---
_id: '46318'
abstract:
- lang: eng
  text: 'Multi-objective (MO) optimization, i.e., the simultaneous optimization of
    multiple conflicting objectives, is gaining more and more attention in various
    research areas, such as evolutionary computation, machine learning (e.g., (hyper-)parameter
    optimization), or logistics (e.g., vehicle routing). Many works in this domain
    mention the structural problem property of multimodality as a challenge from two
    classical perspectives: (1) finding all globally optimal solution sets, and (2)
    avoiding to get trapped in local optima. Interestingly, these streams seem to
    transfer many traditional concepts of single-objective (SO) optimization into
    claims, assumptions, or even terminology regarding the MO domain, but mostly neglect
    the understanding of the structural properties as well as the algorithmic search
    behavior on a problem’s landscape. However, some recent works counteract this
    trend, by investigating the fundamentals and characteristics of MO problems using
    new visualization techniques and gaining surprising insights. Using these visual
    insights, this work proposes a step towards a unified terminology to capture multimodality
    and locality in a broader way than it is usually done. This enables us to investigate
    current research activities in multimodal continuous MO optimization and to highlight
    new implications and promising research directions for the design of benchmark
    suites, the discovery of MO landscape features, the development of new MO (or
    even SO) optimization algorithms, and performance indicators. For all these topics,
    we provide a review of ideas and methods but also an outlook on future challenges,
    research potential and perspectives that result from recent developments.'
author:
- first_name: Christian
  full_name: Grimme, Christian
  last_name: Grimme
- first_name: Pascal
  full_name: Kerschke, Pascal
  last_name: Kerschke
- first_name: Pelin
  full_name: Aspar, Pelin
  last_name: Aspar
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Mike
  full_name: Preuss, Mike
  last_name: Preuss
- first_name: André H.
  full_name: Deutz, André H.
  last_name: Deutz
- first_name: Hao
  full_name: Wang, Hao
  last_name: Wang
- first_name: Michael
  full_name: Emmerich, Michael
  last_name: Emmerich
citation:
  ama: 'Grimme C, Kerschke P, Aspar P, et al. Peeking beyond peaks: Challenges and
    research potentials of continuous multimodal multi-objective optimization. <i>Computers
    &#38; Operations Research</i>. 2021;136:105489. doi:<a href="https://doi.org/10.1016/j.cor.2021.105489">https://doi.org/10.1016/j.cor.2021.105489</a>'
  apa: 'Grimme, C., Kerschke, P., Aspar, P., Trautmann, H., Preuss, M., Deutz, A.
    H., Wang, H., &#38; Emmerich, M. (2021). Peeking beyond peaks: Challenges and
    research potentials of continuous multimodal multi-objective optimization. <i>Computers
    &#38; Operations Research</i>, <i>136</i>, 105489. <a href="https://doi.org/10.1016/j.cor.2021.105489">https://doi.org/10.1016/j.cor.2021.105489</a>'
  bibtex: '@article{Grimme_Kerschke_Aspar_Trautmann_Preuss_Deutz_Wang_Emmerich_2021,
    title={Peeking beyond peaks: Challenges and research potentials of continuous
    multimodal multi-objective optimization}, volume={136}, DOI={<a href="https://doi.org/10.1016/j.cor.2021.105489">https://doi.org/10.1016/j.cor.2021.105489</a>},
    journal={Computers &#38; Operations Research}, author={Grimme, Christian and Kerschke,
    Pascal and Aspar, Pelin and Trautmann, Heike and Preuss, Mike and Deutz, André
    H. and Wang, Hao and Emmerich, Michael}, year={2021}, pages={105489} }'
  chicago: 'Grimme, Christian, Pascal Kerschke, Pelin Aspar, Heike Trautmann, Mike
    Preuss, André H. Deutz, Hao Wang, and Michael Emmerich. “Peeking beyond Peaks:
    Challenges and Research Potentials of Continuous Multimodal Multi-Objective Optimization.”
    <i>Computers &#38; Operations Research</i> 136 (2021): 105489. <a href="https://doi.org/10.1016/j.cor.2021.105489">https://doi.org/10.1016/j.cor.2021.105489</a>.'
  ieee: 'C. Grimme <i>et al.</i>, “Peeking beyond peaks: Challenges and research potentials
    of continuous multimodal multi-objective optimization,” <i>Computers &#38; Operations
    Research</i>, vol. 136, p. 105489, 2021, doi: <a href="https://doi.org/10.1016/j.cor.2021.105489">https://doi.org/10.1016/j.cor.2021.105489</a>.'
  mla: 'Grimme, Christian, et al. “Peeking beyond Peaks: Challenges and Research Potentials
    of Continuous Multimodal Multi-Objective Optimization.” <i>Computers &#38; Operations
    Research</i>, vol. 136, 2021, p. 105489, doi:<a href="https://doi.org/10.1016/j.cor.2021.105489">https://doi.org/10.1016/j.cor.2021.105489</a>.'
  short: C. Grimme, P. Kerschke, P. Aspar, H. Trautmann, M. Preuss, A.H. Deutz, H.
    Wang, M. Emmerich, Computers &#38; Operations Research 136 (2021) 105489.
date_created: 2023-08-04T07:28:34Z
date_updated: 2023-10-16T12:58:42Z
department:
- _id: '34'
- _id: '819'
doi: https://doi.org/10.1016/j.cor.2021.105489
intvolume: '       136'
keyword:
- Multimodal optimization
- Multi-objective continuous optimization
- Landscape analysis
- Visualization
- Benchmarking
- Theory
- Algorithms
language:
- iso: eng
page: '105489'
publication: Computers & Operations Research
publication_identifier:
  issn:
  - 0305-0548
status: public
title: 'Peeking beyond peaks: Challenges and research potentials of continuous multimodal
  multi-objective optimization'
type: journal_article
user_id: '15504'
volume: 136
year: '2021'
...