---
_id: '63053'
author:
- first_name: Carlos
  full_name: Hernández, Carlos
  last_name: Hernández
- first_name: Angel E.
  full_name: Rodriguez-Fernandez, Angel E.
  last_name: Rodriguez-Fernandez
- first_name: Lennart
  full_name: Schäpermeier, Lennart
  last_name: Schäpermeier
- first_name: Oliver
  full_name: Cuate, Oliver
  last_name: Cuate
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Oliver
  full_name: Schütze, Oliver
  last_name: Schütze
citation:
  ama: Hernández C, Rodriguez-Fernandez AE, Schäpermeier L, Cuate O, Trautmann H,
    Schütze O. An Evolutionary Approach for the Computation of ∈-Locally Optimal Solutions
    for Multi-Objective Multimodal Optimization. <i>IEEE Transactions on Evolutionary
    Computation</i>. Published online 2025:1-1. doi:<a href="https://doi.org/10.1109/TEVC.2025.3637276">10.1109/TEVC.2025.3637276</a>
  apa: Hernández, C., Rodriguez-Fernandez, A. E., Schäpermeier, L., Cuate, O., Trautmann,
    H., &#38; Schütze, O. (2025). An Evolutionary Approach for the Computation of
    ∈-Locally Optimal Solutions for Multi-Objective Multimodal Optimization. <i>IEEE
    Transactions on Evolutionary Computation</i>, 1–1. <a href="https://doi.org/10.1109/TEVC.2025.3637276">https://doi.org/10.1109/TEVC.2025.3637276</a>
  bibtex: '@article{Hernández_Rodriguez-Fernandez_Schäpermeier_Cuate_Trautmann_Schütze_2025,
    title={An Evolutionary Approach for the Computation of ∈-Locally Optimal Solutions
    for Multi-Objective Multimodal Optimization}, DOI={<a href="https://doi.org/10.1109/TEVC.2025.3637276">10.1109/TEVC.2025.3637276</a>},
    journal={IEEE Transactions on Evolutionary Computation}, author={Hernández, Carlos
    and Rodriguez-Fernandez, Angel E. and Schäpermeier, Lennart and Cuate, Oliver
    and Trautmann, Heike and Schütze, Oliver}, year={2025}, pages={1–1} }'
  chicago: Hernández, Carlos, Angel E. Rodriguez-Fernandez, Lennart Schäpermeier,
    Oliver Cuate, Heike Trautmann, and Oliver Schütze. “An Evolutionary Approach for
    the Computation of ∈-Locally Optimal Solutions for Multi-Objective Multimodal
    Optimization.” <i>IEEE Transactions on Evolutionary Computation</i>, 2025, 1–1.
    <a href="https://doi.org/10.1109/TEVC.2025.3637276">https://doi.org/10.1109/TEVC.2025.3637276</a>.
  ieee: 'C. Hernández, A. E. Rodriguez-Fernandez, L. Schäpermeier, O. Cuate, H. Trautmann,
    and O. Schütze, “An Evolutionary Approach for the Computation of ∈-Locally Optimal
    Solutions for Multi-Objective Multimodal Optimization,” <i>IEEE Transactions on
    Evolutionary Computation</i>, pp. 1–1, 2025, doi: <a href="https://doi.org/10.1109/TEVC.2025.3637276">10.1109/TEVC.2025.3637276</a>.'
  mla: Hernández, Carlos, et al. “An Evolutionary Approach for the Computation of
    ∈-Locally Optimal Solutions for Multi-Objective Multimodal Optimization.” <i>IEEE
    Transactions on Evolutionary Computation</i>, 2025, pp. 1–1, doi:<a href="https://doi.org/10.1109/TEVC.2025.3637276">10.1109/TEVC.2025.3637276</a>.
  short: C. Hernández, A.E. Rodriguez-Fernandez, L. Schäpermeier, O. Cuate, H. Trautmann,
    O. Schütze, IEEE Transactions on Evolutionary Computation (2025) 1–1.
date_created: 2025-12-12T06:13:06Z
date_updated: 2025-12-12T06:13:51Z
department:
- _id: '819'
doi: 10.1109/TEVC.2025.3637276
keyword:
- Optimization
- Evolutionary computation
- Hands
- Proposals
- Convergence
- Computational efficiency
- Artificial intelligence
- Accuracy
- Approximation algorithms
- Aerospace electronics
- Multi-objective optimization
- evolutionary algorithms
- nearly optimal solutions
- multimodal optimization
- archiving
- continuation
language:
- iso: eng
page: 1-1
publication: IEEE Transactions on Evolutionary Computation
status: public
title: An Evolutionary Approach for the Computation of ∈-Locally Optimal Solutions
  for Multi-Objective Multimodal Optimization
type: journal_article
user_id: '15504'
year: '2025'
...
---
_id: '56221'
author:
- first_name: Angel E.
  full_name: Rodriguez-Fernandez, Angel E.
  last_name: Rodriguez-Fernandez
- first_name: Lennart
  full_name: Schäpermeier, Lennart
  last_name: Schäpermeier
- first_name: Carlos
  full_name: Hernández, Carlos
  last_name: Hernández
- first_name: Pascal
  full_name: Kerschke, Pascal
  last_name: Kerschke
- first_name: Heike
  full_name: Trautmann, Heike
  id: '100740'
  last_name: Trautmann
  orcid: 0000-0002-9788-8282
- first_name: Oliver
  full_name: Schütze, Oliver
  last_name: Schütze
citation:
  ama: Rodriguez-Fernandez AE, Schäpermeier L, Hernández C, Kerschke P, Trautmann
    H, Schütze O. Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal
    Optimization. <i>IEEE Transactions on Evolutionary Computation</i>. Published
    online 2024:1-1. doi:<a href="https://doi.org/10.1109/TEVC.2024.3458855">10.1109/TEVC.2024.3458855</a>
  apa: Rodriguez-Fernandez, A. E., Schäpermeier, L., Hernández, C., Kerschke, P.,
    Trautmann, H., &#38; Schütze, O. (2024). Finding ϵ-Locally Optimal Solutions for
    Multi-Objective Multimodal Optimization. <i>IEEE Transactions on Evolutionary
    Computation</i>, 1–1. <a href="https://doi.org/10.1109/TEVC.2024.3458855">https://doi.org/10.1109/TEVC.2024.3458855</a>
  bibtex: '@article{Rodriguez-Fernandez_Schäpermeier_Hernández_Kerschke_Trautmann_Schütze_2024,
    title={Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal Optimization},
    DOI={<a href="https://doi.org/10.1109/TEVC.2024.3458855">10.1109/TEVC.2024.3458855</a>},
    journal={IEEE Transactions on Evolutionary Computation}, author={Rodriguez-Fernandez,
    Angel E. and Schäpermeier, Lennart and Hernández, Carlos and Kerschke, Pascal
    and Trautmann, Heike and Schütze, Oliver}, year={2024}, pages={1–1} }'
  chicago: Rodriguez-Fernandez, Angel E., Lennart Schäpermeier, Carlos Hernández,
    Pascal Kerschke, Heike Trautmann, and Oliver Schütze. “Finding ϵ-Locally Optimal
    Solutions for Multi-Objective Multimodal Optimization.” <i>IEEE Transactions on
    Evolutionary Computation</i>, 2024, 1–1. <a href="https://doi.org/10.1109/TEVC.2024.3458855">https://doi.org/10.1109/TEVC.2024.3458855</a>.
  ieee: 'A. E. Rodriguez-Fernandez, L. Schäpermeier, C. Hernández, P. Kerschke, H.
    Trautmann, and O. Schütze, “Finding ϵ-Locally Optimal Solutions for Multi-Objective
    Multimodal Optimization,” <i>IEEE Transactions on Evolutionary Computation</i>,
    pp. 1–1, 2024, doi: <a href="https://doi.org/10.1109/TEVC.2024.3458855">10.1109/TEVC.2024.3458855</a>.'
  mla: Rodriguez-Fernandez, Angel E., et al. “Finding ϵ-Locally Optimal Solutions
    for Multi-Objective Multimodal Optimization.” <i>IEEE Transactions on Evolutionary
    Computation</i>, 2024, pp. 1–1, doi:<a href="https://doi.org/10.1109/TEVC.2024.3458855">10.1109/TEVC.2024.3458855</a>.
  short: A.E. Rodriguez-Fernandez, L. Schäpermeier, C. Hernández, P. Kerschke, H.
    Trautmann, O. Schütze, IEEE Transactions on Evolutionary Computation (2024) 1–1.
date_created: 2024-09-24T08:01:14Z
date_updated: 2024-09-24T08:01:47Z
doi: 10.1109/TEVC.2024.3458855
keyword:
- Optimization
- Evolutionary computation
- Approximation algorithms
- Benchmark testing
- Vectors
- Surveys
- Pareto optimization
- multi-objective optimization
- evolutionary computation
- multimodal optimization
- local solutions
language:
- iso: eng
page: 1-1
publication: IEEE Transactions on Evolutionary Computation
status: public
title: Finding ϵ-Locally Optimal Solutions for Multi-Objective Multimodal Optimization
type: journal_article
user_id: '15504'
year: '2024'
...
---
_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'
...