recent work on the definition of multimodality in multiobjective optimization (MO) and the introduction of a test bed for multimodal MO problems. This goes beyond well-known diversity maintenance approaches but instead focuses on the landscape topology induced by the objective functions. More general multimodal MO problems are considered by allowing ellipsoid contours for single-objective subproblems. An experimental analysis compares two MO algorithms, one that explicitly relies on hypervolume gradient approximation, and one that is based on local search, both on a selection of generated example problems. We do not focus on performance but on the interaction induced by the problems and algorithms, which can be described by means of specific characteristics explicitly designed for the multimodal MO setting. Furthermore, we widen the scope of our analysis by additionally applying visualization techniques in the decision space. This strengthens and extends the foundations for Exploratory Landscape Analysis (ELA) in MO.},
added-at = {2024-09-10T11:54:51.000+0200},
author = {Kerschke, P and Wang, H and Preuss, M and Grimme, C and Deutz, A H and Trautmann, H and Emmerich, M T M},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/29bc751e28b56bacca447f588e3118a23/scadsfct},
interhash = {b301a7aa765119b6d1848386dce086b7},
intrahash = {9bc751e28b56bacca447f588e3118a23},
journal = {Evol. Comput.},
keywords = {Multiobjective analysis; ascent; gradient hypervolume landscape multimodality; optimization. optimization; set-based},
language = {en},
number = 4,
pages = {577--609},
publisher = {MIT Press - Journals},
timestamp = {2024-09-10T11:54:51.000+0200},
title = {Search dynamics on multimodal multiobjective problems},
volume = 27,
year = 2019
}
